Useful IRT Functions {cacIRT} R Documentation

## 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.

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)

```

[Package cacIRT version 1.4 Index]