  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.
