Bayesian Networks in Educational Assessment
Tutorial
Session III: Bayes Net with R
Duanli Yan, Diego Zapata, ETS
Russell Almond, FSU
2021 NCME Tutorial: Bayesian Networks in Educational Assessment
SESSION __ __ __ __ TOPIC __ __ __ __ __ __ __ __ __ __ __ __ __ __ PRESENTERS
Session 1 : Evidence Centered Design Diego Zapata Bayesian Networks
Session 2 : Bayes Net Applications Duanli Yan & ACED: ECD in Action Russell Almond
Session 3 : Bayes Nets with R Russell Almond & Duanli Yan
Session 4 : Refining Bayes Nets with Duanli Yan & Data Russell Almond
Too many parameters to comfortably elicit
Certain cases might be rare in population \(</span> <span style="color:#000000">Very High </span> <span style="color:#000000">on </span> <span style="color:#000000"> _Skill 1_ </span> <span style="color:#000000"> and </span> <span style="color:#000000">Very Low </span> <span style="color:#000000">on </span> <span style="color:#000000"> _Skill 2_ </span> <span style="color:#000000">\)
Want to capture intuition of experts on how skills interact to generate performace.
All input skills needed to solve problem
Bypass parameter for Skill j , q j
Slip probability \(overall\), q 0
Probability of correct outcome
NIDA/DINA
Single parent version
Map each level of parent state to “effective theta” on IRT \(N\(0\,1\)) scale,
Now plug into Samejima graded response model to get probability of outcome
Uses standard IRT parameters, “difficulty” and “discrimination”
DiBello--Normal model uses regression model rather than graded response
equally spaced normal quantiles
Introduce new parameter d inc _ _ as spread between difficulties in Samejima model
b i,Full _ = b_ j _ + d_ inc /2 b j,Partial _ = b_ j _ - d_ inc /2
Conditional probability table for _ d_ inc _ _ = 1 is then…
Effective theta scale is a logit scale corresponds to mean 0 SD 1 in a “standard” population.
Want the effective theta values to be equally spaced on this scale
Want the marginal distribution implied by the effective thetas to be uniform \(unit of the combination operator\)
What the effective theta transformation to be effectively invertible \(this is reason to add the 1\.7 to the IRT equation\).
Suppose variable has M states: 0,…,M-1
Want the midpoint of the interval going from probability m/M to \(m\+1\)/M .
Solution is to map state m onto
R code: qnorm\(\(1:M\)-.5)/M)