Testing heterogeneity in quantile regression: a multigroup approach

Abstract

The paper aims to introduce a multigroup approach to assess group effects in quantile regression. The procedure estimates the same regression model at different quantiles, and for different groups of observations. Such groups are defined by the levels of one or more stratification variables. The proposed approach exploits a computational procedure to test group effects. In particular, a bootstrap parametric test and a permutation test are compared through artificial data taking into account different sample sizes, and comparing their performance in detecting low, medium, and high differences among coefficients pertaining different groups. An empirical analysis on MOOC students’ performance is used to show the proposal in action. The effect of the two main drivers impacting on performance, learning and engagement, is explored at different conditional quantiles, and comparing self-paced courses with instructor-paced courses, offered on the EdX platform.