irt.item.diff.rasch: Simple function to estimate item difficulties using IRT concepts

Description

Steps toward a very crude and preliminary IRT program. These two functions estimate item difficulty and discrimination parameters.

Usage

irt.item.diff.rasch(items)
irt.discrim(item.diff,theta,items)

Arguments

items

a matrix of items

item.diff

a vector of item difficulties (found by irt.item.diff)

theta

ability estimate from irt.person.theta

Value

a vector of item difficulties or item discriminations.

Details

Item Response Theory (aka "The new psychometrics") models individual responses to items with a logistic function and an individual (theta) and item difficulty (diff) parameter.

irt.item.diff.rasch finds item difficulties with the assumption of theta=0 for all subjects and that all items are equally discriminating.

irt.discrim takes those difficulties and theta estimates from irt.person.rasch to find item discrimination (beta) parameters.

A far better package with these features is the ltm package. The IRT functions in the psych-package are for pedagogical rather than production purposes. They are believed to be accurate, but are not guaranteed. They do seem to be slightly more robust to missing data structures associated with SAPA data sets than the ltm package.

Examples

Run this code

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## The function is currently defined as
function(items) {
 ncases <- nrow(items)
 item.mean <- colMeans(items,na.rm=TRUE)
 item.mean[item.mean<(1/ncases)] <- 1/ncases
 irt.item.diff.rasch <- log((1/item.mean)- 1) }
 
 
 "irt.discrim" <- 
function(item.diff,theta,items) {
#find the item discrimination parameter  (beta)
#find the item discrimination parameter -- optimized by item.discrim
 irt.item.discrim <- function(x,diff,theta,scores) {
  fit <- -1*(log(scores/(1+exp(x*(diff-theta))) + (1-scores)/(1+exp(x*(theta-diff)))))
  mean(fit,na.rm=TRUE)
  }
 nitems <- length(item.diff)
 discrim <- matrix(NA,nitems,2)
 for (i in 1:nitems) {
    item.fit <- optimize(irt.item.discrim,c(-5,5),diff=item.diff[i],theta=theta,scores = items[,i])
   discrim[i,1] <- item.fit$minimum
   discrim[i,2] <- item.fit$objective}
  irt.discrim <- discrim
 }