March 18, 2019

Four Packages

Peanut Package Dependencies

  • RNetica – Low-level R/Netica Interface
  • CPTtools – Design patterns for Conditional Probability Tables
    • Independent of other packages
  • Peanut – Object-oriented parameterized Bayesian Networks
    • Implementation independent
    • Uses CPTtools
  • PNetica – RNetica implementation of Peanut protocols

https://pluto.coe.fsu.edu/RNetica

RNetica License Agreements

  • R: GPL-3 (Free and open source)
  • RNetica, CPTtools, Peanut, PNetica: Artistic-2.0 (Free and open source)
  • Netica.dll/libNetica.so: Commercial (openAPI, but not open source)
    • Free Student/Demo Version
      • Limited number of nodes.
      • Limited Usage (education, evaluation of Netica)
    • Paid version (see http://www.norsys.com/ for price information).
      • Need to purchase API, not GUI verison of Netica for RNetica
      • May want GUI for network visualization.
    • Netica.dll/libNetica.so included with binary distributions by permission of Norsys
      • License key still must be purchased.

Installing non-CRAN packages

  • Windows and MacOS X: Download object package from pluto
    • Windows: RNetica-0.5-2.zip
    • MacOS: RNetica-0.5-2.tgz
  • RStudio: Use Tools> Install Packages …, select "Install From" = "Package Archive File"

  • install.packages("RNetica-0.5-2.zip", repos=NULL)

  • Source Installation:
    • Download Source tarball: RNetica-0.5-2.tar.gz
    • Download and unpack Netica C API from https://norsys.com/
    • From Command Line:
      R CMD INSTALL RNetica --configure-args='--with-netica=/path/to/Netica_API_504'
    • Windows, need to set a NETICA_HOME environmental variable, see INSTALLATION FILE.
  • Now load RNetica

Netica Session: R and Netica Memory

Netica Session and Netica Heap

  • R and Netica have two different workspaces (memory heaps)
  • R workspace is saved and restored automatically when you quick and restart R.
  • Netica heap must be reconnected manually.
  • Netica Session object
    • Provides link to Netica Memory Space
    • Is a container for all NeticaNetwork objects
    • Must be reconnected every R session, using startSession() ## Installing a License Key
  • When you purchase a license, Norsys will send you a license key. Something that looks like: “+Course/FloridaSU/Ex15-05-30,120,310/XXXXX” (Where I’ve obscured the last 5 security digits)

  • To install the license key, start R in your project directory and type:

#DefaultNeticaSession <- NeticaSession(LicenseKey="+Course/FloridaSU/Ex15-05-30,120,310/XXXXX") 
#q("yes")

Restart R and type

#library(RNetica)
#startSession(DefaultNeticaSession)
  • If license key is not installed, then you will get the limited/student mode. Most of these examples will run

When to use the session object.

  • When starting/restarting Netica
  • When creating a network, or reading one from a file.
  • When searching for networks.
  • Certain global properties

NeticaNetwork objects have a $session proprty which points back to the session.

NeticaNode objects have a $node property which points back to the network (which points to the session).

Active and Inactive Pointers

Netica Session and Netica Heap

  • When RNetica creates/finds a Netica object it creates a corresponding R object
  • R NeticaBN objects live in the NeticaSession object.
    • R NeticaNode objects live in the NeticaBN.
  • If the pointer gets broken (saving & restarting R, deleting the network/node) then the R object becomes inactive.
  • The function is.active() tests to see if the node/net/session is active

A simple example

Starting The Netica Interface

Load Libraries

library(RNetica)
library(CPTtools)
## Loading required package: lattice
## 
## Attaching package: 'CPTtools'
## The following objects are masked from 'package:RNetica':
## 
##     as.CPA, as.CPF, is.CPA, is.CPF

Create a session object and start it.

Session object can be reused across workspaces, but it needs to be started again everytime R is connected.

sess <- NeticaSession() # Could add License Key as argument)
startSession(sess)
## Netica 5.04 Linux (AF), (C) 1992-2012 Norsys Software Corp.
## 
## Netica operating without a password; there are some limitations.

Must start a session every time R is started. As a fallback, RNetica, will look for an object called DefaultNeticaSession and try to start that.

Reloading Nets and Nodes

Note that load networks needs a session as an argument (as networks are created within a session).

Networks must be reloaded every time R is started.

Note also, that the nodes must be reconnected to R objects. NetworkAllNodes() is the easiest way of doing this.

## Read in Network -- Do this every time R is started.
##DeleteNetwork(motif1)
motif1 <- ReadNetworks("../Nets/ACEDMotif1.dne",session = sess)

## Reconnect nodes -- Do this every time R is restarted
m1.nodes <- NetworkAllNodes(motif1)
m1.sgp <- m1.nodes$SolveGeometricProblems
m1.obs <- NetworkNodesInSet(motif1,"Observables")
m1.obs
## $X3Hard1
## Discrete  Netica Node named  X3Hard1 in network  GeometricMotif 
##   Node is currently active.
## States are:  True, False 
## 
## $X3Medium1
## Discrete  Netica Node named  X3Medium1 in network  GeometricMotif 
##   Node is currently active.
## States are:  True, False 
## 
## $X3Easy
## Discrete  Netica Node named  X3Easy in network  GeometricMotif 
##   Node is currently active.
## States are:  True, False 
## 
## $X3Hard
## Discrete  Netica Node named  X3Hard in network  GeometricMotif 
##   Node is currently active.
## States are:  True, False 
## 
## $X3Medium
## Discrete  Netica Node named  X3Medium in network  GeometricMotif 
##   Node is currently active.
## States are:  True, False 
## 
## $CREasy
## Discrete  Netica Node named  CREasy in network  GeometricMotif 
##   Node is currently active.
## States are:  True, False

Node Sets

Netica defines a node set functionality which Adds a collection of labels (sets) to each node Defines a collection of nodes with that label Netica GUI really only offers the opportunity to color nodes by set RNetica can loop over node sets (lists of nodes)

## Node Sets
NetworkNodeSets(motif1)
## [1] "Observables"   "Proficiencies"
NetworkNodesInSet(motif1,"Proficiencies")
## $RecursiveRuleGeometric
## Discrete  Netica Node named  RecursiveRuleGeometric in network  GeometricMotif 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $ExplicitGeometric
## Discrete  Netica Node named  ExplicitGeometric in network  GeometricMotif 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $VerbalRuleGeometric
## Discrete  Netica Node named  VerbalRuleGeometric in network  GeometricMotif 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $AlgebraRuleGeometric
## Discrete  Netica Node named  AlgebraRuleGeometric in network  GeometricMotif 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $InduceRulesGeometric
## Discrete  Netica Node named  InduceRulesGeometric in network  GeometricMotif 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $TableGeometric
## Discrete  Netica Node named  TableGeometric in network  GeometricMotif 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $VisualGeometric
## Discrete  Netica Node named  VisualGeometric in network  GeometricMotif 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $CommonRatio
## Discrete  Netica Node named  CommonRatio in network  GeometricMotif 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $SolveGeometricProblems
## Discrete  Netica Node named  SolveGeometricProblems in network  GeometricMotif 
##   Node is currently active.
## States are:  High, Medium, Low
NodeSets(m1.sgp)
## [1] "Proficiencies"
## These are all settable
NodeSets(m1.sgp) <- c(NodeSets(m1.sgp),"HighLevel")
NodeSets(m1.sgp)
## [1] "HighLevel"     "Proficiencies"

RNetica Functions

## Querying Nodes
NodeStates(m1.sgp)   #List states
##     High   Medium      Low 
##   "High" "Medium"    "Low"
NodeParents(m1.sgp)  #List parents
## named list()
NodeLevels(m1.sgp)   #List numeric values associated with states
##   High Medium    Low 
##     NA     NA     NA
NodeProbs(m1.sgp) # Conditional Probability Table (as array)
## SolveGeometricProblems
##   High Medium    Low 
## 0.1532 0.2784 0.5684 
## attr(,"class")
## [1] "CPA"   "array"

Can use the [] notation for viewing, setting CPTs

m1.sgp[] # Conditional Probability Table (as data frame)
##   SolveGeometricProblems.High SolveGeometricProblems.Medium 
##                        0.1532                        0.2784 
##    SolveGeometricProblems.Low 
##                        0.5684
## These are all settable (can be used on RHS of <-) for 
## model construction
motif1$nodes$X3Medium[]
##    theta X3Medium.True X3Medium.False
## 1   High        0.7246         0.2754
## 2 Medium        0.5000         0.5000
## 3    Low        0.2754         0.7246

Inference

Before doing inference, must compile the network. This is the lightning bolt icon on the GUI.

CompileNetwork(motif1) #Lightning bolt on GUI 
## Must do this before inference
## Recompiling an already compiled network is harmless
## [1] "@NO FINDING"
##   High Medium    Low 
##      1      1      1
## Query beliefs
NodeBeliefs(m1.sgp) #Current probability (given entered evidence)
##   High Medium    Low 
## 0.1532 0.2784 0.5684

If we associate numeric values with a node, we can calculate expected values.

NodeLevels(m1.sgp) <- c(-1,0,1)
NodeExpectedValue(m1.sgp)
## [1] 0.4152
## attr(,"std_dev")
## [1] 0.7410863

Enter Evidence

Direct Evidence can be entered with the setter method of NodeFinding

NodeStates(m1.obs$X3Medium)
##    True   False 
##  "True" "False"
NodeFinding(m1.obs$X3Medium) <- "True"

Can also enter virtual evidence in the form of a likelihood.

## Enter Evidence "Not Low" ("High or Medium")
NodeLikelihood(motif1$nodes$TableGeometric) <- c(1,1,0)

Query the nodes again, and the values should have changed.

NodeBeliefs(m1.sgp) #Current probability (given entered evidence)
##      High    Medium       Low 
## 0.3052434 0.3976996 0.2970570
NodeExpectedValue(m1.sgp) #If node has values, EAP
## [1] -0.00818643
## attr(,"std_dev")
## [1] 0.776037

Retract Evidence

Can retract evidence node by node, or on entire network.

RetractNodeFinding(m1.obs$X3Medium)
RetractNetFindings(motif1)

Query the nodes again, and the values should have returned to the baselines.

Query the nodes again, and the values should have changed.

NodeBeliefs(m1.sgp) #Current probability (given entered evidence)
##   High Medium    Low 
## 0.1532 0.2784 0.5684
NodeExpectedValue(m1.sgp) #If node has values, EAP
## [1] 0.4152
## attr(,"std_dev")
## [1] 0.7410863

Many more examples

help(RNetica)

Mini-ACED Proficiency Model

Mini-ACED EM Fragments

  • All ACED tasks were scored correct/incorrect
  • Each evidence model is represented by a fragment consisting of observables with stub edges indicating where it should be adjoined with the network.

Common Ratio Easy:

Model Extend Table Hard:

Task to EM Map

  • Need a table to tell which EM to use with which task
  • Row names are Task IDs
  • EM column contains evidence model name.
  • EM filename has suffix ".dne" attached.
## Read in task->evidence model mapping
EMtable <- read.csv("../Nets/MiniACEDEMTable.csv",row.names=1,
                    as.is=2) #Keep EM names as strings
EMtable
##                                                  EM    X   Y
## tCommonRatio1a                    CommonRatioEasyEM  108 294
## tCommonRatio1b                    CommonRatioEasyEM  108 414
## tCommonRatio2a                     CommonRatioMedEM  108 534
## tCommonRatio2b                     CommonRatioMedEM  108 654
## tCommonRatio3a                    CommonRatioHardEM  108 774
## tCommonRatio3b                    CommonRatioHardEM  108 894
## tExamplesGeometric1a                 ExamplesEasyEM  342 294
## tExamplesGeometric1b                 ExamplesEasyEM  342 414
## tExamplesGeometric2a                  ExamplesMedEM  342 534
## tExamplesGeometric2b                  ExamplesMedEM  342 654
## tExamplesGeometric3a                 ExamplesHardEM  342 774
## tExamplesGeometric3b                 ExamplesHardEM  342 894
## tExtendGeometric1a                     ExtendEasyEM  588 294
## tExtendGeometric1b                     ExtendEasyEM  588 414
## tExtendGeometric2a                      ExtendMedEM  588 534
## tExtendGeometric2b                      ExtendMedEM  588 654
## tExtendGeometric3a                     ExtendHardEM  588 774
## tExtendGeometric3b                     ExtendHardEM  588 894
## tTableExtendGeometric1a           TableExtendEasyEM 1134 282
## tTableExtendGeometric1b           TableExtendEasyEM 1134 402
## tTableExtendGeometric2a            TableExtendMedEM 1134 522
## tTableExtendGeometric2b            TableExtendMedEM 1134 642
## tTableExtendGeometric3a           TableExtendHardEM 1134 762
## tTableExtendGeometric3b           TableExtendHardEM 1134 882
## tModelExtendTableGeometric1a ModelTableExtendEasyEM  858 288
## tModelExtendTableGeometric1b ModelTableExtendEasyEM  858 408
## tModelExtendTableGeometric2a  ModelTableExtendMedEM  858 528
## tModelExtendTableGeometric2b  ModelTableExtendMedEM  858 648
## tModelExtendTableGeometric3a ModelTableExtendHardEM  858 768
## tModelExtendTableGeometric3b ModelTableExtendHardEM  858 888

Scoring Script

  1. Start RNetica Session
  2. Open Profiency Model netowrk
  3. Load EM to net table.

When Student evidence comes in: 1. Find SM for that student (clone PM if no SM) 2. Find EM for the task 3. Adjoin the two models. 4. Instantiate observable variables. 5. Drop EM. 6. Record Statistics & save SM

Load the Proficiency Model

## Read in network – Do this every time R is restarted
profModel <- ReadNetworks("../Nets/miniACEDPnet-1.dne",session=sess)
## If profModels already exists could also use
## ReadNewtorks(profModel)

## Reconnect nodes – Do this every time R is restarted
allNodes <- NetworkAllNodes(profModel)
sgp <- allNodes$SolveGeometricProblems
profNodes <- NetworkNodesInSet(profModel,"Proficiencies")

A student walks into the test center …

  • Student gives the name “Fred”
  • Student is the right grade/age for ACED (8th or 9th grader, pre-algebra)
  • Bayes net has three states
    • Fred logs into ACED
    • Fred attempts the task tCommonRatio1a and gets it right
    • Fred attempts the task tCommonRatio2a and gets it wrong

Start a New Student

## Copy the master proficiency model
## to make student model
Fred.SM <- CopyNetworks(profModel,"Fred")
Fred.SMvars <- NetworkAllNodes(Fred.SM)
CompileNetwork(Fred.SM)

## Setup score history
prior <- NodeBeliefs(Fred.SMvars$SolveGeometricProblems)
Fred.History <- matrix(prior,1,3)
row.names(Fred.History) <- "*Baseline*"
colnames(Fred.History) <- names(prior)
Fred.History
##                 High    Medium       Low
## *Baseline* 0.3333333 0.3333333 0.3333334

Score 1st Task

### Fred does a task
t.name <- "tCommonRatio1a"
t.isCorrect <- "Yes"

## Adjoin SM and EM
EMnet <- ReadNetworks(file.path("..","Nets",
                    paste(EMtable[t.name,"EM"],"dne",sep=".")),
                    session=sess)
obs <- AdjoinNetwork(Fred.SM,EMnet)
#NodeVisPos(obs$isCorrect) <- EMtable[t.name,c("X","Y")]
NetworkAllNodes(Fred.SM) 
## $SolveGeometricProblems
## Discrete  Netica Node named  SolveGeometricProblems in network  Fred 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $CommonRatio
## Discrete  Netica Node named  CommonRatio in network  Fred 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $ExamplesGeometric
## Discrete  Netica Node named  ExamplesGeometric in network  Fred 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $ExtendGeometric
## Discrete  Netica Node named  ExtendGeometric in network  Fred 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $ModelGeometric
## Discrete  Netica Node named  ModelGeometric in network  Fred 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $TableGeometric
## Discrete  Netica Node named  TableGeometric in network  Fred 
##   Node is currently active.
## States are:  High, Medium, Low 
## 
## $isCorrect
## Discrete  Netica Node named  isCorrect in network  Fred 
##   Node is currently active.
## States are:  Yes, No
## Fred.SM is now the Motif for the current task.
CompileNetwork(Fred.SM)

## Enter finding
NodeFinding(obs$isCorrect) <- t.isCorrect

Stats for 1st Task

##                         High    Medium       Low
## *Baseline*         0.3333333 0.3333333 0.3333334
## tCommonRatio1a=Yes 0.3616656 0.3429957 0.2953387

Cleanup from 1st Task

## Cleanup and Observable no longer needed, so absorb it:
DeleteNetwork(EMnet) ## Delete EM
AbsorbNodes(obs)
## Creating node list.
## Absorbing 1 nodes.
## First node address f8f2a360.
## Its name is isCorrect.
## Absorbed.
## Currently, there is a Netica bug with Absorb Nodes, we will leave
## this node in place as that is mostly harmless.

2nd Task

Write a script for scoring the second task.
This time Fred attempts the task tCommonRatio2a and gets it incorrect.

### Fred does another task
t.name <- "tCommonRatio2a"
t.isCorrect <- "No"

## Load Evidence Model and adjoin

## Recompile

## Add Evidence

## Check Finding and add to history

## Clean up

Answer for 2nd Task

### Fred does another task
t.name <- "tCommonRatio2a"
t.isCorrect <- "No"

EMnet <- ReadNetworks(file.path("..","Nets",
                      paste(EMtable[t.name,"EM"],"dne", 
                            sep=".")),
                      session=sess)
obs <- AdjoinNetwork(Fred.SM,EMnet)
#NodeVisPos(obs$isCorrect) <- EMtable[t.name,c("X","Y")]
## Fred.SM is now the Motif for the current task.
CompileNetwork(Fred.SM)

NodeFinding(obs[[1]]) <- t.isCorrect
post <- NodeBeliefs(Fred.SMvars$SolveGeometricProblems)
Fred.History <- rbind(Fred.History,new=post)
rownames(Fred.History)[nrow(Fred.History)] <- 
      paste(t.name,t.isCorrect,sep="=")
Fred.History
##                         High    Medium       Low
## *Baseline*         0.3333333 0.3333333 0.3333334
## tCommonRatio1a=Yes 0.3616656 0.3429957 0.2953387
## tCommonRatio2a=No  0.2340327 0.3149439 0.4510235
## Cleanup:  Delete EM and Absorb observables
DeleteNetwork(EMnet) ## Delete EM
AbsorbNodes(obs)
## Creating node list.
## Absorbing 1 nodes.
## First node address f8c576c0.
## Its name is isCorrect.
## Absorbed.

Save and Restore

## Fred logs out
WriteNetworks(Fred.SM,"FredSM.dne")
DeleteNetwork(Fred.SM)
is.active(Fred.SM)  
## [1] FALSE
## No longer active in Netica space

## Fred logs back in
Fred.SM <- ReadNetworks("FredSM.dne",session=sess)
is.active(Fred.SM)
## [1] TRUE

Getting Serious

  • ACED field test has 230 students attempt all 63 tasks.
  • File miniACED-Geometric contains 30 task subset
    • There may be data registration issues here, don’t publish using these data before checking with me for an update
  • Each row is one student Record
  • Lets score the first student
    • And build a score history

Setup for mini-ACED

miniACED.data <- read.csv("../Nets/miniACED-Geometric.csv",row.names=1)
miniACED.data
##      Class Treatment Sequencing Feedback Total.Items Correct Incorrect
## S055     1         1          2        2          63       8        55
## S058     1         1          2        2          63      33        30
## S053     1         2          2        1          63      12        51
## S061     1         1          2        2          63      21        42
## S063     1         1          2        2          63      21        42
## S066     1         1          2        2          63      19        44
## S062     1         2          2        1          63      12        49
## S054     1         3          1        1          63      34        29
## S057     1         3          1        1          63      25        28
## S060     1         3          1        1          63      28        35
## S067     1         2          2        1          63       6        54
## S056     1         2          2        1          63      20        43
## S059     1         2          2        1          63      20        37
## S064     1         2          2        1          63      36        27
## S065     1         3          1        1          63      30        33
## S068     1         3          1        1          63      16        47
## S052     1         1          2        2          63      20        14
## S241    10         2          2        1          63      34        29
## S230    10         3          1        1          63      41        22
## S232    10         2          2        1          63      21        42
## S233    10         3          1        1          63      45        18
## S236    10         3          1        1          63      16        47
## S235    10         2          2        1          63      30        33
## S240    10         1          2        2          63      22        41
## S239    10         3          1        1          63      38        25
## S234    10         1          2        2          63      14        49
## S231    10         1          2        2          63      37        25
## S243    10         1          2        2          63      24        39
## S228    10         1          2        2          63      18        45
## S238    10         2          2        1          63      33        30
## S229    10         2          2        1          63      24        39
## S242    10         3          1        1          63      32        31
## S237    10         1          2        2          63      26        23
## S260    11         3          1        1          63      29        34
## S257    11         3          1        1          63      20        43
## S258    11         1          2        2          63      24        39
## S249    11         1          2        2          63      15        48
## S253    11         2          2        1          63      20        43
## S263    11         3          1        1          63      28        35
## S252    11         1          2        2          63       7        56
## S255    11         1          2        2          63      34        29
## S254    11         3          1        1          63      46        17
## S261    11         1          2        2          63      23        40
## S262    11         2          2        1          63      18        45
## S251    11         3          1        1          63      26        37
## S250    11         2          2        1          63      26        37
## S259    11         2          2        1          63      35        27
## S256    11         2          2        1          63      13        49
## S284    12         1          2        2          63       6        57
## S283    12         3          1        1          63      13        50
## S273    12         2          2        1          63       7        56
## S285    12         2          2        1          63       5        58
## S272    12         1          2        2          63       8        22
## S274    12         3          1        1          63      10        53
## S281    12         1          2        2          63       9        30
## S276    12         2          2        1          63       5        24
## S275    12         1          2        2          63       2        36
## S280    12         3          1        1          63       9        41
## S282    12         2          2        1          63       7        23
## S270    12         2          2        1          63      12        22
## S269    12         1          2        2          63      16        22
## S278    12         1          2        2          63       9        54
## S279    12         2          2        1          63       3        17
## S271    12         3          1        1          63      11        29
## S277    12         3          1        1          63      13        50
## S298    13         2          2        1          63      19        21
## S308    13         3          1        1          63      10        53
## S299    13         3          1        1          63      18        39
## S302    13         3          1        1          63      28        35
## S307    13         2          2        1          63      12        49
## S291    13         1          2        2          63       7        56
## S297    13         1          2        2          63      17        46
## S296    13         3          1        1          63      24        39
## S292    13         2          2        1          63      12        51
## S304    13         2          2        1          63      12        18
## S301    13         2          2        1          63      14        47
## S305    13         3          1        1          63      37        19
## S294    13         1          2        2          63      14        49
## S295    13         2          2        1          63      16        46
## S303    13         1          2        2          63      14        31
## S306    13         1          2        2          63      15        29
## S300    13         1          2        2          63      11        52
## S293    13         3          1        1          63       9        54
## S316    14         2          2        1          63      11         9
## S319    14         2          2        1          63      18        45
## S317    14         3          1        1          63      18        45
## S318    14         1          2        2          63      16        47
## S320    14         3          1        1          63      21        32
## S315    14         1          2        2          63      18        45
## S334    15         3          1        1          63      26        37
## S324    15         2          2        1          63      17        46
## S325    15         3          1        1          63      42        21
## S328    15         3          1        1          63      34        29
## S327    15         2          2        1          63      11        45
## S323    15         1          2        2          63      40        22
## S336    15         2          2        1          63       8        55
## S333    15         2          2        1          63      37        22
## S332    15         1          2        2          63      28        35
## S331    15         3          1        1          63      13        50
## S329    15         1          2        2          63      20        43
## S326    15         1          2        2          63      11        13
## S338    15         1          2        2          63      19        39
## S335    15         1          2        2          63      34        28
## S337    15         3          1        1          63      11        52
## S330    15         2          2        1          63      29        34
## S091     2         3          1        1          63      21        42
## S075     2         2          2        1          63      35        27
## S074     2         1          2        2          63      20        43
## S088     2         3          1        1          63      20        43
## S082     2         3          1        1          63      18        45
## S083     2         1          2        2          63      13        50
## S086     2         1          2        2          63      36        27
## S087     2         2          2        1          63      22        41
## S080     2         1          2        2          63       9        54
## S078     2         2          2        1          63      20        43
## S085     2         3          1        1          63      25        38
## S084     2         2          2        1          63      26        37
## S076     2         3          1        1          63      33        30
## S081     2         2          2        1          63      21        42
## S077     2         1          2        2          63      21        42
## S089     2         1          2        2          63      14        35
## S090     2         2          2        1          63      13        50
## S079     2         3          1        1          63      27        36
## S113     3         2          2        1          63      44        18
## S101     3         2          2        1          63      14        49
## S099     3         3          1        1          63      20        43
## S111     3         3          1        1          63      22        41
## S114     3         3          1        1          63      32        31
## S102     3         3          1        1          63      33        30
## S098     3         2          2        1          63      18        45
## S100     3         1          2        2          63      14        49
## S106     3         1          2        2          63      33        22
## S103     3         1          2        2          63      32        18
## S110     3         2          2        1          63      42        19
## S107     3         2          2        1          63      11        46
## S109     3         1          2        2          63      37        26
## S112     3         1          2        2          63      21        15
## S105     3         3          1        1          63      23        40
## S104     3         2          2        1          63       9        54
## S108     3         3          1        1          63      35        22
## S097     3         1          2        2          63      30        33
## S129     4         2          2        1          63      47        15
## S128     4         1          2        2          63      27        36
## S120     4         2          2        1          63      35        28
## S136     4         3          1        1          63      43        18
## S122     4         1          2        2          63      34        29
## S124     4         3          1        1          63      33        30
## S127     4         3          1        1          63      34        29
## S126     4         2          2        1          63       8        55
## S134     4         1          2        2          63      29        34
## S125     4         1          2        2          63      18        45
## S132     4         2          2        1          63      24        39
## S121     4         3          1        1          63      40        23
## S123     4         2          2        1          63      42        20
## S130     4         3          1        1          63      30        33
## S135     4         2          2        1          63      39        24
## S131     4         1          2        2          63      37        26
## S119     4         1          2        2          63      28        35
## S133     4         3          1        1          63      37        26
## S154     5         3          1        1          63      51        12
## S156     5         2          2        1          63      40        22
## S143     5         1          2        2          63      34        27
## S152     5         1          2        2          63      31        21
## S146     5         1          2        2          63      20        23
## S142     5         3          1        1          63      25        38
## S141     5         2          2        1          63      41        21
## S145     5         3          1        1          63      19        44
## S148     5         3          1        1          63      40        23
## S144     5         2          2        1          63      41         7
## S140     5         1          2        2          63      15        17
## S151     5         3          1        1          63      29        34
## S147     5         2          2        1          63      38        24
## S149     5         1          2        2          63      42        20
## S155     5         1          2        2          63      28        31
## S150     5         2          2        1          63      32        31
## S153     5         2          2        1          63      22        41
## S160     6         1          2        2          63      33        29
## S159     6         3          1        1          63      25        38
## S165     6         3          1        1          63      17        46
## S166     6         1          2        2          63      14        49
## S169     6         1          2        2          63      19        44
## S164     6         2          2        1          63      22        41
## S157     6         1          2        2          63      19        44
## S163     6         1          2        2          63      18        45
## S170     6         2          2        1          63      21        42
## S167     6         2          2        1          63      18        45
## S161     6         2          2        1          63      27        36
## S168     6         3          1        1          63      10        53
## S158     6         2          2        1          63      37        25
## S171     6         3          1        1          63      20        43
## S162     6         3          1        1          63       8        55
## S179     7         3          1        1          63      23        39
## S182     7         3          1        1          63      29        34
## S183     7         1          2        2          63      20        43
## S187     7         2          2        1          63      13        50
## S184     7         2          2        1          63      10        53
## S178     7         2          2        1          63      21        42
## S186     7         1          2        2          63      18        45
## S181     7         2          2        1          63       8        55
## S177     7         1          2        2          63       9        54
## S188     7         3          1        1          63      11        52
## S180     7         1          2        2          63      22        41
## S189     7         1          2        2          63      14        47
## S201     8         2          2        1          63      18        45
## S198     8         2          2        1          63      12        51
## S197     8         1          2        2          63      11        52
## S194     8         1          2        2          63       4        59
## S195     8         2          2        1          63      10        53
## S202     8         3          1        1          63      25        38
## S199     8         3          1        1          63      17        46
## S204     8         2          2        1          63      26        37
## S203     8         1          2        2          63      13        50
## S200     8         1          2        2          63      27        36
## S196     8         3          1        1          63      23        40
## S208     9         1          2        2          63      16        12
## S209     9         2          2        1          63      24        39
## S216     9         3          1        1          63      45        18
## S214     9         1          2        2          63      20        43
## S218     9         2          2        1          63      33        30
## S217     9         1          2        2          63      22        41
## S223     9         1          2        2          63      14        49
## S212     9         2          2        1          63      20        43
## S210     9         3          1        1          63      23        40
## S220     9         1          2        2          63      30        33
## S222     9         3          1        1          63      14        47
## S211     9         1          2        2          63      17        46
## S221     9         2          2        1          63      26        37
## S215     9         2          2        1          63      38        25
## S219     9         3          1        1          63      25        38
## S213     9         3          1        1          63      16        47
##      Remaining tCommonRatio1a tCommonRatio1b tCommonRatio3a tCommonRatio3b
## S055         0              1              1              2              1
## S058         0              2              2              2              1
## S053         0              1              1              1              1
## S061         0              1              1              1              1
## S063         0              1              2              2              1
## S066         0              1              2              1              1
## S062         0              1              1              1              1
## S054         0              1              1              1              1
## S057        10              3              1              2              1
## S060         0              1              2              2              1
## S067         0              1              1              1              1
## S056         0              1              2              2              1
## S059         6              1              1              1              1
## S064         0              3              2              2              1
## S065         0              1              1              2              2
## S068         0              1              1              1              1
## S052        29              1             NA             NA             NA
## S241         0              2              2              2              2
## S230         0              1              2              2              1
## S232         0              1              2              2              1
## S233         0              2              2              2              2
## S236         0              1              1              2              1
## S235         0              2              2              2              2
## S240         0              1              2              2              1
## S239         0              1              2              2              1
## S234         0              1              1              1              1
## S231         1              1              1              1              1
## S243         0              1              2              2              1
## S228         0              1              1              1              1
## S238         0              1              2              2              2
## S229         0              1              1              1              1
## S242         0              2              1              2              1
## S237        14              1              1              2              1
## S260         0              1              1              1              1
## S257         0              1              2              2              1
## S258         0              2              1              2              1
## S249         0              1              1              2              1
## S253         0              1              1              2              1
## S263         0              1              2              2              1
## S252         0              1              1              1              1
## S255         0              1              2              2              2
## S254         0              3              2              2              1
## S261         0              2              2              2              1
## S262         0              1              2              2              1
## S251         0              1              1              2              1
## S250         0              1              2              2              2
## S259         1              1              2              2              1
## S256         0              1              1              1              1
## S284         0              1              1              1              1
## S283         0              1              1              1              1
## S273         0              1              1              1              1
## S285         0              1              1              1              1
## S272        33              1              2             NA              1
## S274         0              1              1              1              1
## S281        23              1              2              1              1
## S276        34              1             NA             NA             NA
## S275        25              1              1              1              1
## S280        13              1              1              2              1
## S282        33              1             NA             NA              1
## S270        29              1              2              1              1
## S269        25              1              2              2              1
## S278         0              1              2              1              1
## S279        43              1             NA             NA             NA
## S271        23              1              1              2              1
## S277         0              1              1              1              1
## S298        23              1             NA             NA              2
## S308         0              1              1              1              1
## S299         6              1              1              1              1
## S302         0              1              1              2              1
## S307         0              1              2              1              1
## S291         0              1              1              1              1
## S297         0              1              1              1              1
## S296         0              1              2              2              2
## S292         0              1              1              1              1
## S304        33              1             NA             NA             NA
## S301         0              1              1              1              1
## S305         7              3              2              2              2
## S294         0              1              1              1              1
## S295         0              1              1              1              1
## S303        16              1              1              1              1
## S306        19              1              2              2              1
## S300         0              1              1              1              1
## S293         0              1              1              1              1
## S316        43              1             NA             NA             NA
## S319         0              1              1              1              1
## S317         0              1              1              2              1
## S318         0              1              1              2              1
## S320        10              1              1              2              1
## S315         0              1              1              1              1
## S334         0              1              2              2              1
## S324         0              1              2              2              1
## S325         0              2              2              2              1
## S328         0              1              2              2              2
## S327         7              1              1              1              1
## S323         1              2              2             NA              1
## S336         0              1              1              1              1
## S333         4              2              2              2              2
## S332         0              2              1              1              1
## S331         0              1              1              1              1
## S329         0              1              2              2              2
## S326        39              2              2             NA             NA
## S338         0              1              1              1              1
## S335         1              1              2              2              1
## S337         0              1              1              1              1
## S330         0              1              1              1              1
## S091         0              1              1              1              1
## S075         1              2              2              2              1
## S074         0              1              1              1              1
## S088         0              1              1              2              1
## S082         0              1              2              2              1
## S083         0              1              1              1              1
## S086         0              1              2              2              1
## S087         0              1              2              2              1
## S080         0              1              1              1              1
## S078         0              1              2              2              1
## S085         0              1              2              2              1
## S084         0              1              2              2              1
## S076         0              1              1              2              1
## S081         0              1              1              1              1
## S077         0              1              1              2              1
## S089        14              1              1              1              1
## S090         0              1              1              1              1
## S079         0              1              1              1              1
## S113         1              3              2              2              1
## S101         0              1              1              1              1
## S099         0              1              1              2              1
## S111         0              1              1              2              1
## S114         0              1              2              2              1
## S102         0              1              2              2              2
## S098         0              1              1              1              1
## S100         0              1              1              1              1
## S106         8              1             NA             NA             NA
## S103        13              1             NA             NA             NA
## S110         2              3              2             NA              1
## S107         1              1              2              2              1
## S109         0              2              2              2              1
## S112        27              1             NA             NA             NA
## S105         0              1              2              2              1
## S104         0              1              1              1              1
## S108         6              3              2              2              1
## S097         0              1              2              2              1
## S129         1              3              2              2              1
## S128         0              1              2              2              1
## S120         0              1              2              2              1
## S136         2              1              2              2              1
## S122         0              1              2              2              1
## S124         0              1              2              2              2
## S127         0              1              2              2              1
## S126         0              1              1              1              1
## S134         0              2              2              2              1
## S125         0              1              1              2              1
## S132         0              1              2              2              1
## S121         0              1              2              2              1
## S123         1              3              2              2              1
## S130         0              1              1              1              1
## S135         0              2              2              2              1
## S131         0              3              2              2              1
## S119         0              2              2              2              1
## S133         0              1              2              2              1
## S154         0              3              2              2              1
## S156         1              3              2              2              2
## S143         2              3              2              2              1
## S152        11              1              2              2             NA
## S146        20              1              2              2              1
## S142         0              1              2              2              1
## S141         1              3              2              2              1
## S145         0              1              2              2              1
## S148         0              1              2              2              1
## S144        15              2             NA             NA             NA
## S140        31              1             NA             NA              2
## S151         0              1              2              2              1
## S147         1              2              1              1              1
## S149         1              1              2              2              1
## S155         4              1              2              2              1
## S150         0              1              2              2              1
## S153         0              1              1              1              1
## S160         1              1              2              2              1
## S159         0              1              1              1              1
## S165         0              1              1              1              1
## S166         0              1              1              1              1
## S169         0              1              1              2              1
## S164         0              1              2              1              1
## S157         0              1              2              2              1
## S163         0              1              1              1              1
## S170         0              1              1              2              1
## S167         0              1              1              2              1
## S161         0              1              2              2              1
## S168         0              1              1              1              1
## S158         1              1              2              2              1
## S171         0              1              1              2              1
## S162         0              1              1              1              1
## S179         1              1              1              2              1
## S182         0              1              1              2              1
## S183         0              1              1              1              1
## S187         0              1              1              1              1
## S184         0              1              1              1              1
## S178         0              1              1              2              1
## S186         0              1              2              2              1
## S181         0              1              1              1              1
## S177         0              1              1              1              1
## S188         0              1              1              1              1
## S180         0              1              1              2              1
## S189         0              1              1              1              1
## S201         0              1              2              2              2
## S198         0              1              1              1              1
## S197         0              1              1              1              1
## S194         0              1              1              1              1
## S195         0              1              2              1              1
## S202         0              1              1              2              2
## S199         0              1              1              1              1
## S204         0              1              2              2              1
## S203         0              1              1              1              1
## S200         0              1              2              2              1
## S196         0              1              1              1              1
## S208        35              1             NA             NA             NA
## S209         0              1              1              1              1
## S216         0              3              2              2              1
## S214         0              1              2              2              1
## S218         0              1              2              2              1
## S217         0              1              2              2              1
## S223         0              1              1              1              1
## S212         0              1              1              1              1
## S210         0              1              1              1              1
## S220         0              2              2              2              1
## S222         0              1              2              2              1
## S211         0              1              1              2              1
## S221         0              1              2              2              1
## S215         0              2              1              2              2
## S219         0              1              1              2              1
## S213         0              1              1              1              2
##      tCommonRatio2a tCommonRatio2b tExamplesGeometric1a
## S055              1              1                    1
## S058              1              2                    2
## S053              1              1                    1
## S061              1              1                    1
## S063              1              1                    2
## S066              1              1                    2
## S062              1              1                    1
## S054              1              1                    2
## S057              1              1                    1
## S060              1              2                    2
## S067              1              1                    1
## S056              1              1                    1
## S059              1              1                    1
## S064              1              2                    2
## S065              1              2                    2
## S068              1              1                    1
## S052             NA             NA                   NA
## S241              2              2                    2
## S230              2              2                    2
## S232              1              1                    1
## S233              2              2                    2
## S236              1              1                    1
## S235              2              1                    2
## S240              1              2                    2
## S239              1              2                    2
## S234              1              1                    1
## S231             NA              2                    2
## S243              1              2                    2
## S228              1              2                    2
## S238              2              1                    2
## S229              1              1                    1
## S242              1              2                    1
## S237              1              1                    1
## S260              1              2                    2
## S257              1              1                    2
## S258              1              1                    2
## S249              1              1                    1
## S253              1              1                    1
## S263              1              1                    1
## S252              1              1                    1
## S255              1              1                    1
## S254              2              2                    2
## S261              1              2                    2
## S262              1              1                    1
## S251              1              2                    2
## S250              1              1                    2
## S259             NA              2                    2
## S256              1              1                    2
## S284              1              1                    1
## S283              1              1                    1
## S273              1              1                    1
## S285              1              1                    1
## S272              2              1                    1
## S274              1              1                    1
## S281              1              1                    1
## S276             NA              1                    1
## S275              1              1                    1
## S280              1              1                    1
## S282             NA              1                    2
## S270              1              1                    1
## S269              1              1                    1
## S278              1              1                    1
## S279             NA             NA                   NA
## S271              1              1                    1
## S277              1              1                    1
## S298              2              1                    1
## S308              1              1                    1
## S299              2              1                    1
## S302              1              1                    2
## S307              1              1                    1
## S291              1              1                    1
## S297              1              1                    1
## S296              1              2                    1
## S292              1              1                    1
## S304             NA             NA                   NA
## S301              1              1                    1
## S305              2              2                    2
## S294              1              1                    1
## S295              1              1                    1
## S303              1              1                    1
## S306              1              1                    2
## S300              1              1                    1
## S293              1              1                    1
## S316             NA             NA                   NA
## S319              1              1                    1
## S317              1              2                    2
## S318              1              2                    1
## S320              1              1                    1
## S315              1              1                    2
## S334              1              2                    2
## S324              1              1                    2
## S325              2              2                    2
## S328              2              1                    2
## S327              1              2                    1
## S323              1              2                    2
## S336              1              1                    1
## S333              2              2                    2
## S332              1              1                    1
## S331              1              2                    2
## S329              1              1                    1
## S326             NA             NA                   NA
## S338              1              1                    1
## S335             NA              2                    2
## S337              1              1                    1
## S330              1              1                    1
## S091              1              1                    1
## S075             NA              1                    2
## S074              1              1                    1
## S088              1              2                    2
## S082              1              2                    2
## S083              1              1                    1
## S086              1              2                    2
## S087              1              2                    2
## S080              1              1                    1
## S078              1              1                    1
## S085              1              2                    1
## S084              1              1                    2
## S076              1              1                    2
## S081              1              1                    1
## S077              1              2                    2
## S089              1              1                    1
## S090              1              1                    1
## S079              1              1                    1
## S113              1              2                    2
## S101              1              1                    1
## S099              1              2                    2
## S111              1              2                    2
## S114              1              1                    2
## S102              2              2                    2
## S098              1              2                    2
## S100              1              2                    1
## S106             NA              2                    2
## S103             NA             NA                   NA
## S110              1              1                    2
## S107              1              1                    1
## S109              1              2                    2
## S112             NA             NA                   NA
## S105              1              1                    2
## S104              1              1                    1
## S108              2              2                    2
## S097              1              1                    2
## S129              1              2                    2
## S128              1              2                    2
## S120              1              2                    2
## S136              2              2                    2
## S122              1              2                    2
## S124              2              2                    2
## S127              1              2                    2
## S126              1              1                    1
## S134              1              1                    1
## S125              1              1                    2
## S132              1              1                    1
## S121              1              2                    2
## S123              1              2                    2
## S130              1              2                    2
## S135              1              2                    2
## S131              2              2                    1
## S119              1              2                    2
## S133              1              2                    2
## S154              2              2                    2
## S156             NA              2                    2
## S143              1              2                    2
## S152             NA              2                    2
## S146              1              1                    1
## S142              1              1                    2
## S141              1              1                    2
## S145              1              1                    2
## S148              2              2                    2
## S144             NA              2                    2
## S140             NA              1                    2
## S151              1              2                    2
## S147              1              1                    2
## S149              1              2                    2
## S155              1              2                    2
## S150              1              2                    2
## S153              1              2                    2
## S160              1              1                    2
## S159              1              2                    2
## S165              1              1                    1
## S166              1              1                    1
## S169              2              1                    2
## S164              1              1                    1
## S157              1              2                    1
## S163              1              1                    1
## S170              1              1                    1
## S167              1              1                    2
## S161              1              2                    2
## S168              1              1                    1
## S158             NA              2                    2
## S171              1              2                    2
## S162              1              1                    1
## S179              1              2                    1
## S182              1              2                    2
## S183              1              1                    1
## S187              1              1                    1
## S184              1              1                    1
## S178              1              1                    1
## S186              1              1                    1
## S181              1              1                    1
## S177              1              1                    2
## S188              2              2                    1
## S180              1              1                    1
## S189              1              1                    1
## S201              2              1                    2
## S198              1              1                    1
## S197              1              1                    1
## S194              1              1                    1
## S195              1              1                    1
## S202              2              2                    2
## S199              1              1                    2
## S204              1              1                    2
## S203              1              1                    1
## S200              1              1                    1
## S196              1              1                    1
## S208             NA             NA                   NA
## S209              1              1                    1
## S216              1              2                    2
## S214              1              1                    1
## S218              1              2                    2
## S217              1              1                    2
## S223              1              1                    1
## S212              1              2                    1
## S210              1              1                    1
## S220              1              2                    2
## S222              1              1                    1
## S211              1              1                    1
## S221              1              1                    1
## S215              2              2                    2
## S219              1              2                    1
## S213              1              2                    1
##      tExamplesGeometric1b tExamplesGeometric3a tExamplesGeometric3b
## S055                    1                    1                    1
## S058                    1                    1                    1
## S053                    1                    1                    1
## S061                    1                    1                    1
## S063                    1                    1                    1
## S066                    1                    1                    1
## S062                    1                    1                    1
## S054                    2                    2                    2
## S057                    1                    2                    1
## S060                    1                    1                    1
## S067                    1                    1                    1
## S056                    1                    1                    1
## S059                    1                   NA                    1
## S064                    1                    1                    1
## S065                    1                    1                    2
## S068                    1                    1                    1
## S052                   NA                   NA                    2
## S241                    2                    2                    2
## S230                    2                    2                    2
## S232                    1                    1                    1
## S233                    2                    2                    2
## S236                    1                    1                    1
## S235                    1                    1                    1
## S240                    2                    2                    1
## S239                    2                    2                    2
## S234                    1                    1                    1
## S231                    1                    1                    1
## S243                    2                    2                    1
## S228                    1                    1                    1
## S238                    2                    2                    2
## S229                    1                    1                    1
## S242                    1                    1                    1
## S237                    2                    2                    1
## S260                    2                    1                    2
## S257                    1                    2                    2
## S258                    1                    1                    1
## S249                    1                    1                    1
## S253                    1                    1                    1
## S263                    1                    1                    1
## S252                    1                    1                    1
## S255                    2                    2                    2
## S254                    2                    2                    2
## S261                    1                    1                    1
## S262                    1                    1                    1
## S251                    1                    1                    1
## S250                    1                    1                    1
## S259                    2                    1                    2
## S256                    1                    2                    1
## S284                    1                    1                    1
## S283                    1                    1                    1
## S273                    1                    1                    1
## S285                    1                    1                    1
## S272                   NA                   NA                   NA
## S274                    2                    1                    1
## S281                    1                   NA                   NA
## S276                   NA                   NA                   NA
## S275                   NA                   NA                    1
## S280                    1                    1                    2
## S282                   NA                   NA                   NA
## S270                   NA                   NA                   NA
## S269                   NA                   NA                   NA
## S278                    1                    1                    1
## S279                   NA                   NA                   NA
## S271                    1                    1                    1
## S277                    1                    2                    1
## S298                    2                    2                    2
## S308                    1                    1                    2
## S299                    1                    1                    2
## S302                    1                    2                    1
## S307                    1                    1                    1
## S291                    1                    1                    1
## S297                    1                    1                    1
## S296                    1                    1                    2
## S292                    1                    1                    1
## S304                   NA                   NA                    1
## S301                    1                    1                    1
## S305                    2                    1                    2
## S294                    1                    1                    1
## S295                    1                    1                    1
## S303                   NA                   NA                    1
## S306                   NA                   NA                    1
## S300                    1                    1                    1
## S293                    1                    1                    1
## S316                   NA                   NA                   NA
## S319                    1                    1                    1
## S317                    1                    1                    1
## S318                    1                    1                    1
## S320                    1                    1                    2
## S315                    1                    1                    1
## S334                    1                    1                    2
## S324                    1                    1                    1
## S325                    1                    2                    2
## S328                    2                    2                    2
## S327                    1                    1                    1
## S323                    2                    2                    2
## S336                    1                    1                    1
## S333                    1                    1                    1
## S332                    1                    1                    1
## S331                    1                    1                    1
## S329                    2                    2                    2
## S326                   NA                   NA                   NA
## S338                    2                    2                    1
## S335                    1                    1                    1
## S337                    2                    1                    1
## S330                    2                    2                    1
## S091                    1                    1                    1
## S075                    2                    2                    1
## S074                    1                    1                    1
## S088                    1                    1                    1
## S082                    1                    1                    1
## S083                    1                    1                    1
## S086                    2                    2                    2
## S087                    1                    1                    1
## S080                    1                    1                    1
## S078                    1                    1                    1
## S085                    1                    1                    1
## S084                    1                    1                    1
## S076                    2                    2                    2
## S081                    1                    1                    1
## S077                    2                    2                    1
## S089                   NA                   NA                    1
## S090                    1                    1                    1
## S079                    2                    2                    2
## S113                    2                    2                    2
## S101                    1                    1                    1
## S099                    1                    1                    1
## S111                    1                    1                    1
## S114                    1                    1                    1
## S102                    1                    1                    2
## S098                    1                    1                    1
## S100                    1                    1                    1
## S106                    1                    1                    1
## S103                    2                    2                    2
## S110                    2                    2                    2
## S107                    1                    1                    1
## S109                    2                    2                    2
## S112                   NA                   NA                    2
## S105                    1                    1                    1
## S104                    1                    1                    1
## S108                    2                    1                    2
## S097                    1                    1                    1
## S129                    2                    2                    2
## S128                    2                    2                    1
## S120                    2                    2                    1
## S136                    2                    2                    2
## S122                    2                    2                    2
## S124                    1                    1                    1
## S127                    1                    1                    1
## S126                    1                    1                    1
## S134                    1                    1                    1
## S125                    1                    1                    1
## S132                    1                    1                    1
## S121                    1                    2                    2
## S123                    2                    2                    2
## S130                    1                    2                    2
## S135                    2                    1                    2
## S131                    2                    2                    2
## S119                    1                    1                    1
## S133                    1                    1                    2
## S154                    2                    1                    2
## S156                    2                    2                    2
## S143                    2                    2                    2
## S152                    2                    2                    2
## S146                    2                    2                    2
## S142                    2                    1                    2
## S141                    2                    2                    2
## S145                    1                    1                    2
## S148                    2                    2                    2
## S144                    2                    1                    2
## S140                   NA                   NA                   NA
## S151                    2                    2                    2
## S147                    2                    2                    2
## S149                    2                    2                    1
## S155                    2                    2                    1
## S150                    2                    2                    2
## S153                    2                    2                    1
## S160                    2                    2                    2
## S159                    1                    1                    1
## S165                    1                    1                    1
## S166                    1                    1                    1
## S169                    1                    1                    1
## S164                    1                    1                    1
## S157                    1                    1                    1
## S163                    1                    1                    1
## S170                    1                    1                    1
## S167                    1                    1                    1
## S161                    2                    2                    1
## S168                    1                    1                    1
## S158                    1                    1                    1
## S171                    1                    1                    1
## S162                    1                    1                    1
## S179                    2                    2                    1
## S182                    1                    1                    1
## S183                    1                    1                    1
## S187                    1                    1                    1
## S184                    1                    1                    1
## S178                    1                    1                    1
## S186                    1                    1                    1
## S181                    1                    1                    1
## S177                    1                    1                    1
## S188                    1                    1                    1
## S180                    1                    1                    1
## S189                    1                    1                    1
## S201                    1                    1                    1
## S198                    1                    1                    1
## S197                    1                    1                    1
## S194                    1                    1                    1
## S195                    1                    1                    1
## S202                    1                    1                    1
## S199                    1                    1                    1
## S204                    2                    2                    2
## S203                    1                    1                    1
## S200                    1                    1                    1
## S196                    1                    1                    1
## S208                   NA                   NA                    2
## S209                    2                    2                    1
## S216                    2                    2                    2
## S214                    1                    2                    1
## S218                    2                    2                    2
## S217                    1                    1                    1
## S223                    1                    1                    1
## S212                    1                    1                    1
## S210                    1                    1                    1
## S220                    2                    2                    2
## S222                    1                    1                    1
## S211                    1                    1                    1
## S221                    1                    2                    2
## S215                    2                    2                    1
## S219                    1                    1                    1
## S213                    1                    1                    1
##      tExamplesGeometric2a tExamplesGeometric2b tExtendGeometric1a
## S055                    1                    1                  1
## S058                    1                    1                  1
## S053                    1                    1                  1
## S061                    1                    1                  2
## S063                    1                    1                  1
## S066                    1                    1                  1
## S062                    1                    1                  1
## S054                    2                    2                  1
## S057                    1                    1                  1
## S060                    1                    1                  1
## S067                    1                    1                  1
## S056                    1                    1                  1
## S059                    1                    1                  2
## S064                    1                    1                  2
## S065                    2                    1                  1
## S068                    1                    1                  1
## S052                    2                    2                 NA
## S241                    2                    1                  1
## S230                    2                    2                  1
## S232                    1                    1                  1
## S233                    2                    1                  1
## S236                    1                    1                  1
## S235                    1                    1                  2
## S240                    2                    1                  2
## S239                    2                    2                  2
## S234                    1                    1                  1
## S231                    1                    1                  1
## S243                    1                    1                  1
## S228                    1                    1                  2
## S238                    1                    2                  2
## S229                    1                    1                  1
## S242                    1                    1                  2
## S237                    1                    1                 NA
## S260                    1                    2                  1
## S257                    2                    1                  1
## S258                    1                    1                  1
## S249                    1                    1                  1
## S253                    1                    1                  1
## S263                    1                    1                  1
## S252                    1                    1                  1
## S255                    2                    2                  1
## S254                    2                    2                  1
## S261                    1                    1                  2
## S262                    1                    1                  1
## S251                    1                    1                  1
## S250                    1                    1                  2
## S259                    2                    1                  1
## S256                    1                    1                  2
## S284                    1                    1                  1
## S283                    1                    1                  1
## S273                    1                    1                  1
## S285                    1                    1                  1
## S272                   NA                    1                 NA
## S274                    1                    1                  1
## S281                   NA                   NA                 NA
## S276                   NA                    1                 NA
## S275                    1                    1                 NA
## S280                    1                    1                  1
## S282                   NA                    1                 NA
## S270                   NA                    1                 NA
## S269                   NA                    1                 NA
## S278                    1                    1                  1
## S279                   NA                   NA                 NA
## S271                    1                    1                  1
## S277                    1                    1                  1
## S298                    2                    1                 NA
## S308                    2                    2                  1
## S299                    1                    2                  2
## S302                    1                    1                  1
## S307                    1                    1                  1
## S291                    1                    1                  1
## S297                    1                    1                  1
## S296                    2                    2                  1
## S292                    1                    1                  2
## S304                   NA                    1                 NA
## S301                    1                    1                  1
## S305                    2                    2                  1
## S294                    1                    1                  1
## S295                    1                    1                  1
## S303                    1                    1                 NA
## S306                    1                    1                 NA
## S300                    1                    1                  1
## S293                    1                    1                  1
## S316                   NA                   NA                 NA
## S319                    1                    1                  2
## S317                    1                    1                  1
## S318                    1                    2                  2
## S320                    1                    1                  1
## S315                    1                    1                  1
## S334                    2                    2                  1
## S324                    1                    1                  1
## S325                    2                    2                  1
## S328                    1                    2                  1
## S327                    1                    1                 NA
## S323                    2                    2                  1
## S336                    1                    1                  1
## S333                    1                    1                  2
## S332                    1                    1                  1
## S331                    1                    1                  1
## S329                    1                    1                  1
## S326                   NA                    1                 NA
## S338                    1                    1                 NA
## S335                    1                    1                  2
## S337                    1                    1                  1
## S330                    1                    1                  1
## S091                    1                    1                  1
## S075                    2                    1                  2
## S074                    1                    1                  1
## S088                    1                    1                  1
## S082                    1                    1                  2
## S083                    1                    1                  2
## S086                    2                    2                  2
## S087                    1                    1                  2
## S080                    1                    1                  1
## S078                    1                    1                  1
## S085                    1                    1                  1
## S084                    1                    1                  1
## S076                    2                    1                  1
## S081                    1                    1                  2
## S077                    1                    1                  1
## S089                    1                    1                  1
## S090                    1                    1                  1
## S079                    2                    2                  1
## S113                    2                    2                  1
## S101                    1                    1                  1
## S099                    1                    1                  2
## S111                    1                    1                  2
## S114                    1                    1                  1
## S102                    2                    1                  2
## S098                    1                    1                  1
## S100                    1                    1                  1
## S106                    1                    1                  2
## S103                    2                    2                  2
## S110                    2                    2                  2
## S107                    1                    1                 NA
## S109                    2                    2                  2
## S112                    2                    2                 NA
## S105                    1                    1                  2
## S104                    1                    1                  1
## S108                    2                    2                  1
## S097                    1                    1                  2
## S129                    2                    2                  1
## S128                    2                    2                  1
## S120                    1                    1                  1
## S136                    2                    2                  1
## S122                    1                    2                  1
## S124                    1                    1                  2
## S127                    1                    1                  1
## S126                    1                    1                  1
## S134                    1                    1                  1
## S125                    1                    1                  2
## S132                    1                    1                  1
## S121                    1                    2                  1
## S123                    1                    2                  1
## S130                    2                    1                  1
## S135                    2                    2                  1
## S131                    2                    1                  1
## S119                    1                    1                  1
## S133                    2                    1                  2
## S154                    2                    2                  2
## S156                    2                    1                  1
## S143                    2                    1                  1
## S152                    1                    1                 NA
## S146                    2                    1                 NA
## S142                    1                    1                  1
## S141                    2                    1                  1
## S145                    1                    1                  1
## S148                    1                    1                  2
## S144                    2                    2                 NA
## S140                   NA                    1                 NA
## S151                    1                    1                  2
## S147                    2                    1                  1
## S149                    2                    2                  2
## S155                    1                    1                  2
## S150                    1                    1                  1
## S153                    1                    1                  1
## S160                    2                    1                  1
## S159                    1                    1                  1
## S165                    1                    1                  1
## S166                    1                    1                  1
## S169                    1                    1                  1
## S164                    1                    1                  2
## S157                    1                    1                  1
## S163                    1                    1                  1
## S170                    1                    1                  1
## S167                    1                    1                  1
## S161                    2                    1                  1
## S168                    1                    1                  2
## S158                    1                    1                  1
## S171                    1                    1                  1
## S162                    1                    1                  1
## S179                    1                    1                  1
## S182                    1                    1                  1
## S183                    1                    1                  2
## S187                    1                    1                  1
## S184                    1                    1                  2
## S178                    1                    1                  1
## S186                    1                    1                  1
## S181                    1                    1                  1
## S177                    1                    1                  1
## S188                    1                    1                  2
## S180                    1                    1                  1
## S189                    1                    1                  1
## S201                    1                    1                  1
## S198                    1                    1                  1
## S197                    1                    1                  1
## S194                    1                    1                  1
## S195                    1                    1                  1
## S202                    1                    1                  1
## S199                    1                    1                  1
## S204                    1                    1                  1
## S203                    1                    1                  1
## S200                    1                    1                  2
## S196                    1                    1                  1
## S208                   NA                    2                 NA
## S209                    2                    1                  1
## S216                    1                    2                  1
## S214                    1                    1                  1
## S218                    2                    2                  1
## S217                    1                    1                  2
## S223                    1                    1                  1
## S212                    1                    1                  1
## S210                    1                    1                  1
## S220                    1                    1                  1
## S222                    1                    1                  1
## S211                    1                    1                  1
## S221                    1                    1                  1
## S215                    2                    2                  1
## S219                    1                    1                  1
## S213                    1                    1                  2
##      tExtendGeometric1b tExtendGeometric3a tExtendGeometric3b
## S055                  1                  2                  1
## S058                  2                  2                  1
## S053                  1                  1                  1
## S061                  2                  1                  1
## S063                  2                  2                  2
## S066                  2                  2                  2
## S062                  2                  2                  1
## S054                  2                  2                  2
## S057                  1                  2                  2
## S060                  2                  2                  2
## S067                  2                  2                  1
## S056                  2                  2                  2
## S059                  1                  1                  2
## S064                  2                  2                  2
## S065                  2                  2                  2
## S068                  1                  1                  1
## S052                 NA                 NA                 NA
## S241                  2                  2                  1
## S230                  2                  2                  2
## S232                  2                  2                  1
## S233                  2                  2                  2
## S236                  1                  1                  1
## S235                  2                  2                  2
## S240                  1                  1                  1
## S239                  2                  2                  2
## S234                  2                  2                  1
## S231                  2                  2                  1
## S243                  2                  2                  2
## S228                  2                  2                  1
## S238                  2                  2                  2
## S229                  2                  2                  2
## S242                  2                  2                  2
## S237                 NA                  2                 NA
## S260                  2                  2                  1
## S257                  2                  2                  2
## S258                  2                  2                  2
## S249                  2                  2                  1
## S253                  2                  2                  1
## S263                  2                  2                  1
## S252                  1                  1                  1
## S255                  2                  2                  2
## S254                  2                  2                  2
## S261                  2                  2                  1
## S262                  2                  2                  2
## S251                  1                  2                  1
## S250                  2                  2                  1
## S259                  2                  2                  2
## S256                  1                  2                  1
## S284                  1                  2                  1
## S283                  2                  2                  1
## S273                  1                  1                  2
## S285                  1                  1                  1
## S272                 NA                 NA                  1
## S274                  1                  1                  1
## S281                  1                  1                  1
## S276                 NA                 NA                  1
## S275                  1                  1                 NA
## S280                  1                  1                  1
## S282                 NA                 NA                  1
## S270                 NA                 NA                 NA
## S269                  2                  2                  1
## S278                  1                  1                  1
## S279                 NA                 NA                 NA
## S271                  2                  2                  1
## S277                  1                  1                  1
## S298                 NA                 NA                  2
## S308                  1                  1                  1
## S299                  2                  2                  2
## S302                  2                  2                  1
## S307                  2                  2                  1
## S291                  1                  1                  1
## S297                  2                  2                  1
## S296                  2                  2                  1
## S292                  2                  2                  1
## S304                 NA                 NA                 NA
## S301                  2                  2                  1
## S305                  2                  2                  2
## S294                  2                  2                  1
## S295                  2                  1                  1
## S303                  2                  2                  1
## S306                  2                  1                  2
## S300                  2                  1                  1
## S293                  2                  2                  1
## S316                 NA                 NA                 NA
## S319                  1                  2                  1
## S317                  2                  2                  1
## S318                  1                  2                  1
## S320                  2                  2                  1
## S315                  2                  2                  2
## S334                  2                  2                  1
## S324                  2                  2                  2
## S325                  2                  2                  2
## S328                  1                  1                  2
## S327                  1                  2                  1
## S323                  1                  2                  2
## S336                  1                  2                  1
## S333                 NA                 NA                 NA
## S332                  2                  2                  2
## S331                  2                  1                  1
## S329                  2                  1                  1
## S326                 NA                 NA                 NA
## S338                  2                  2                  2
## S335                  2                  2                  2
## S337                  2                  1                  1
## S330                  2                  2                  1
## S091                  2                  2                  1
## S075                  2                  1                  2
## S074                  2                  2                  2
## S088                  2                  2                  1
## S082                  2                  2                  1
## S083                  1                  2                  1
## S086                  2                  2                  2
## S087                  2                  1                  2
## S080                  2                  2                  1
## S078                  2                  2                  2
## S085                  2                  2                  2
## S084                  1                  2                  2
## S076                  2                  2                  2
## S081                  2                  2                  2
## S077                  2                  2                  2
## S089                  1                  2                  2
## S090                  1                  2                  1
## S079                  2                  2                  1
## S113                  2                 NA                  2
## S101                  2                  2                  2
## S099                  2                  2                  2
## S111                  2                  2                  2
## S114                  2                  2                  2
## S102                  2                  2                  1
## S098                  1                  2                  1
## S100                  2                  2                  1
## S106                 NA                 NA                 NA
## S103                 NA                 NA                 NA
## S110                  2                 NA                  2
## S107                  2                  2                  1
## S109                  2                  2                  1
## S112                 NA                 NA                 NA
## S105                  2                  2                  2
## S104                  1                  1                  2
## S108                  2                  2                  2
## S097                  2                  1                  2
## S129                  2                 NA                  2
## S128                  2                  2                  1
## S120                  2                  2                  1
## S136                  2                  2                  2
## S122                  2                  2                  2
## S124                  2                  2                  2
## S127                  2                  2                  2
## S126                  2                  2                  2
## S134                  2                  2                  2
## S125                  1                  2                  2
## S132                  2                  2                  2
## S121                  2                  2                  2
## S123                  2                 NA                  1
## S130                  2                  2                  1
## S135                  2                  2                  2
## S131                  2                  2                  2
## S119                  2                  2                  2
## S133                  2                  2                  1
## S154                  2                  2                  2
## S156                  2                  2                  1
## S143                  2                  2                  2
## S152                 NA                 NA                  2
## S146                 NA                 NA                 NA
## S142                  2                  2                  1
## S141                  2                 NA                  1
## S145                  1                  2                  1
## S148                  2                  2                  2
## S144                 NA                 NA                 NA
## S140                  1                 NA                 NA
## S151                  2                  1                  2
## S147                  2                 NA                  2
## S149                  2                 NA                  2
## S155                  2                  2                  1
## S150                  2                  2                  1
## S153                  1                  2                  1
## S160                  2                  2                  2
## S159                  2                  2                  2
## S165                  2                  2                  1
## S166                  2                  2                  1
## S169                  2                  2                  1
## S164                  2                  1                  1
## S157                  2                  2                  2
## S163                  2                  1                  1
## S170                  2                  2                  2
## S167                  2                  2                  1
## S161                  2                  2                  2
## S168                  1                  2                  1
## S158                  2                  2                  1
## S171                  1                  2                  1
## S162                  1                  1                  1
## S179                  2                  2                  2
## S182                  1                  2                  2
## S183                  1                  2                  1
## S187                  2                  2                  1
## S184                  1                  2                  1
## S178                  2                  2                  1
## S186                  1                  2                  1
## S181                  1                  1                  2
## S177                  1                  2                  1
## S188                  2                  1                  1
## S180                  2                  2                  2
## S189                  1                  1                  1
## S201                  2                  2                  1
## S198                  1                  2                  1
## S197                  2                  2                  2
## S194                  1                  1                  1
## S195                  1                  1                  1
## S202                  2                  2                  2
## S199                  2                  2                  2
## S204                  1                  1                  2
## S203                  1                  2                  1
## S200                  2                  2                  2
## S196                  1                  2                  2
## S208                 NA                 NA                 NA
## S209                  2                  2                  1
## S216                  2                  2                  2
## S214                  2                  2                  2
## S218                  2                  2                  1
## S217                  2                  2                  1
## S223                  1                  2                  1
## S212                  2                  2                  1
## S210                  2                  2                  2
## S220                  2                  2                  1
## S222                  1                  2                  2
## S211                  2                  2                  2
## S221                  2                  2                  2
## S215                  2                  2                  1
## S219                  2                  2                  2
## S213                  2                  2                  2
##      tExtendGeometric2a tExtendGeometric2b tModelExtendTableGeometric1a
## S055                  1                  1                            1
## S058                  2                  1                            2
## S053                  1                  1                            1
## S061                  1                  2                            1
## S063                  2                  1                            1
## S066                  1                  1                            2
## S062                  2                  2                            1
## S054                  2                  1                            2
## S057                  2                  2                            2
## S060                  2                  2                            2
## S067                  1                  1                            1
## S056                  1                  2                            1
## S059                  1                  1                            1
## S064                  2                  1                            1
## S065                  2                  1                            2
## S068                  1                  1                            2
## S052                 NA                 NA                           NA
## S241                  2                  2                            2
## S230                  2                  2                            1
## S232                  1                  1                            1
## S233                  2                  2                            2
## S236                  1                  1                            1
## S235                  1                  2                            1
## S240                  1                  2                            1
## S239                  1                  2                            1
## S234                  1                  1                            1
## S231                  2                  2                            2
## S243                  1                  2                            2
## S228                  2                  1                            2
## S238                  2                  1                            1
## S229                  2                  2                            1
## S242                  2                  2                            2
## S237                 NA                 NA                           NA
## S260                  1                  2                            2
## S257                  2                  2                            1
## S258                  1                  2                            1
## S249                  1                  2                            1
## S253                  2                  2                            1
## S263                  2                  2                            1
## S252                  1                  1                            1
## S255                  1                  2                            2
## S254                  2                  2                            2
## S261                  1                  1                            1
## S262                  2                  1                            1
## S251                  2                  1                            1
## S250                  1                  2                            2
## S259                  1                  1                            2
## S256                  1                  1                            1
## S284                  1                  2                            1
## S283                  1                  1                            1
## S273                  1                  1                            1
## S285                  1                  1                            1
## S272                 NA                  1                            1
## S274                  1                  1                            1
## S281                  1                  1                            1
## S276                 NA                  1                            1
## S275                 NA                  1                            1
## S280                  1                  1                            1
## S282                  1                  1                            1
## S270                 NA                 NA                           NA
## S269                  2                  2                            1
## S278                  1                  1                            1
## S279                 NA                 NA                            1
## S271                  1                  1                            1
## S277                  1                  1                            1
## S298                 NA                  1                            2
## S308                  1                  1                            1
## S299                  1                  1                            1
## S302                  1                  2                            1
## S307                  1                  1                            2
## S291                  1                  1                            1
## S297                  1                  1                            1
## S296                  1                  2                            2
## S292                  1                  1                            1
## S304                 NA                 NA                           NA
## S301                  1                  1                            1
## S305                  2                  2                            2
## S294                  1                  1                            2
## S295                  1                  1                            1
## S303                  1                  1                            1
## S306                  2                  2                            1
## S300                  1                  1                            1
## S293                  1                  2                            1
## S316                 NA                 NA                           NA
## S319                  1                  1                            1
## S317                  2                  1                            1
## S318                  1                  2                            1
## S320                  1                  1                            1
## S315                  1                  2                            1
## S334                  2                  1                            2
## S324                  2                  1                            1
## S325                  2                  2                            2
## S328                  2                  2                            2
## S327                  1                  1                            2
## S323                  2                  2                            1
## S336                  1                  1                            1
## S333                 NA                  1                            2
## S332                  2                  2                            1
## S331                  1                  2                            1
## S329                  1                  1                            1
## S326                 NA                 NA                           NA
## S338                  1                  1                            1
## S335                  2                  2                            1
## S337                  1                  1                            1
## S330                  1                  2                            2
## S091                  1                  1                            2
## S075                  1                  2                            2
## S074                  2                  1                            1
## S088                  1                  1                            2
## S082                  1                  1                            1
## S083                  1                  1                            1
## S086                  2                  2                            2
## S087                  2                  2                            1
## S080                  1                  1                            1
## S078                  1                  2                            1
## S085                  1                  2                            1
## S084                  2                  2                            2
## S076                  1                  1                            2
## S081                  2                  2                            1
## S077                  1                  1                            2
## S089                  2                  1                            1
## S090                  1                  1                            1
## S079                  2                  2                            1
## S113                  2                  2                            1
## S101                  2                  1                            1
## S099                  1                  1                            1
## S111                  2                  2                            2
## S114                  2                  2                            1
## S102                  1                  2                            2
## S098                  2                  2                            1
## S100                  1                  2                            1
## S106                 NA                  1                            2
## S103                 NA                 NA                           NA
## S110                  2                  2                            2
## S107                  2                  1                            1
## S109                  2                  2                            2
## S112                 NA                 NA                           NA
## S105                  2                  2                            1
## S104                  1                  1                            1
## S108                  2                  2                            1
## S097                  1                  2                            2
## S129                  2                  2                            2
## S128                  1                  1                            2
## S120                  1                  2                            2
## S136                  2                  2                            2
## S122                  1                  2                            2
## S124                  2                  1                            2
## S127                  2                  2                            1
## S126                  1                  1                            1
## S134                  2                  2                            1
## S125                  1                  1                            1
## S132                  1                  1                            2
## S121                  2                  2                            2
## S123                  1                  1                            2
## S130                  1                  2                            2
## S135                  2                  2                            1
## S131                  1                  2                            1
## S119                  2                  2                            1
## S133                  2                  2                            2
## S154                  2                  2                            1
## S156                  2                  2                            2
## S143                  2                  2                            2
## S152                 NA                  2                            2
## S146                 NA                 NA                           NA
## S142                  2                  1                            2
## S141                  2                  2                            2
## S145                  2                  2                            2
## S148                  2                  2                            1
## S144                 NA                 NA                           NA
## S140                 NA                 NA                           NA
## S151                  1                  1                            1
## S147                  2                  2                            1
## S149                  2                  2                            2
## S155                  2                  2                            2
## S150                  2                  2                            1
## S153                  2                  1                            1
## S160                  1                  1                            2
## S159                  1                  1                            1
## S165                  1                  2                            1
## S166                  1                  2                            2
## S169                  1                  2                            1
## S164                  1                  2                            2
## S157                  2                  2                            1
## S163                  1                  2                            2
## S170                  1                  2                            2
## S167                  1                  1                            1
## S161                  1                  1                            2
## S168                  1                  1                            1
## S158                  1                  2                            1
## S171                  1                  2                            2
## S162                  1                  1                            1
## S179                  1                  2                            1
## S182                  2                  1                            2
## S183                  1                  1                            1
## S187                  1                  1                            1
## S184                  2                  1                            1
## S178                  1                  1                            1
## S186                  1                  1                            1
## S181                  1                  1                            1
## S177                  1                  1                            1
## S188                  1                  2                            1
## S180                  1                  1                            1
## S189                  1                  1                            1
## S201                  2                  2                            1
## S198                  1                  1                            1
## S197                  2                  1                            1
## S194                  1                  1                            1
## S195                  1                  1                            1
## S202                  2                  2                            1
## S199                  2                  1                            1
## S204                  1                  2                            1
## S203                  1                  2                            1
## S200                  2                  1                            1
## S196                  2                  2                            1
## S208                 NA                 NA                           NA
## S209                  1                  1                            1
## S216                  2                  2                            2
## S214                  2                  1                            1
## S218                  1                  1                            1
## S217                  2                  1                            1
## S223                  2                  2                            1
## S212                  1                  1                            2
## S210                  1                  2                            1
## S220                  2                  1                            1
## S222                  2                  2                            2
## S211                  1                  1                            2
## S221                  1                  2                            1
## S215                  2                  2                            2
## S219                  2                  2                            1
## S213                  2                  1                            1
##      tModelExtendTableGeometric1b tModelExtendTableGeometric3a
## S055                            1                            1
## S058                            2                            2
## S053                            1                            2
## S061                            2                            2
## S063                            2                            1
## S066                            1                            2
## S062                            2                            1
## S054                            2                            2
## S057                            2                            2
## S060                            1                            1
## S067                            2                            2
## S056                            1                            1
## S059                            2                            2
## S064                            2                            2
## S065                            2                            2
## S068                            1                            1
## S052                            2                            2
## S241                            2                            2
## S230                            2                            2
## S232                            2                            2
## S233                            2                            2
## S236                            1                            1
## S235                            2                            1
## S240                            2                            2
## S239                            2                            1
## S234                            1                            2
## S231                            2                            2
## S243                            2                            2
## S228                            1                            1
## S238                            2                            1
## S229                            2                            2
## S242                            2                            2
## S237                            2                            2
## S260                            2                            2
## S257                            1                            1
## S258                            2                            2
## S249                            2                            1
## S253                            1                            2
## S263                            2                            2
## S252                            1                            1
## S255                            2                            2
## S254                            2                            2
## S261                            1                            1
## S262                            1                            1
## S251                            2                            2
## S250                            2                            2
## S259                            2                            2
## S256                            1                            1
## S284                            1                            1
## S283                            1                            2
## S273                            1                            1
## S285                            1                            1
## S272                            1                           NA
## S274                            2                            1
## S281                            1                            1
## S276                            1                            2
## S275                            1                            1
## S280                            2                            1
## S282                            1                            1
## S270                            1                            1
## S269                            1                            1
## S278                            1                            1
## S279                           NA                           NA
## S271                            1                            1
## S277                            1                            1
## S298                            2                            2
## S308                            1                            1
## S299                            1                            1
## S302                            2                            2
## S307                            2                            1
## S291                            1                            1
## S297                            1                            1
## S296                            2                            1
## S292                            1                            1
## S304                            2                            2
## S301                            1                            1
## S305                            1                            2
## S294                            1                            1
## S295                            1                            1
## S303                            1                            2
## S306                            2                            1
## S300                            1                            1
## S293                            1                            2
## S316                           NA                           NA
## S319                            1                            2
## S317                            1                            1
## S318                            1                            1
## S320                            2                            2
## S315                            2                            1
## S334                            2                            2
## S324                            2                            1
## S325                            2                            2
## S328                            2                            1
## S327                            2                            1
## S323                            2                            2
## S336                            1                            1
## S333                            2                            2
## S332                            2                            1
## S331                            2                            1
## S329                            1                            2
## S326                            2                            1
## S338                            1                            1
## S335                            2                            2
## S337                            1                            1
## S330                            2                            1
## S091                            2                            1
## S075                            2                            1
## S074                            2                            1
## S088                            2                            1
## S082                            2                            2
## S083                            1                            2
## S086                            2                            2
## S087                            1                            1
## S080                            2                            1
## S078                            2                            1
## S085                            2                            1
## S084                            2                            2
## S076                            2                            2
## S081                            2                            1
## S077                            2                            1
## S089                            2                            1
## S090                            1                            1
## S079                            2                            2
## S113                            2                            2
## S101                            2                            1
## S099                            1                            1
## S111                            2                            2
## S114                            2                            2
## S102                            2                            2
## S098                            2                            1
## S100                            1                            1
## S106                            2                            2
## S103                            2                            1
## S110                            2                            2
## S107                            1                            1
## S109                            2                            1
## S112                            2                            2
## S105                            2                            1
## S104                            2                            1
## S108                            2                            2
## S097                            2                            2
## S129                            2                            2
## S128                            2                            1
## S120                            2                            2
## S136                            2                            2
## S122                            2                            2
## S124                            2                            1
## S127                            1                            2
## S126                            1                            1
## S134                            2                            2
## S125                            1                            1
## S132                            2                            2
## S121                            2                            2
## S123                            2                            1
## S130                            2                            2
## S135                            2                            2
## S131                            2                            2
## S119                            1                            1
## S133                            2                            2
## S154                            2                            2
## S156                            2                            2
## S143                            2                            2
## S152                            2                            2
## S146                            2                            2
## S142                            2                            2
## S141                            2                            1
## S145                            1                            1
## S148                            1                            2
## S144                            2                            2
## S140                            2                            1
## S151                            2                            2
## S147                            2                            1
## S149                            2                            2
## S155                            1                            2
## S150                            2                            2
## S153                            2                            1
## S160                            2                            2
## S159                            2                            2
## S165                            1                            1
## S166                            1                            2
## S169                            1                            1
## S164                            2                            1
## S157                            2                            1
## S163                            1                            1
## S170                            1                            1
## S167                            2                            1
## S161                            2                            2
## S168                            1                            1
## S158                            2                            2
## S171                            2                            2
## S162                            1                            1
## S179                            1                            2
## S182                            2                            1
## S183                            1                            2
## S187                            1                            2
## S184                            1                            1
## S178                            2                            2
## S186                            2                            1
## S181                            1                            1
## S177                            1                            2
## S188                            1                            1
## S180                            2                            1
## S189                            1                            1
## S201                            1                            1
## S198                            2                            1
## S197                            1                            1
## S194                            1                            1
## S195                            2                            1
## S202                            2                            2
## S199                            2                            2
## S204                            2                            1
## S203                            1                            1
## S200                            2                            2
## S196                            2                            2
## S208                            2                           NA
## S209                            2                            1
## S216                            2                            2
## S214                            2                            1
## S218                            2                            1
## S217                            2                            2
## S223                            1                            1
## S212                            2                            2
## S210                            1                            2
## S220                            2                            1
## S222                            1                            1
## S211                            2                            1
## S221                            1                            1
## S215                            2                            1
## S219                            2                            2
## S213                            1                            1
##      tModelExtendTableGeometric3b tModelExtendTableGeometric2a
## S055                            1                            1
## S058                            2                            1
## S053                            1                            1
## S061                            1                            1
## S063                            2                            1
## S066                            2                            1
## S062                            2                            1
## S054                            2                            1
## S057                            1                            2
## S060                            1                            2
## S067                            1                            1
## S056                            2                            2
## S059                            1                            2
## S064                            1                            1
## S065                            2                            1
## S068                            1                            1
## S052                            1                            1
## S241                            1                            1
## S230                            1                            2
## S232                            2                            2
## S233                            1                            2
## S236                            1                            1
## S235                            1                            1
## S240                            1                            1
## S239                            2                            2
## S234                            1                            1
## S231                            2                            2
## S243                            1                            1
## S228                            1                            1
## S238                            2                            1
## S229                            2                            1
## S242                            1                            2
## S237                            2                            2
## S260                            1                            2
## S257                            1                            1
## S258                            1                            2
## S249                            1                            1
## S253                            1                            1
## S263                            1                            1
## S252                            1                            1
## S255                            1                            2
## S254                            1                            2
## S261                            2                            1
## S262                            2                            1
## S251                            1                            2
## S250                            1                            2
## S259                            2                            2
## S256                            1                            1
## S284                            1                            1
## S283                            1                            1
## S273                            1                            1
## S285                            1                            2
## S272                           NA                           NA
## S274                            1                            1
## S281                           NA                           NA
## S276                           NA                           NA
## S275                           NA                           NA
## S280                            2                            1
## S282                           NA                           NA
## S270                            1                            1
## S269                           NA                           NA
## S278                            1                            1
## S279                           NA                           NA
## S271                            1                            2
## S277                            1                            1
## S298                            1                            1
## S308                            1                            1
## S299                            1                            1
## S302                            1                            2
## S307                            1                            2
## S291                            1                            2
## S297                            1                            2
## S296                            1                            2
## S292                            1                            1
## S304                            1                            1
## S301                            1                            1
## S305                            1                            2
## S294                            1                            1
## S295                            1                            1
## S303                            1                            2
## S306                            1                            1
## S300                            1                            1
## S293                            1                            1
## S316                            2                            2
## S319                            1                            1
## S317                            1                            2
## S318                            1                            1
## S320                            2                            2
## S315                            1                            1
## S334                            1                            1
## S324                            1                            1
## S325                            1                            2
## S328                            1                            1
## S327                            1                            1
## S323                            2                            2
## S336                            1                            1
## S333                            2                            2
## S332                            1                            2
## S331                            1                            1
## S329                            2                            1
## S326                            1                            1
## S338                            1                            2
## S335                            1                            1
## S337                            2                            1
## S330                            2                            1
## S091                            1                            1
## S075                            2                            2
## S074                            1                            1
## S088                            1                            2
## S082                            1                            2
## S083                            2                            1
## S086                            1                            1
## S087                            1                            2
## S080                            2                            1
## S078                            1                            2
## S085                            1                            2
## S084                            1                            1
## S076                            2                            1
## S081                            1                            1
## S077                            1                            1
## S089                            1                            1
## S090                            1                            2
## S079                            1                            1
## S113                            1                            1
## S101                            1                            1
## S099                            1                            1
## S111                            1                            1
## S114                            2                            2
## S102                            1                            2
## S098                            1                            2
## S100                            1                            1
## S106                            2                            2
## S103                            1                            2
## S110                            1                            2
## S107                            2                            2
## S109                            1                            2
## S112                            1                            1
## S105                            1                            1
## S104                            1                            1
## S108                            1                            1
## S097                            2                            2
## S129                            1                            2
## S128                            1                            1
## S120                            2                            2
## S136                            1                            1
## S122                            1                            1
## S124                            1                            1
## S127                            2                            2
## S126                            1                            1
## S134                            1                            1
## S125                            1                            1
## S132                            2                            1
## S121                            2                            2
## S123                            2                            2
## S130                            2                            2
## S135                            1                            2
## S131                            1                            2
## S119                            2                            1
## S133                            2                            2
## S154                            2                            2
## S156                            2                            1
## S143                            1                            1
## S152                            1                            2
## S146                            2                            2
## S142                            1                            1
## S141                            2                            1
## S145                            1                            1
## S148                            2                            1
## S144                            2                            2
## S140                            2                            2
## S151                            1                            2
## S147                            2                            2
## S149                            1                            2
## S155                            1                            1
## S150                            1                            1
## S153                            1                            1
## S160                            2                            2
## S159                            1                            1
## S165                            1                            1
## S166                            1                            1
## S169                            1                            1
## S164                            1                            1
## S157                            1                            1
## S163                            1                            1
## S170                            1                            1
## S167                            1                            1
## S161                            1                            1
## S168                            1                            1
## S158                            1                            1
## S171                            1                            1
## S162                            1                            2
## S179                            1                            2
## S182                            1                            1
## S183                            1                            2
## S187                            1                            1
## S184                            1                            1
## S178                            1                            1
## S186                            1                            1
## S181                            1                            1
## S177                            1                            2
## S188                            1                            1
## S180                            1                            1
## S189                            1                            1
## S201                            1                            1
## S198                            1                            1
## S197                            2                            1
## S194                            2                            1
## S195                            1                            1
## S202                            2                            2
## S199                            1                            1
## S204                            1                            2
## S203                            1                            1
## S200                            1                            1
## S196                            1                            2
## S208                            2                            1
## S209                            1                            2
## S216                            2                            2
## S214                            1                            2
## S218                            1                            2
## S217                            1                            1
## S223                            2                            1
## S212                            1                            1
## S210                            1                            2
## S220                            1                            1
## S222                            1                            2
## S211                            1                            1
## S221                            2                            2
## S215                            1                            2
## S219                            1                            1
## S213                            1                            1
##      tModelExtendTableGeometric2b tTableExtendGeometric1a
## S055                            1                       1
## S058                            2                       1
## S053                            2                       1
## S061                            1                       1
## S063                            1                       2
## S066                            1                       2
## S062                            2                       1
## S054                            2                       2
## S057                            2                       2
## S060                            2                       2
## S067                            1                       1
## S056                            2                       1
## S059                            1                       1
## S064                            2                       1
## S065                            1                       1
## S068                            2                       2
## S052                            2                      NA
## S241                            2                       2
## S230                            2                       1
## S232                            2                       2
## S233                            2                       2
## S236                            2                       1
## S235                            1                       2
## S240                            1                       1
## S239                            2                       1
## S234                            2                       2
## S231                            2                       2
## S243                            1                       2
## S228                            2                       1
## S238                            1                       1
## S229                            2                       2
## S242                            2                       1
## S237                            2                       2
## S260                            2                       1
## S257                            2                       2
## S258                            2                       2
## S249                            1                       2
## S253                            2                       2
## S263                            2                       2
## S252                            1                       1
## S255                            2                       1
## S254                            2                       2
## S261                            1                       2
## S262                            1                       2
## S251                            2                       2
## S250                            1                       2
## S259                            2                       2
## S256                            1                       1
## S284                            1                       1
## S283                            1                       1
## S273                            1                       1
## S285                            1                       1
## S272                           NA                       1
## S274                            2                       1
## S281                            1                       1
## S276                           NA                       2
## S275                            1                       1
## S280                            1                       2
## S282                           NA                       1
## S270                            2                      NA
## S269                            1                       2
## S278                            1                       1
## S279                           NA                      NA
## S271                            1                      NA
## S277                            1                       1
## S298                            2                      NA
## S308                            1                       1
## S299                            1                       2
## S302                            2                       2
## S307                            2                       1
## S291                            1                       1
## S297                            2                       1
## S296                            1                       2
## S292                            1                       2
## S304                            2                      NA
## S301                            2                       1
## S305                            2                       2
## S294                            1                       2
## S295                            1                       2
## S303                            2                       1
## S306                            1                       1
## S300                            2                       2
## S293                            1                       1
## S316                            2                      NA
## S319                            1                       1
## S317                            1                       2
## S318                            2                       1
## S320                            2                       2
## S315                            2                       1
## S334                            2                       2
## S324                            2                       1
## S325                            2                       2
## S328                            1                       2
## S327                            1                       1
## S323                            2                       2
## S336                            1                       1
## S333                            2                       2
## S332                            2                       2
## S331                            2                       1
## S329                            1                       1
## S326                            2                      NA
## S338                            2                       2
## S335                            2                       2
## S337                            2                       1
## S330                            2                       2
## S091                            2                       2
## S075                            2                       1
## S074                            2                       2
## S088                            1                       2
## S082                            1                       2
## S083                            2                       1
## S086                            2                       2
## S087                            2                       1
## S080                            2                       1
## S078                            1                       1
## S085                            2                       2
## S084                            2                       2
## S076                            2                       2
## S081                            2                       1
## S077                            2                       1
## S089                            2                       1
## S090                            2                       2
## S079                            2                       1
## S113                            2                       2
## S101                            2                       1
## S099                            1                       2
## S111                            2                       1
## S114                            2                       2
## S102                            2                       2
## S098                            1                       1
## S100                            2                       1
## S106                            2                       2
## S103                            2                       1
## S110                            2                       2
## S107                            2                       1
## S109                            2                       1
## S112                            2                       1
## S105                            2                       2
## S104                            2                       1
## S108                            2                       2
## S097                            2                       1
## S129                            2                       2
## S128                            2                       2
## S120                            2                       2
## S136                            2                       2
## S122                            2                       2
## S124                            2                       2
## S127                            2                       2
## S126                            1                       1
## S134                            2                       2
## S125                            2                       2
## S132                            1                       1
## S121                            2                       2
## S123                            2                       2
## S130                            2                       2
## S135                            2                       1
## S131                            2                       2
## S119                            1                       1
## S133                            2                       1
## S154                            2                       2
## S156                            1                       2
## S143                            2                       2
## S152                            2                       2
## S146                            2                       1
## S142                            1                       2
## S141                            2                       2
## S145                            1                       2
## S148                            2                       2
## S144                            2                       2
## S140                            2                      NA
## S151                            2                       2
## S147                            2                       2
## S149                            2                       2
## S155                            2                       1
## S150                            2                       2
## S153                            2                       2
## S160                            2                       2
## S159                            2                       2
## S165                            1                       2
## S166                            1                       2
## S169                            1                       2
## S164                            2                       2
## S157                            2                       1
## S163                            1                       2
## S170                            2                       2
## S167                            2                       1
## S161                            2                       2
## S168                            2                       1
## S158                            2                       2
## S171                            1                       1
## S162                            1                       1
## S179                            2                       2
## S182                            2                       1
## S183                            2                       2
## S187                            2                       1
## S184                            1                       1
## S178                            2                       2
## S186                            2                       2
## S181                            2                       1
## S177                            1                       1
## S188                            1                       1
## S180                            2                       2
## S189                            2                       1
## S201                            2                       2
## S198                            1                       1
## S197                            1                       1
## S194                            1                       1
## S195                            1                       2
## S202                            2                       1
## S199                            2                       2
## S204                            2                       2
## S203                            2                       1
## S200                            2                       2
## S196                            2                       1
## S208                            2                      NA
## S209                            2                       2
## S216                            2                       2
## S214                            2                       1
## S218                            2                       1
## S217                            2                       1
## S223                            1                       1
## S212                            1                       2
## S210                            2                       2
## S220                            1                       2
## S222                            2                       1
## S211                            1                       2
## S221                            2                       2
## S215                            2                       1
## S219                            2                       1
## S213                            1                       1
##      tTableExtendGeometric1b tTableExtendGeometric3a
## S055                       1                       1
## S058                       1                       1
## S053                       1                       1
## S061                       1                       1
## S063                       1                       1
## S066                       1                       1
## S062                       1                       1
## S054                       2                       2
## S057                       1                       1
## S060                       2                       1
## S067                       1                       1
## S056                       1                       2
## S059                       1                       1
## S064                       1                       2
## S065                       2                       2
## S068                       2                       2
## S052                      NA                       1
## S241                       2                       1
## S230                       1                       1
## S232                       1                       2
## S233                       1                       2
## S236                       1                       1
## S235                       2                       1
## S240                       1                       1
## S239                       2                       1
## S234                       2                       2
## S231                       1                       1
## S243                       2                       1
## S228                       1                       1
## S238                       1                       1
## S229                       2                       1
## S242                       1                       2
## S237                       2                       1
## S260                       2                       2
## S257                       1                       1
## S258                       1                       1
## S249                       1                       1
## S253                       1                       1
## S263                       2                       2
## S252                       1                       1
## S255                       1                       1
## S254                       2                       2
## S261                       1                       1
## S262                       1                       1
## S251                       1                       2
## S250                       1                       1
## S259                       1                       1
## S256                       1                       1
## S284                       1                       1
## S283                       1                       1
## S273                       1                       1
## S285                       1                       1
## S272                       1                      NA
## S274                       1                       1
## S281                       1                       1
## S276                       2                       2
## S275                       1                      NA
## S280                       1                       1
## S282                      NA                       1
## S270                      NA                       2
## S269                       2                       2
## S278                       1                       1
## S279                      NA                      NA
## S271                      NA                      NA
## S277                       1                       1
## S298                      NA                       1
## S308                       1                       1
## S299                       1                       1
## S302                       2                       2
## S307                       1                       1
## S291                       1                       1
## S297                       1                       1
## S296                       1                       2
## S292                       2                       1
## S304                      NA                       2
## S301                       2                       2
## S305                       2                       2
## S294                       1                       1
## S295                       2                       1
## S303                       2                       2
## S306                       2                       1
## S300                       1                       2
## S293                       1                       1
## S316                      NA                       2
## S319                       1                       1
## S317                       2                       2
## S318                       1                       1
## S320                       1                       1
## S315                       1                       2
## S334                       1                       2
## S324                       2                       1
## S325                       2                       2
## S328                       2                       2
## S327                       2                       1
## S323                       2                       1
## S336                       1                       1
## S333                       2                       1
## S332                       1                       1
## S331                       1                       1
## S329                       1                       1
## S326                      NA                       1
## S338                       1                       1
## S335                       2                       1
## S337                       1                       1
## S330                       2                       2
## S091                       2                       1
## S075                       1                       1
## S074                       2                       1
## S088                       2                       1
## S082                       2                       1
## S083                       1                       1
## S086                       1                       1
## S087                       1                       1
## S080                       1                       1
## S078                       1                       1
## S085                       2                       2
## S084                       1                       2
## S076                       1                       1
## S081                       1                       1
## S077                       1                       1
## S089                       1                       1
## S090                       1                       2
## S079                       1                       2
## S113                       2                       2
## S101                       2                       1
## S099                       2                       1
## S111                       1                       1
## S114                       2                       1
## S102                       2                       2
## S098                       1                       1
## S100                       1                       2
## S106                       2                       1
## S103                      NA                       2
## S110                       1                       2
## S107                       1                       1
## S109                       1                       2
## S112                       2                       2
## S105                       2                       1
## S104                       1                       2
## S108                       2                       1
## S097                       1                       2
## S129                       2                       1
## S128                       2                       1
## S120                       2                       1
## S136                       2                       2
## S122                       2                       1
## S124                       2                       1
## S127                       2                       2
## S126                       1                       2
## S134                       2                       1
## S125                       2                       1
## S132                       2                       1
## S121                       2                       1
## S123                       2                       1
## S130                       2                       1
## S135                       1                       1
## S131                       1                       1
## S119                       1                       1
## S133                       2                       2
## S154                       2                       2
## S156                       2                       1
## S143                       2                       1
## S152                       2                       1
## S146                       1                       2
## S142                       1                       1
## S141                       2                       1
## S145                       1                       1
## S148                       2                       2
## S144                       2                       2
## S140                      NA                       1
## S151                       2                       1
## S147                       2                       2
## S149                       1                       1
## S155                       1                       2
## S150                       2                       2
## S153                       2                       2
## S160                       1                       2
## S159                       2                       2
## S165                       2                       1
## S166                       2                       2
## S169                       1                       2
## S164                       1                       1
## S157                       1                       1
## S163                       2                       1
## S170                       1                       2
## S167                       1                       1
## S161                       1                       2
## S168                       1                       1
## S158                       2                       2
## S171                       1                       1
## S162                       1                       1
## S179                       2                       1
## S182                       2                       2
## S183                       1                       1
## S187                       1                       1
## S184                       1                       1
## S178                       1                       1
## S186                       1                       1
## S181                       1                       1
## S177                       1                       1
## S188                       1                       1
## S180                       2                       2
## S189                       1                       1
## S201                       1                       1
## S198                       1                       2
## S197                       1                       1
## S194                       1                       1
## S195                       1                       1
## S202                       1                       2
## S199                       1                       1
## S204                       1                       1
## S203                       1                       1
## S200                       1                       2
## S196                       1                       2
## S208                      NA                       2
## S209                       1                       1
## S216                       2                       1
## S214                       1                       1
## S218                       1                       1
## S217                       1                       1
## S223                       1                       2
## S212                       1                       1
## S210                       1                       2
## S220                       2                       1
## S222                       1                       1
## S211                       2                       2
## S221                       2                       1
## S215                       1                       2
## S219                       1                       1
## S213                       1                       2
##      tTableExtendGeometric3b tTableExtendGeometric2a
## S055                       1                       1
## S058                       2                       1
## S053                       2                       1
## S061                       2                       1
## S063                       1                       1
## S066                       2                       2
## S062                       1                       1
## S054                       2                       2
## S057                       2                       1
## S060                       2                       2
## S067                       1                       1
## S056                       2                       2
## S059                       1                       1
## S064                       2                       1
## S065                       2                       2
## S068                       2                       1
## S052                       2                       2
## S241                       2                       1
## S230                       1                       1
## S232                       2                       2
## S233                       2                       1
## S236                       1                       1
## S235                       1                       1
## S240                       2                       1
## S239                       2                       2
## S234                       2                       1
## S231                       2                       1
## S243                       1                       2
## S228                       2                       2
## S238                       1                       1
## S229                       2                       1
## S242                       1                       1
## S237                       2                       1
## S260                       2                       1
## S257                       2                       1
## S258                       2                       1
## S249                       1                       1
## S253                       2                       1
## S263                       2                       1
## S252                       2                       1
## S255                       2                       1
## S254                       2                       2
## S261                       2                       1
## S262                       2                       1
## S251                       2                       1
## S250                       2                       1
## S259                       2                       1
## S256                       2                       1
## S284                       2                       1
## S283                       2                       1
## S273                       2                       1
## S285                       1                       1
## S272                      NA                       1
## S274                       1                       2
## S281                       1                       1
## S276                       2                       1
## S275                      NA                       1
## S280                       1                       2
## S282                      NA                       1
## S270                       2                       1
## S269                       2                       1
## S278                       1                       1
## S279                      NA                       1
## S271                      NA                      NA
## S277                       2                       1
## S298                       1                       1
## S308                       2                       1
## S299                       1                       1
## S302                       2                       2
## S307                       1                       1
## S291                       1                       1
## S297                       2                       1
## S296                       2                       1
## S292                       1                       1
## S304                       2                       1
## S301                       2                       1
## S305                       1                       1
## S294                       1                       1
## S295                       2                       1
## S303                       1                       1
## S306                       2                       1
## S300                       2                       1
## S293                       1                       1
## S316                       2                       1
## S319                       2                       1
## S317                       2                       1
## S318                       2                       1
## S320                       1                       1
## S315                       1                       1
## S334                       1                       2
## S324                       2                       1
## S325                       2                       1
## S328                       2                       2
## S327                       2                       1
## S323                       2                       1
## S336                       1                       1
## S333                       2                       2
## S332                       1                       2
## S331                       1                       1
## S329                       2                       1
## S326                      NA                      NA
## S338                       1                       1
## S335                       2                       1
## S337                       1                       1
## S330                       2                       1
## S091                       2                       1
## S075                       2                       2
## S074                       2                       2
## S088                       2                       2
## S082                       2                       1
## S083                       1                       1
## S086                       2                       1
## S087                       1                       1
## S080                       1                       1
## S078                       2                       1
## S085                       2                       1
## S084                       1                       1
## S076                       1                       2
## S081                       2                       1
## S077                       2                       1
## S089                       2                       2
## S090                       2                       1
## S079                       1                       1
## S113                       2                       2
## S101                       2                       1
## S099                       2                       1
## S111                       1                       1
## S114                       2                       2
## S102                       2                       2
## S098                       1                       1
## S100                       2                       1
## S106                       2                       2
## S103                       2                       2
## S110                       2                       1
## S107                       1                       1
## S109                       2                       1
## S112                       2                       1
## S105                       1                       1
## S104                       2                       1
## S108                       2                       2
## S097                       2                       1
## S129                       1                       2
## S128                       1                       2
## S120                       2                       1
## S136                       2                       2
## S122                       2                       1
## S124                       2                       1
## S127                       2                       2
## S126                       2                       1
## S134                       2                       1
## S125                       2                       1
## S132                       2                       2
## S121                       2                       1
## S123                       2                       2
## S130                       2                       2
## S135                       1                       1
## S131                       2                       1
## S119                       2                       1
## S133                       2                       2
## S154                       2                       2
## S156                       2                       1
## S143                       1                       1
## S152                       2                       1
## S146                       2                       1
## S142                       2                       1
## S141                       2                       1
## S145                       1                       1
## S148                       2                       2
## S144                       2                       2
## S140                       2                       1
## S151                       2                       1
## S147                       2                       1
## S149                       2                       2
## S155                       2                       1
## S150                       2                       1
## S153                       2                       1
## S160                       1                       2
## S159                       2                       1
## S165                       1                       1
## S166                       2                       1
## S169                       2                       1
## S164                       2                       2
## S157                       2                       1
## S163                       2                       1
## S170                       2                       1
## S167                       2                       1
## S161                       2                       1
## S168                       1                       1
## S158                       2                       1
## S171                       1                       1
## S162                       1                       1
## S179                       2                       1
## S182                       2                       2
## S183                       2                       1
## S187                       1                       1
## S184                       1                       1
## S178                       1                       1
## S186                       2                       2
## S181                       2                       1
## S177                       2                       1
## S188                       2                       1
## S180                       1                       2
## S189                       2                       1
## S201                       1                       1
## S198                       2                       1
## S197                       2                       1
## S194                       1                       1
## S195                       1                       1
## S202                       1                       1
## S199                       1                       2
## S204                       2                       1
## S203                       1                       1
## S200                       2                       1
## S196                       2                       1
## S208                      NA                      NA
## S209                       2                       1
## S216                       1                       1
## S214                       1                       1
## S218                       2                       2
## S217                       1                       1
## S223                       2                       1
## S212                       2                       1
## S210                       2                       1
## S220                       1                       2
## S222                       2                       1
## S211                       2                       1
## S221                       1                       1
## S215                       2                       2
## S219                       2                       1
## S213                       1                       1
##      tTableExtendGeometric2b
## S055                       2
## S058                       1
## S053                       1
## S061                       1
## S063                       1
## S066                       2
## S062                       1
## S054                       2
## S057                       2
## S060                       2
## S067                       1
## S056                       1
## S059                       1
## S064                       2
## S065                       2
## S068                       1
## S052                       2
## S241                       1
## S230                       2
## S232                       1
## S233                       1
## S236                       1
## S235                       1
## S240                       2
## S239                       2
## S234                       1
## S231                       2
## S243                       2
## S228                       1
## S238                       2
## S229                       1
## S242                       2
## S237                       2
## S260                       1
## S257                       1
## S258                       1
## S249                       1
## S253                       2
## S263                       1
## S252                       2
## S255                       2
## S254                       1
## S261                       1
## S262                       1
## S251                       1
## S250                       1
## S259                       1
## S256                       1
## S284                       1
## S283                       1
## S273                       1
## S285                       1
## S272                       1
## S274                       1
## S281                       2
## S276                       1
## S275                       1
## S280                       1
## S282                       1
## S270                       1
## S269                       1
## S278                       1
## S279                       1
## S271                      NA
## S277                       2
## S298                       1
## S308                       1
## S299                       1
## S302                       2
## S307                       1
## S291                       1
## S297                       2
## S296                       1
## S292                       1
## S304                       1
## S301                       1
## S305                       1
## S294                       2
## S295                       2
## S303                       2
## S306                       1
## S300                       2
## S293                       1
## S316                       1
## S319                       1
## S317                       1
## S318                       1
## S320                       2
## S315                       1
## S334                       1
## S324                       1
## S325                       2
## S328                       2
## S327                       1
## S323                       1
## S336                       1
## S333                       2
## S332                       2
## S331                       1
## S329                       2
## S326                      NA
## S338                       2
## S335                       1
## S337                       1
## S330                       2
## S091                       2
## S075                       1
## S074                       2
## S088                       1
## S082                       1
## S083                       1
## S086                       2
## S087                       2
## S080                       2
## S078                       1
## S085                       1
## S084                       1
## S076                       2
## S081                       1
## S077                       1
## S089                       1
## S090                       1
## S079                       1
## S113                       2
## S101                       1
## S099                       1
## S111                       1
## S114                       2
## S102                       2
## S098                       1
## S100                       2
## S106                       2
## S103                       2
## S110                       2
## S107                       1
## S109                       1
## S112                       2
## S105                       1
## S104                       1
## S108                       2
## S097                       1
## S129                       2
## S128                       2
## S120                       2
## S136                       2
## S122                       2
## S124                       1
## S127                       2
## S126                       1
## S134                       1
## S125                       1
## S132                       2
## S121                       2
## S123                       2
## S130                       2
## S135                       2
## S131                       1
## S119                       1
## S133                       2
## S154                       2
## S156                       2
## S143                       1
## S152                       2
## S146                       1
## S142                       2
## S141                       2
## S145                       1
## S148                       2
## S144                       2
## S140                       1
## S151                       1
## S147                       2
## S149                       2
## S155                       1
## S150                       1
## S153                       2
## S160                       2
## S159                       2
## S165                       2
## S166                       1
## S169                       2
## S164                       1
## S157                       1
## S163                       1
## S170                       2
## S167                       2
## S161                       1
## S168                       1
## S158                       2
## S171                       1
## S162                       1
## S179                       1
## S182                       2
## S183                       1
## S187                       1
## S184                       1
## S178                       2
## S186                       2
## S181                       1
## S177                       1
## S188                       1
## S180                       2
## S189                       2
## S201                       2
## S198                       1
## S197                       1
## S194                       1
## S195                       1
## S202                       1
## S199                       2
## S204                       1
## S203                       1
## S200                       1
## S196                       1
## S208                      NA
## S209                       2
## S216                       2
## S214                       1
## S218                       2
## S217                       1
## S223                       1
## S212                       1
## S210                       1
## S220                       1
## S222                      NA
## S211                       1
## S221                       2
## S215                       2
## S219                       1
## S213                       1
## Mark columns of table corresponding to tasks
first.task <- 9
last.task <- ncol(miniACED.data)
## Code key for numeric values
t.vals <- c("No","Yes")

Setup new Student

## Pick a student, we might normally iterate over this.
Student.row <- 1

## Setup for student in sample
## Create Student Model from Proficiency Model
Student.SM <- CopyNetworks(profModel,"Student")
Student.SMvars <- NetworkAllNodes(Student.SM)
CompileNetwork(Student.SM)

## Initialize history list
prior <- NodeBeliefs(Student.SMvars$SolveGeometricProblems)
Student.History <- matrix(prior,1,3)
row.names(Student.History) <- "*Baseline*"
colnames(Student.History) <- names(prior)

Processing Loop

## Now loop over tasks
for (itask in first.task:last.task) {
  
  ## Look up the EM for the task, and adjoin it.
  tid <- names(miniACED.data)[itask]
  EMnet <- ReadNetworks(file.path("..","Nets",
                        paste(EMtable[tid,"EM"],"dne",sep=".")),
                        session=sess)
  obs <- AdjoinNetwork(Student.SM,EMnet)
  CompileNetwork(Student.SM)

  ## Add the evidence
  t.val <- t.vals[miniACED.data[Student.row,itask]] #Decode integer
  NodeFinding(obs[[1]]) <- t.val
## Update the history
  post <- NodeBeliefs(Student.SMvars$SolveGeometricProblems)
  Student.History <- rbind(Student.History,new=post)
  rownames(Student.History)[nrow(Student.History)] <- paste(tid,t.val,sep="=")

  ## Cleanup, Delete EM and Absob Observables
  DeleteNetwork(EMnet)
  AbsorbNodes(obs) # Still broken
}
## Creating node list.
## Absorbing 1 nodes.
## First node address f72f1100.
## Its name is isCorrect.
## Absorbed.
## Creating node list.
## Absorbing 1 nodes.
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Weight of Evidence

  • Good (1985)

  • \(H\) is a binary hypothesis, e.g., Proficiency > medium
  • \(E\) is evidence for that hypothesis
  • Weight of Evidence of \(E\) for \(H\) (WOE) is \[ W(H:E) = \log\frac{\Pr(E|H)}{\Pr(E|\overline{H})} = \log \frac{\Pr(H|E)}{\Pr(\overline{H}|E)} - \log \frac{\Pr(H)}{\Pr(\overline{H}} \]

Conditional weight of evidence

  • Observe two different pieces of evidence, \(E_1\) and \(E_2\).
  • Conditional Weight of Evidence is \[ W(H:E_2|E_1) = \log \frac{\Pr(E_2|H,E_1)}{\Pr(E_2|\overline{H},E_1)} \]
  • Nice Additive Properties \[ W(H:E_1, E_2) = W(H:E_1) + W(H: E_2|E_1)\]
  • Order Sensitive:
    • Earlier terms have higher WOE
    • Total WOE is always the same
  • WOE Balance Sheet (Madigan, Mosurski & Almond, 1997)

Weight Of Evidence Balance Sheet

Weight of Evidences can be calculated by differencing the log values in the history.

Student.History
##                                         High      Medium       Low
## *Baseline*                      3.333333e-01 0.333333313 0.3333334
## tCommonRatio1a=No               1.238987e-01 0.261908591 0.6141927
## tCommonRatio1b=No               3.842749e-02 0.211766571 0.7498059
## tCommonRatio3a=Yes              1.205092e-01 0.270862073 0.6086287
## tCommonRatio3b=No               9.013028e-02 0.259188741 0.6506810
## tCommonRatio2a=No               4.954598e-02 0.233125374 0.7173287
## tCommonRatio2b=No               3.490408e-02 0.216613680 0.7484822
## tExamplesGeometric1a=No         1.005295e-02 0.145315900 0.8446311
## tExamplesGeometric1b=No         5.908299e-03 0.127308875 0.8667828
## tExamplesGeometric3a=No         5.698630e-03 0.126277551 0.8680238
## tExamplesGeometric3b=No         5.543364e-03 0.125432283 0.8690243
## tExamplesGeometric2a=No         5.186467e-03 0.123196520 0.8716170
## tExamplesGeometric2b=No         4.986964e-03 0.121875346 0.8731377
## tExtendGeometric1a=No           6.572015e-04 0.049339782 0.9500030
## tExtendGeometric1b=No           1.208575e-04 0.032974172 0.9669050
## tExtendGeometric3a=Yes          6.723817e-04 0.054701813 0.9446258
## tExtendGeometric3b=No           4.459546e-04 0.049828812 0.9497252
## tExtendGeometric2a=No           1.896276e-04 0.040176421 0.9596339
## tExtendGeometric2b=No           1.098957e-04 0.034829482 0.9650606
## tModelExtendTableGeometric1a=No 7.804838e-06 0.015482896 0.9845093
## tModelExtendTableGeometric1b=No 1.187362e-06 0.009638987 0.9903598
## tModelExtendTableGeometric3a=No 9.925629e-07 0.009404771 0.9905942
## tModelExtendTableGeometric3b=No 8.516319e-07 0.009189405 0.9908097
## tModelExtendTableGeometric2a=No 5.280224e-07 0.008351044 0.9916484
## tModelExtendTableGeometric2b=No 3.584744e-07 0.007693673 0.9923060
## tTableExtendGeometric1a=No      3.248774e-07 0.006830624 0.9931691
## tTableExtendGeometric1b=No      3.076568e-07 0.006449320 0.9935504
## tTableExtendGeometric3a=No      3.069094e-07 0.006432992 0.9935667
## tTableExtendGeometric3b=No      3.061927e-07 0.006417527 0.9935822
## tTableExtendGeometric2a=No      3.030247e-07 0.006352164 0.9936475
## tTableExtendGeometric2b=Yes     3.464628e-07 0.007213552 0.9927861
woeHist(Student.History,c("High","Medium"),"Low")
##               tCommonRatio1a=No               tCommonRatio1b=No 
##                     -50.2964166                     -27.4737650 
##              tCommonRatio3a=Yes               tCommonRatio3b=No 
##                      28.4908326                      -7.8382306 
##               tCommonRatio2a=No               tCommonRatio2b=No 
##                     -13.4290529                      -6.9176446 
##         tExamplesGeometric1a=No         tExamplesGeometric1b=No 
##                     -26.1690290                      -7.8046967 
##         tExamplesGeometric3a=No         tExamplesGeometric3b=No 
##                      -0.4685993                      -0.3805303 
##         tExamplesGeometric2a=No         tExamplesGeometric2b=No 
##                      -0.9976840                      -0.5931907 
##           tExtendGeometric1a=No           tExtendGeometric1b=No 
##                     -44.1031050                     -18.6839843 
##          tExtendGeometric3a=Yes           tExtendGeometric3b=No 
##                      23.3668646                      -4.4295518 
##           tExtendGeometric2a=No           tExtendGeometric2b=No 
##                      -9.9841460                      -6.5150052 
## tModelExtendTableGeometric1a=No tModelExtendTableGeometric1b=No 
##                     -36.1909340                     -20.8559402 
## tModelExtendTableGeometric3a=No tModelExtendTableGeometric3b=No 
##                      -1.0793572                      -1.0160879 
## tModelExtendTableGeometric2a=No tModelExtendTableGeometric2b=No 
##                      -4.1926906                      -3.5902171 
##      tTableExtendGeometric1a=No      tTableExtendGeometric1b=No 
##                      -5.2050450                      -2.5113118 
##      tTableExtendGeometric3a=No      tTableExtendGeometric3b=No 
##                      -0.1108048                      -0.1052084 
##      tTableExtendGeometric2a=No     tTableExtendGeometric2b=Yes 
##                      -0.4474560                       5.5604248

We can graph this as a balansh sheet.

woeBal(Student.History,c("High","Medium"),"Low",
       title=paste("Evidence Balance Sheet for ",                      
       rownames(miniACED.data)[Student.row]))

Stacked Bar Charts

These are like ordinary stacked bar charts, but offset at a given level.

stackedBars(t(Student.History[1:4,]),1,
           col=hsv(223/360,.2,0.15*(3:1)+.5) )

margins <- data.frame (
 Trouble=c(Novice=.19,Semester1=.24,Semester2=.28,Semseter3=.20,Semester4=.09),
 NDK=c(Novice=.01,Semester1=.09,Semester2=.35,Semseter3=.41,Semester4=.14),
 Model=c(Novice=.19,Semester1=.28,Semester2=.31,Semseter3=.18,Semester4=.04)
)

stackedBars(margins,3,
            main="Marginal Distributions for NetPASS skills",
            sub="Baseline at 3rd Semester level.",
            cex.names=.75, col=hsv(148/360,.2,0.10*(5:1)+.5))

Comparing multiple students

Compare one student to class average. Subgroup to full group Two groups to each other. Before to after.

margins.prior <- data.frame (
 Trouble=c(Novice=.19,Semester1=.24,Semester2=.28,Semseter3=.20,Semester4=.09),
 NDK=c(Novice=.01,Semester1=.09,Semester2=.35,Semseter3=.41,Semester4=.14),
 Model=c(Novice=.19,Semester1=.28,Semester2=.31,Semseter3=.18,Semester4=.04)
)

margins.post <- data.frame(
 Trouble=c(Novice=.03,Semester1=.15,Semester2=.39,Semseter3=.32,Semester4=.11),
 NDK=c(Novice=.00,Semester1=.03,Semester2=.28,Semseter3=.52,Semester4=.17),
 Model=c(Novice=.10,Semester1=.25,Semester2=.37,Semseter3=.23,Semester4=.05))

compareBars(margins.prior,margins.post,3,c("Prior","Post"),
            main="Margins before/after Medium Trouble Shooting Task",
            sub="Observables:  cfgCor=Medium, logCor=High, logEff=Medium",
            legend.loc = "topright",legend.cex=.1,
            cex.names=.75, col1=hsv(h=.1,s=.2*1:5-.1,alpha=1),
            col2=hsv(h=.6,s=.2*1:5-.1,alpha=1))

stopSession(sess)