IRT function

A collection of useful IRT functions.

Modified from the package irtoys.

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.

References

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

Author(s)

Quinn N. Lathrop

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)