Multilevel mixture IRT models: an application to the university teaching evaluation

Aim of the contribution is to illustrate the use of a three-level mixture Item Response Theory (IRT) model to classify university courses in homogeneous classes with respect to the level of students’ satisfaction. We rely on the Ital- ian questionnaire concerning the university teaching evaluation and composed by polytomously-scored items. Firstly, we detect the latent variables measured by the questionnaire items, performing a model-based hierarchical clustering. Secondly, we estimate a special case of multilevel mixture factor model characterized by (i) an IRT parametrization and (ii) discrete latent variables at all hierarchical levels. It has three-levels taking into account the hierarchical structure of the data: item re- sponses at level 1, students at level 2, and university courses at level 3. The proposed model is illustrated through an application on students’ satisfaction about courses of the Faculty of Political Sciences of the University of Perugia.