Beyond the Average: Hypothesis Testing with Quantile Mixture

Empirical hypothesis testing is often based on the analysis of average effects, thereby overlooking the potential heterogeneity in the data. This paper devotes more attention to the distribution of the dependent variable and introduces finite quantile mixture models to examine heterogeneous effects across the distribution. I discuss how to frame corresponding conditional hypotheses and demonstrate how the finite quantile mixture models succeed in estimating simultaneously multiple conditional effects from the conditional hypotheses. A series of simulations are performed to demonstrate additional gains of using the finite quantile mixture models in identifying heterogeneous effects compared to other commonly adopted approaches. Real-world examples are also examined to show the use of the finite quantile mixture models. An open source software is available to estimate the models.