  We propose a class of Item Response Theory models for items with ordinal
polytomous responses, which extends an existing class of multidimensional
models for dichotomously-scored items measuring more than one latent trait. In
the proposed approach, the random vector used to represent the latent traits is
assumed to have a discrete distribution with support points corresponding to
different latent classes in the population. We also allow for different
parameterizations for the conditional distribution of the response variables
given the latent traits - such as those adopted in the Graded Response model,
in the Partial Credit model, and in the Rating Scale model - depending on both
the type of link function and the constraints imposed on the item parameters.
For the proposed models we outline how to perform maximum likelihood estimation
via the Expectation-Maximization algorithm. Moreover, we suggest a strategy for
model selection which is based on a series of steps consisting of selecting
specific features, such as the number of latent dimensions, the number of
latent classes, and the specific parametrization. In order to illustrate the
proposed approach, we analyze data deriving from a study on anxiety and
depression as perceived by oncological patients.
