A Multidimensional Latent Class IRT Model for Non-Ignorable Missing Responses

A relevant problem in applications of Item Response Theory (IRT) models is due to non- ignorable missing responses. We propose a multidimensional latent class IRT model for binary items in which the missingness mechanism is driven by a latent variable (propensity to answer) correlated with the latent variable for the ability (or latent variables for the abilities) measured by the test items. These latent variables are assumed to have a joint discrete distribution. This assumption is convenient both from the point of view of estimation, since the manifest distribution of the responses may be simply obtained, and for the decisional process, since individuals are classified in homogeneous groups having common latent variable values. Moreover, this assumption avoids parametric formulations for the distribution of the latent variables, giving rise to a semiparametric model. The basic model, which can be expressed in terms of a Rasch or a two-parameters logistic parameterization, is also extended to allow for covariates that influence the weights of latent classes. The resulting model may be efficiently estimated through the discrete marginal maximum likelihood method, making use of the Expectation-Maximization algorithm. The proposed approach is illustrated through an application to data coming from a Students’ Entry Test for the admission to the courses in Economics in an Italian University