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

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