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We propose a class of Item Response Theory models for items with ordinalpolytomous responses, which extends an existing class of multidimensionalmodels for dichotomously-scored items measuring more than one latent trait. Inthe proposed approach, the random vector used to represent the latent traits isassumed to have a discrete distribution with support points corresponding todifferent latent classes in the population. We also allow for differentparameterizations for the conditional distribution of the response variablesgiven 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 boththe type of link function and the constraints imposed on the item parameters.For the proposed models we outline how to perform maximum likelihood estimationvia the Expectation-Maximization algorithm. Moreover, we suggest a strategy formodel selection which is based on a series of steps consisting of selectingspecific features, such as the number of latent dimensions, the number oflatent classes, and the specific parametrization. In order to illustrate theproposed approach, we analyze data deriving from a study on anxiety anddepression as perceived by oncological patients.

A class of Multidimensional Latent Class IRT models for ordinal polytomous item responses