Useful IRT Functions {cacIRT}

A collection of useful IRT functions.

Description

Modified from the package irtoys.

Usage

iif(ip, x, D = 1.7)
irf(ip, x, D = 1.7)
MLE(resp, ip, D = 1.7, min= -4, max = 4)
normal.qu(n = 15, lower = -4, upper = 4, mu = 0, sigma = 1)
SEM(ip, x, D = 1.7)
sim(ip, x, D = 1.7)
tif(ip, x, D = 1.7)

Arguments

ip

A Jx3 matrix of item parameters. Columns are discrimination, difficulty, and guessing

x

Vector of theta points

resp

Response data matrix, subjects by items

min, max

MLE is undefined for perfect scores. These parameters define the range in which to search for the MLE, if the score is perfect, the min or max will be returned.

n

Number of quadrature points wanted

lower, upper

Range of points wanted

mu, sigma

The normal distribution from which points and weights are taken

D

The scaling constant for the IRT parameters, defaults to 1.7, alternatively often set to 1.

Details

iif gives item information, irf gives item response function, MLE returns maximum likelihood estimates of theta (perfect scores get +-4), normal.qu returns a list length 2 of normal quadrature points and weights, SEM gives the standard error of measurement at the given ability points, sim returns simulated response matrix, tif gives the test information function.

Author(s)

Quinn N. Lathrop

References

Partchev, I. (2014) irtoys: Simple interface to the estimation and plotting of IRT models. R package version 0.1.7.

Examples

params<-matrix(c(1,1,1,1,-2,1,0,1,0,0,0,0),4,3)
rdm<-sim(params, rnorm(100))

theta.hat <- MLE(rdm, params)
theta.se  <- SEM(rdm, params)

## transform a cut score of theta = 0 to the expected true score scale

	t.cut <- 0
	x.cut <- sum(irf(params, t.cut)$f)