Mixed Effect Modeling and Variable Selection for Quantile Regression

TL;DR

This paper extends quantile regression to include random effects and variable selection using an EM algorithm, demonstrating improved performance through simulations and real data applications.

Contribution

It introduces a novel EM-based approach for mixed effect quantile regression with variable selection, enhancing model flexibility and accuracy.

Findings

The proposed method outperforms lasso-based variable selection in simulations.

Convergence of the algorithm is established as a generalized alternating minimization.

Applications include hospital stay analysis and gene expression data prediction.

Abstract

It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent generalized inverse-Gaussian variables. This fact is exploited here to extend QR to allow for random effects in the linear predictor. Convergence of the algorithm in this setting is established by showing that it is a generalized alternating minimization (GAM) procedure. Another modification of the EM algorithm also allows us to adapt a recently proposed method for variable selection in mean regression models to the QR setting. Simulations show the resulting method significantly outperforms variable selection in QR models using the lasso penalty. Applications to real data include a frailty QR analysis of hospital stays, and variable selection for age at onset of lung cancer and for riboflavin production rate using high-dimensional gene expression arrays for prediction.