MultiLCIRT: An R package for multidimensional latent class item response models

TL;DR

This paper introduces MultiLCIRT, an R package for multidimensional latent class IRT models that handle binary and ordinal items, allowing for flexible modeling of latent traits and providing tools for estimation, model selection, and clustering.

Contribution

The paper presents a new R package, MultiLCIRT, enabling estimation and model selection for multidimensional latent class IRT models with flexible parameterizations.

Findings

Successful application to datasets on mathematics ability and mental health assessment.

Demonstrated model-based hierarchical clustering of items.

Guidelines for model selection and fit assessment.

Abstract

We illustrate a class of Item Response Theory (IRT) models for binary and ordinal polythomous items and we describe an R package for dealing with these models, which is named MultiLCIRT. The models at issue extend traditional IRT models allowing for (i) multidimensionality and (ii) discreteness of latent traits. This class of models also allows for different parameterizations for the conditional distribution of the response variables given the latent traits, depending on both the type of link function and the constraints imposed on the discriminating and the difficulty item parameters. We illustrate how the proposed class of models may be estimated by the maximum likelihood approach via an Expectation-Maximization algorithm, which is implemented in the MultiLCIRT package, and we discuss in detail issues related to model selection. In order to illustrate this package, we analyze two datasets: one concerning binary items and referred to the measurement of ability in mathematics and the other one coming from the administration of ordinal polythomous items for the assessment of anxiety and depression. In the first application, we illustrate how aggregating items in homogeneous groups through a model-based hierarchical clustering procedure which is implemented in the proposed package. In the second application, we describe the steps to select a specific model having the best fit in our class of IRT models.