  In certain academic systems, a student can enroll for an exam immediately
after the end of the teaching period or can postpone it to any later
examination session, so that the grade is missing until the exam is not
attempted. We propose an approach for the evaluation in itinere of a student's
proficiency accounting also for non-attempted exams. The approach is based on
considering each exam as an item, so that responding to the item amounts to
attempting the exam, and on an Item Response Theory model that includes two
latent variables corresponding to the student's ability and the propensity to
attempt the exam. In this way, we explicitly account for non-ignorable missing
observations as the indicators of item response also contribute to measure the
ability. The two latent variables are assumed to have a discrete distribution
defining latent classes of students that are homogeneous in terms of ability
and priority assigned to exams. The model, which also allows for individual
covariates in its structural part, is fitted by the Expectation-Maximization
algorithm. The approach is illustrated through the analysis of data about the
first-year exams of freshmen of the School of Economics at the University of
Florence (Italy).
