Two-part expectile regression models for longitudinal data: an application to students’ academic performance

This paper proposes a novel two-part random-effects expectile regression model for longitudinal data. Expectiles provides a more detailed picture of the conditional distribution of the response than averages and offer several advantages over classical quantiles. Time-constant heterogeneity is modeled flexibly through a bivariate discrete distribution of the random effects, linking the binary decision process and the positive outcomes. Model parameters are estimated in a Maximum Likelihood approach via an Expectation–Maximization algorithm using the Asymmetric Normal distribution as the working likelihood. The practical advantages of our approach are illustrated with an application on university students’ achievement followed over three years.