---
title: "Kappa, Lambda & Gamma Examples"
author: "Russell Almond"
date: "9/28/2021"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Language Testing Example

This is based on a made up language testing example by Bob Mislevey:

![Language Model](ILanguage.png)

### Reading

```{r}
Reading <- matrix(c(0.229,0.025,0.00,0.025,0.445,0.029,0,.040,0.207),3,3,byrow=TRUE)
Reading
```
Load the vcd library for Kappa statistic
```{r Load}
library(vcd)
gkLambda <- function (tab) {
  pmax <- max(apply(tab,1,sum))
  lambda <- (sum(diag(tab)) - pmax)/(sum(tab)-pmax)
  return(lambda)
}
```
```{r Kappa}
Kappa(Reading)
gkLambda(Reading)
```

```{r}
agreementplot(Reading)
```