A multidimensional finite mixture SEM for non-ignorable missing responses to test items

A st ruct ural equat ion model is proposed t o deal wit h dichot omously-scored it ems in t he presence of missing not at random responses. Two types of latent variables are introduced: one refers to the abilities measured by the questionnaire and the other describes the propensity to answer. A semi- parametric approach is adopted, where both types of latent variable are discretely distributed. In such a way, the proposed structural equation model reduces to a multidimensional latent class item response t heory model. Individual covariat es may also be included in order t o explain t he probabilit ies of belonging to each latent class. For this aim, a multinomial logistic parametrization is introduced. A simulation study is then performed to evaluate the finite-sample properties of the parameter estimates.