A Bayesian Approach for Robust Longitudinal Envelope Models

TL;DR

This paper introduces RoLEM, a Bayesian robust envelope model for longitudinal data that handles outliers and complex correlation structures, improving over traditional methods.

Contribution

The paper develops a novel Bayesian envelope model for longitudinal data using scale mixtures and Grassmann manifold priors, addressing outliers and correlation complexities.

Findings

RoLEM outperforms existing methods in simulations.

Demonstrates robustness to outliers in real data.

Provides flexible modeling of repeated measures.

Abstract

The envelope model provides a dimension-reduction framework for multivariate linear regression. However, existing envelope methods typically assume normally distributed random errors and do not accommodate repeated measures in longitudinal studies. To address these limitations, we propose the robust longitudinal envelope model (RoLEM). RoLEM employs a scale mixture of matrix-variate normal distributions to model random errors, allowing it to handle potential outliers, and incorporates flexible correlation structures for repeated measurements. In addition, we introduce new prior and proposal distributions on the Grassmann manifold to facilitate Bayesian inference for RoLEM. Simulation studies and real data analysis demonstrate the superior performance of the proposed method.