## ----package, message=FALSE, warning=FALSE,include=TRUE-------------------------------------------
library(lme4)


## ----indata---------------------------------------------------------------------------------------
lsat <- read.table(file="C:/Users/cja/Dropbox/edps587/lectures/10 logreg/lsat6_long_data.txt", header=TRUE)
head(lsat, n=25)
tail(lsat, n=10)


## ----gauss----------------------------------------------------------------------------------------
rasch.quad <- glmer(y ~ -1 + i1 + i2 + i3 +i4 + i5 + (1 | id),data=lsat,family=binomial, nAGQ=10 )
summary(rasch.quad)


## ----laplace--------------------------------------------------------------------------------------
rasch.laplace <- glmer(y ~ -1 + i1 + i2 + i3 +i4 + i5 + (1 | id),data=lsat, family=binomial)
summary(rasch.laplace)


## -------------------------------------------------------------------------------------------------
lsat$ycorrect <- ifelse (lsat$y==0, 1, 0)

rasch2.quad <- glmer(ycorrect ~ -1 + i1 + i2 + i3 +i4 + i5 + (1 | id),data=lsat,family=binomial, nAGQ=10 )
summary(rasch2.quad)


## ----icc------------------------------------------------------------------------------------------
x <- seq(from=0, to=8, by=0.1)
theta<- x-4
item1 <-  exp(theta +2.73001)/(1 +exp(theta +2.73001))
item2 <-  exp(theta +0.99862)/(1 +exp(theta +0.99862))
item3 <-  exp(theta +0.23986)/(1 +exp(theta +0.23986))
item4 <-  exp(theta +1.30646)/(1 +exp(theta +1.30646))
item5 <-  exp(theta +2.09940)/(1 +exp(theta +2.09940))


plot(theta,item1, type='l', 
     col='blue', ylim=c(0,1),
     ylab='Probability Correct', 
     main='Item Characteristic Curves: Rasch (lsat6)')
lines(theta,item2,col='red')
lines(theta,item3,col='green')
lines(theta,item4,col='black')
lines(theta,item5,color='cyan')
abline(h=.5)