New univariate and multivariate three-part generalized quantile regression model for complex longitudinal structures

The goal of this thesis is to develop a unified class of quantile-based models for complex longitudinal data in which repeated measurements involve both a binary event and multiple semi-positive outcomes characterized by excess zeros, skewness, and heavy tails. The statistical analysis focuses on univariate and multivariate approaches proposing three-part finite-mixture generalized quantile regression models. The framework combines: (i) a logistic regression for the probability of event occurrence, (ii) a binary specification for the probability of a positive versus zero outcome, and (iii) a generalized quantile model for the strictly positive responses. The dissertation is organized into three chapters addressing the same longitudinal structure, but relying on different model specifications, progressively extending the framework from a univariate to a multivariate setting for regression quantiles and expectiles. The proposed methodologies are illustrated using simulation studies and real-world data. Their applicability in higher-education studies is demonstrated starting from an empirical question concerning the investigation of student dropout and academic performance among Sapienza University of Rome bachelor students.