An analysis of student performances through a finite mixture IRT model

We focus on the analysis of the performance of university students, with reference to first year compulsory courses, with the main goal of clustering students in ability classes on the basis of their performance. The performance is measured account for two distinct elements: (i) the sets of passed and unpassed exams; (ii) the grade attained at the passed exams. We assume that data related with not passed exams are missing data and are informative about the students' ability, thus the missingness cannot be ignored in the estimation process. In the analysis, we also consider some background characteristics of the students influencing their performance, such as high school grade and type, and some characteristics of exams, such as the average evaluation related to the clarity of teacher.