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

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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.

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... Building on the literature and the information gathered from the focus group analysis and to test the research hypotheses, we collected data through a questionnaire with 1,111 respondents representing Millennials and GenZ university students in the Northwest of Italy. Finally, following the methodology proposed recently by Davino and Vistocco (2018), we implemented a quantile regression analysis considering the presence of group effects (afraid or not afraid of . ...
... Apart from the fact that quantile regression allows us to consider the impact of the covariates on the entire distribution of y, an additional advantage is that it is more robust to non-normal errors and outliers, and invariant to monotonic transformations. In this study, we consider a quantile regression analysis considering the presence of group effects (afraid or not afraid of COVID-19) following the methodology proposed recently by Davino and Vistocco (2018). ...
... Davino and Vistocco (2018) proposed a methodology which uncovers the heterogeneity between different groups based on a single estimation process. The methodology includes first a global estimation, then recognition of the best model for each individual/unit, followed by recognition of the best model for each set and, finally, partial estimation (Davino and Vistocco, 2018). In particular, the first step, which includes the global estimation in the quantile regression model, is estimated by excluding the group variable (afraid or not COVID-19): ...
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