University drop-out is a topic of increasing concern in Italy as well as in other countries. In empirical analysis, university drop-out is generally measured by means of a binary variable indicating the drop-out versus retention. In this paper, we argue that the withdrawal decision is one of the possible outcomes of a set of four alternatives: retention in the same faculty, drop out, change of faculty within the same university, and change of institution. We examine individual-level data collected by the administrative offices of “Sapienza” University of Rome, which cover 117 072 students enrolling full-time for a 3-year degree in the academic years from 2001/2002 to 2006/2007. Relying on a non-parametric maximum likelihood approach in a finite mixture context, we introduce a multinomial latent effects model with endogeneity that accounts for both heterogeneity and omitted covariates. Our estimation results show that the decisions to change faculty or university have their own peculiarities, thus we suggest that caution should be used in interpreting results obtained without modeling all the relevant alternatives that students face.