# mirt v1.33.2

## Multidimensional Item Response Theory

Analysis of dichotomous and polytomous response data using
unidimensional and multidimensional latent trait models under the Item
Response Theory paradigm (Chalmers (2012) <doi:10.18637/jss.v048.i06>).
Exploratory and confirmatory models can be estimated with quadrature (EM)
or stochastic (MHRM) methods. Confirmatory
bi-factor and two-tier analyses are available for modeling item testlets.
Multiple group analysis and mixed effects designs also are available for
detecting differential item and test functioning as well as modeling
item and person covariates. Finally, latent class models such as the DINA,
DINO, multidimensional latent class, and several other discrete latent
variable models, including mixture and zero-inflated response models,
are supported.

## Readme

# mirt

Multidimensional item response theory in R.

## Description

Analysis of dichotomous and polytomous response data using unidimensional and multidimensional latent trait models under the Item Response Theory paradigm. Exploratory and confirmatory models can be estimated with quadrature (EM) or stochastic (MHRM) methods. Confirmatory bi-factor and two-tier analyses are available for modeling item testlets. Multiple group analysis and mixed effects designs also are available for detecting differential item functioning and modeling item and person covariates.

## Examples and evaluated help files are available on the wiki

Various examples and worked help files have been compiled using the `knitr`

package to generate
HTML output, and are available on the package wiki.
User contributions are welcome!

## Installing from source

It's recommended to use the development version of this package since it is more likely to be up to date than the version on CRAN. To install this package from source:

1) Obtain recent gcc, g++, and gfortran compilers. Windows users can install the Rtools suite while Mac users will have to download the necessary tools from the Xcode suite and its related command line tools (found within Xcode's Preference Pane under Downloads/Components); most Linux distributions should already have up to date compilers (or if not they can be updated easily). Windows users should include the checkbox option of installing Rtools to their path for easier command line usage.

2) Install the `devtools`

package (if necessary). In R, paste the following into the console:

```
install.packages('devtools')
```

3) Load the `devtools`

package (requires version 1.4+) and install from the Github source code.

```
library('devtools')
install_github('philchalmers/mirt')
```

### Installing from source via git

If the `devtools`

approach does not work on your system, then you can download and install the
repository directly.

1) Obtain recent gcc, g++, and gfortran compilers (see above instructions).

2) Install the git command line tools.

3) Open a terminal/command-line tool. The following code will download the repository code to your computer, and install the package directly using R tools (Windows users may also have to add R and git to their path)

```
git clone https://github.com/philchalmers/mirt
R CMD INSTALL mirt
```

### Special Mac OS X Installation Instructions

In some reported cases `XCode`

does not install the appropriate `gfortran`

compilers in the correct location, therefore they have to be installed manually instead. This is accomplished by inputing the following instructions into the terminal:

```
curl -O http://r.research.att.com/libs/gfortran-4.8.2-darwin13.tar.bz2
sudo tar fvxz gfortran-4.8.2-darwin13.tar.bz2 -C /
```

# Licence

This package is free and open source software, licensed under GPL (>= 3).

# Bugs and Questions

Bug reports are always welcome and the preferred way to address these bugs is through the Github 'issues'. Feel free to submit issues or feature requests on the site, and I'll address them ASAP. Also, if you have any questions about the package, or IRT in general, then feel free to create a 'New Topic' in the mirt-package Google group. Cheers!

## Functions in mirt

Name | Description | |

MixedClass-class | Class "MixedClass" | |

LSAT7 | Description of LSAT7 data | |

LSAT6 | Description of LSAT6 data | |

DiscreteClass-class | Class "DiscreteClass" | |

SIBTEST | Simultaneous Item Bias Test (SIBTEST) | |

createGroup | Create a user defined group-level object with correct generic functions | |

Science | Description of Science data | |

M2 | Compute the M2 model fit statistic | |

MDIFF | Compute multidimensional difficulty index | |

anova-method | Compare nested models with likelihood-based statistics | |

MixtureClass-class | Class "MixtureClass" | |

SingleGroupClass-class | Class "SingleGroupClass" | |

bfactor | Full-Information Item Bi-factor and Two-Tier Analysis | |

coef-method | Extract raw coefs from model object | |

boot.mirt | Calculate bootstrapped standard errors for estimated models | |

boot.LR | Parametric bootstrap likelihood-ratio test | |

MDISC | Compute multidimensional discrimination index | |

createItem | Create a user defined item with correct generic functions | |

DRF | Differential Response Functioning statistics | |

RMSD_DIF | RMSD effect size statistic to quantify category-level DIF | |

DTF | Differential test functioning statistics | |

Bock1997 | Description of Bock 1997 data | |

expand.table | Expand summary table of patterns and frequencies | |

extract.item | Extract an item object from mirt objects | |

DIF | Differential item functioning statistics | |

fixedCalib | Fixed-item calibration method | |

expected.item | Function to calculate expected value of item | |

extract.mirt | Extract various elements from estimated model objects | |

SAT12 | Description of SAT12 data | |

fixef | Compute latent regression fixed effect expected values | |

mdirt | Multidimensional discrete item response theory | |

MultipleGroupClass-class | Class "MultipleGroupClass" | |

PLCI.mirt | Compute profiled-likelihood (or posterior) confidence intervals | |

key2binary | Score a test by converting response patterns to binary data | |

empirical_ES | Empirical effect sizes based on latent trait estimates | |

itemplot | Displays item surface and information plots | |

expected.test | Function to calculate expected test score | |

averageMI | Collapse values from multiple imputation draws | |

areainfo | Function to calculate the area under a selection of information curves | |

thetaComb | Create all possible combinations of vector input | |

plot,MultipleGroupClass,missing-method | Plot various test-implied functions from models | |

poly2dich | Change polytomous items to dichotomous item format | |

iteminfo | Function to calculate item information | |

empirical_plot | Function to generate empirical unidimensional item and test plots | |

itemfit | Item fit statistics | |

testinfo | Function to calculate test information | |

extract.group | Extract a group from a multiple group mirt object | |

mirt-package | Full information maximum likelihood estimation of IRT models. | |

numerical_deriv | Compute numerical derivatives | |

deAyala | Description of deAyala data | |

imputeMissing | Imputing plausible data for missing values | |

lagrange | Lagrange test for freeing parameters | |

likert2int | Convert ordered Likert-scale responses (character or factors) to integers | |

itemGAM | Parametric smoothed regression lines for item response probability functions | |

draw_parameters | Draw plausible parameter instantiations from a given model | |

mirt.model | Specify model information | |

summary-method | Summary of model object | |

simdata | Simulate response patterns | |

mirt | Full-Information Item Factor Analysis (Multidimensional Item Response Theory) | |

personfit | Person fit statistics | |

print.mirt_list | Print generic for customized list console output | |

logLik-method | Extract log-likelihood | |

print.mirt_matrix | Print generic for customized matrix console output | |

empirical_rxx | Function to calculate the empirical (marginal) reliability | |

probtrace | Function to calculate probability trace lines | |

randef | Compute posterior estimates of random effect | |

estfun.AllModelClass | Extract Empirical Estimating Functions | |

fscores | Compute factor score estimates (a.k.a, ability estimates, latent trait estimates, etc) | |

print-method | Print the model objects | |

print.mirt_df | Print generic for customized data.frame console output | |

remap.distance | Remap item categories to have integer distances of 1 | |

marginal_rxx | Function to calculate the marginal reliability | |

read.mirt | Translate mirt parameters into suitable structure for plink package | |

gen.difficulty | Generalized item difficulty summaries | |

wald | Wald statistics for mirt models | |

residuals-method | Compute model residuals | |

mod2values | Convert an estimated mirt model to a data.frame | |

show-method | Show model object | |

mixedmirt | Mixed effects modeling for MIRT models | |

mirtCluster | Define a parallel cluster object to be used in internal functions | |

multipleGroup | Multiple Group Estimation | |

traditional2mirt | Convert traditional IRT metric into slope-intercept form used in mirt | |

vcov-method | Extract parameter variance covariance matrix | |

No Results! |

## Vignettes of mirt

Name | ||

mirt-vignettes.Rmd | ||

No Results! |

## Details

Type | Package |

VignetteBuilder | knitr |

ByteCompile | yes |

LazyLoad | yes |

LazyData | yes |

LinkingTo | Rcpp, RcppArmadillo |

License | GPL (>= 3) |

Repository | CRAN |

URL | https://github.com/philchalmers/mirt, https://github.com/philchalmers/mirt/wiki, https://groups.google.com/forum/#!forum/mirt-package |

BugReports | https://github.com/philchalmers/mirt/issues?state=open |

RoxygenNote | 7.1.1 |

suggests | boot , directlabels , knitr , latticeExtra , markdown , mirtCAT , nloptr , plink , Rsolnp , shiny , sirt |

imports | dcurver , Deriv , GPArotation , mgcv , Rcpp , splines , vegan |

depends | lattice , methods , R (>= 3.6.0) , stats , stats4 |

linkingto | RcppArmadillo |

Contributors | KwonHyun Kim, Adam Meade, Joshua Pritikin, Alexander Robitzsch, Mateusz Zoltak, Carl F. Falk, David King, Lennart Schneider, Chen-Wei Liu, Ogreden Oguzhan |

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```
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```