Handling heterogeneity among units in quantile regression. Investigating the impact of students' features on University outcome

In many real data applications, statistical units belong to different groups and statistical models should be tailored to incorporate and exploit this heterogeneity among units. This paper proposes an innovative approach to identify group effects through a quantile regression model. The method assigns a conditional quantile to each group and provides a separate analysis of the dependence structure inside the groups. The relevance of the proposal is provided through an empirical analysis investigating the impact of students' features on University outcome. The analysis is performed on a sample of graduated students; the degree mark is the response variable, a set of variables describing the students' profile are used as regressors, and the attended School determines the group effects. A working example and a small simulation study are introduced to highlight the main features of the proposed approach.