Finite mixtures of linear quantile regressions with concomitant variables: a solution to endogeneity in longitudinal data modeling

Longitudinal studies give the chance to control for time-constant heterogeneity, by adding unit-specific effects to the model formulation. When a random effect specification is adopted, issues of endogeneity may arise. We discuss quantile regression models for longitudinal data using a finite mixture approach, and propose a concomitant variable framework to address endogeneity. Specifically, we account for dependence between random effects and observed covariates in the model by assuming that the mixing distribution depends on time-constant covariates, as well as on time-constant summaries of time-varying covariates. We show, in a large scale simulation study, that this approach provides a simple, efficient, and general solution to the aforementioned problem. The performance of the proposed model is also examined using an application to original real data on the distribution of the Mini-Mental state Examination (MMSE) scores in a sample of elderly subjects.