ltm-package | R Documentation |

This package provides a flexible framework for Item Response Theory analyses for dichotomous and polytomous data under a Marginal Maximum Likelihood approach. The fitting algorithms provide valid inferences under Missing At Random missing data mechanisms.

Package: | ltm |

Type: | Package |

Version: | 1.2-0 |

Date: | 2022-02-18 |

License: | GPL |

The following options are available:

- Descriptives:
samples proportions, missing values information, biserial correlation of items with total score, pairwise associations between items, Cronbach's

*alpha*, unidimensionality check using modified parallel analysis, nonparametric correlation coefficient, plotting of sample proportions versus total score.- Dichotomous data:
Rasch Model, Two Parameter Logistic Model, Birnbaum's Three Parameter Model, and Latent Trait Model up to two latent variables (allowing also for nonlinear terms between the latent traits).

- Polytomous data:
Samejima's Graded Response Model and the Generalized Partial Credit Model.

- Goodness-of-Fit:
Bootstrapped Pearson

*χ^2*for Rasch and Generalized Partial Credit models, fit on the two- and three-way margins for all models, likelihood ratio tests between nested models (including AIC and BIC criteria values), and item- and person-fit statistics.- Factor Scoring - Ability Estimates:
Empirical Bayes (i.e., posterior modes), Expected a posteriori (i.e., posterior means), Multiple Imputed Empirical Bayes, and Component Scores for dichotomous data.

- Test Equating:
Alternate Form Equating (where common and unique items are analyzed simultaneously) and Across Sample Equating (where different sets of unique items are analyzed separately based on previously calibrated anchor items).

- Plotting:
Item Characteristic Curves, Item Information Curves, Test Information Functions, Standard Error of Measurement, Standardized Loadings Scatterplot (for the two-factor latent trait model), Item Operation Characteristic Curves (for ordinal polytomous data), Item Person Maps.

Dimitris Rizopoulos

Maintainer: Dimitris Rizopoulos <d.rizopoulos@erasmusmc.nl>

Baker, F. and Kim, S-H. (2004) *Item Response Theory*, 2nd ed.
New York: Marcel Dekker.

Rizopoulos, D. (2006) **ltm**: An R package for latent variable modelling and item response theory analyses.
*Journal of Statistical Software*, **17(5)**, 1–25. URL doi: 10.18637/jss.v017.i05

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