A two-part finite mixture quantile regression model for semi-continuous longitudinal data

TL;DR

This paper introduces a novel two-part finite mixture quantile regression model tailored for semi-continuous longitudinal data, capturing heterogeneity in both binary and positive outcomes without strict distributional assumptions.

Contribution

It develops a flexible modeling approach that links heterogeneity sources affecting binary responses to the distribution of positive outcomes, using an EM algorithm-based estimation method.

Findings

Applied to RAND Health Insurance data, demonstrating practical utility.

Provides a variable selection mechanism via penalized EM algorithm.

Offers insights into the distribution of semi-continuous health data.

Abstract

This paper develops a two-part finite mixture quantile regression model for semi-continuous longitudinal data. The proposed methodology allows heterogeneity sources that influence the model for the binary response variable, to influence also the distribution of the positive outcomes. As is common in the quantile regression literature, estimation and inference on the model parameters are based on the Asymmetric Laplace distribution. Maximum likelihood estimates are obtained through the EM algorithm without parametric assumptions on the random effects distribution. In addition, a penalized version of the EM algorithm is presented to tackle the problem of variable selection. The proposed statistical method is applied to the well-known RAND Health Insurance Experiment dataset which gives further insights on its empirical behavior.