Robust multi-outcome regression with correlated covariate blocks using fused LAD-lasso

TL;DR

This paper introduces a robust multi-outcome regression method combining LAD-lasso with group fusion penalties to handle correlated covariate blocks, outliers, and non-normal outcomes, demonstrated through simulations and real data.

Contribution

It develops a novel robust multi-outcome regression approach that incorporates covariate block correlation and fusion penalties, improving variable selection and estimation in complex data.

Findings

The method performs well in simulations with correlated covariates and outliers.

It effectively models skewed, heteroscedastic real-world data.

Fusion penalties improve estimation accuracy for neighboring covariate effects.

Abstract

Lasso is a popular and efficient approach to simultaneous estimation and variable selection in high-dimensional regression models. In this paper, a robust LAD-lasso method for multiple outcomes is presented that addresses the challenges of non-normal outcome distributions and outlying observations. Measured covariate data from space or time, or spectral bands or genomic positions often have natural correlation structure arising from measuring distance between the covariates. The proposed multi-outcome approach includes handling of such covariate blocks by a group fusion penalty, which encourages similarity between neighboring regression coefficient vectors by penalizing their differences for example in sequential data situation. Properties of the proposed approach are first illustrated by extensive simulations, and secondly the method is applied to a real-life skewed data example on retirement behavior with heteroscedastic explanatory variables.