Modeling nonignorable missingness in multidimensional latent class IRT models

A relevant problem in applications of Item Response Theory (IRT) models is the presence of nonignorable missing responses. We propose a multidimensional latent class IRT model in which the missingness mechanism is driven by a latent variable (propensity to answer) correlated with the latent variable for the ability (or abilities) measured by the test items. These two latent variables are assumed to have a joint discrete distribution. This assumption is convenient both from the computational point of view and for the decisional process, since individuals are classified in homogeneous latent classes which may be associated to the same treatment. Moreover, this assumption avoids parametric formulations for the distribution of the latent variables, giving rise to a semiparametric model. 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.