---
title: "IRT on crossword data"
author: "Shane Mueller"
date: "2/16/2021"
output: html_document
---

```{r }

options(max.print=200)
knitr::opts_chunk$set(echo = TRUE)

data <- read.csv("http://pages.mtu.edu/~shanem/psy5220/daily/Day10-11/crossword.csv")

qs <- read.csv("http://pages.mtu.edu/~shanem/psy5220/daily/Day10-11/answers.csv")


library(ltm)
responses <- data[,-(1:5)]
d <- descript(responses,chi.squared=F,n.print=100)
d
plot(d)
```


```{r}
m1 <- rasch(responses)

m1
BIC(m1)
plot(m1)

plot(m1,type="IIC")
plot(m1,type="IIC",items=0)

margins(m1)
plot(d,items=c(13,44))
```


```{r}

m2 <- ltm(responses~z1)
coef(m2)
BIC(m2)  #The smaller the better

par(mfrow=c(1,2))
plot(coef(m1)[,1],coef(m2)[,1],main="Difficulty")
plot(coef(m1)[,1],coef(m2)[,2],main="Discriminability")


anova(m1,m2)

plot(m2)
plot(m2,type="IIC")
plot(m2,type="IIC",items=0)
```

```{r}

m3 <- ltm(responses~z1+z2)
coef(m3)
BIC(m3)
```

```{r}
##compare intercept to model1 difficulty:
par(mfrow=c(1,3))
plot(coef(m1)[,1],coef(m3)[,1])
plot(coef(m1)[,1],coef(m3)[,2])
plot(coef(m1)[,1],coef(m3)[,3])


plot(coef(m2)[,2],coef(m3)[,2])
plot(coef(m2)[,2],coef(m3)[,3])

```