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%\VignetteEngine{knitr::knitr}
%\VignetteIndexEntry{How to perform common IRT diagnostics}
\documentclass{article}
\begin{document}
<<setup, cache=FALSE, include=FALSE>>=
library(rpf)
library(ggplot2)
library(reshape2)
library(gridExtra)
@
\section{How to perform common IRT diagnostics}
Here's how to create an item characteristic curve plot for any 1
dimensional item. These are random item parameters so the curves
change every time the documentation is recreated.
<<fig.height=2.5>>=
plot.icc <- function(item, param, width=3) {
pm <- t(rpf.prob(item, param, seq(-width, width, .1)))
icc <- as.data.frame(melt(pm, varnames=c("theta",'category')))
icc$theta <- seq(-width, width, .1)
icc$category <- as.factor(icc$category)
ggplot(icc, aes(theta, value)) +
geom_line(aes(color=category)) +
ylim(0,1) + xlim(-width,width)
}
i1 <- rpf.gpcm(5)
i1.p <- rpf.rparam(i1)
i2 <- rpf.drm()
i2.p <- rpf.rparam(i2)
grid.arrange(plot.icc(i1, i1.p),
plot.icc(i2, i2.p), ncol=2)
@
Now let us look at some real data.
<<fig.height=3.5, cache=TRUE>>=
data(ms.items)
spec <- list()
spec[1:10] <- rpf.gpcm(5)
plot.info <- function(spec, param, i.name, width=3) {
if (missing(i.name)) {
i.name <- paste0('i', 1:length(spec))
}
grid <- seq(-width,width,.1)
df <- list(score=grid)
total <- numeric(length(grid))
for (ix in 1:length(spec)) {
id <- i.name[ix]
s <- spec[[ix]]
df[[id]] <- rpf.info(s, param[ix,1:rpf.numParam(s)], grid)
total <- total + df[[id]]
}
df$total <- total
df <- as.data.frame(df)
long<- melt(df, id.vars=c('score'), variable.name="item")
long$item <- factor(long$item)
ggplot(long, aes(score, value, group=item)) +
geom_line(size=1.1,aes(linetype=item, color=item)) + ylab("information")
}
param <- ms.items[,c('slope',paste0('b',1:4))]
plot.info(spec, param, ms.items[,'name'])
@
<<fig.height=3, cache=TRUE>>=
data(ms.people)
data.vs.model <- function(spec1, param, espt, item.name, width=3, data.bins=10) {
pm <- t(rpf.prob(spec1, param[1:rpf.numParam(spec1)], seq(-width, width, .1)))
icc <- as.data.frame(melt(pm, varnames=c("theta",'category')))
icc$theta <- seq(-width, width, .1)
icc$category <- as.ordered(1+max(icc$category)-icc$category) #parscale reverses stuff
icc$type <- 'model'
breaks <- seq(min(espt$score, na.rm=TRUE),
max(espt$score, na.rm=TRUE),
length.out=data.bins+1)
bin <- unclass(cut(espt$score, breaks, include.lowest = TRUE))
est <- tabulate(bin, length(levels(bin)))
if (any(est < 10)) {
warning("Some bins have less than 10 samples; try fewer data.bins")
}
eout <- array(dim=c(data.bins, spec1@outcomes+1))
for (px in 1:data.bins) {
t <- table(espt[[item.name]][bin==px], useNA="no")
eout[px,2:(spec1@outcomes+1)] <- t / sum(t)
}
eout[,1] <- ((c(breaks,0) + c(0,breaks))/2)[2:(data.bins+1)]
edf <- melt(as.data.frame(eout), id.vars=c('V1'),
variable.name="category")
edf$category <- ordered(unclass(edf$category))
edf$theta <- edf$V1
edf$V1 <- NULL
edf$type <- 'data'
both <- rbind(edf, icc)
both$type <- factor(both$type)
ggplot(both, aes(theta, value)) +
geom_line(aes(color=category, linetype=category)) + facet_wrap(~type) +
ylim(0,1) + xlim(-width,width) + labs(y="probability", x="score")
}
name <- 'msCause'
item.x <- match(name,ms.items$name)
param <- ms.items[item.x, c('slope',paste0('b',1:4))]
data.vs.model(spec[[item.x]], param,ms.people , name, data.bins=12) +
labs(title = paste0(name, ", slope = ",param[1]))
@
Let us plot one more. For msShared, categories 2 and 4 are never the
most likely choice. You can see this visually by confirming that the
curves for categories 2 and 4 are already beneath the curves for other
categories.
<<fig.height=3, cache=TRUE>>=
name <- 'msShared'
item.x <- match(name,ms.items$name)
param <- ms.items[item.x, c('slope',paste0('b',1:4))]
data.vs.model(spec[[item.x]], param,ms.people , name, data.bins=12) +
labs(title = paste0(name, ", slope = ",param[1]))
@
Item-wise covariance of residuals can be informative.
<<>>=
param <- ms.items[, c('slope',paste0('b',1:4))]
res <- rpf.1dim.residual(spec, param, ms.people[,ms.items$name], ms.people$score)
res <- res[!apply(is.na(res), 1, any),]
res.cov <- cov(res)
dimnames(res.cov) <- list(ms.items$id, ms.items$id)
round(cov(res.cov),1)
@
Let's take another dataset and look at item fit. This will show the
most overfitting and underfitting items.
<<>>=
data(science.items)
data(science.people)
scores <- science.people$trait
params <- cbind(1, science.items[,c(paste0('b',1:2))])
rownames(params) <- as.character(science.items$name)
items<-list()
items[1:25] <- rpf.gpcm(3)
responses <- science.people[,as.character(science.items$name)]
rownames(responses) <- science.people$name
fit <- rpf.1dim.fit(items, params, responses, scores, 2)
head(fit[order(-fit$outfit),])
tail(fit[order(-fit$outfit),])
@
And we can do the same with people.
<<>>=
fit <- rpf.1dim.fit(items, params, responses, scores, 1)
head(fit[order(-fit$outfit),])
tail(fit[order(-fit$outfit),])
@
\end{document}
|
