# A collection of useful IRT functions.

### Description

Modified from the package `irtoys`

.

### Usage

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### 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

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