A Bayesian Approach for Robust Longitudinal Envelope Models

2025-12-10

AI Summary

Existing envelope methods typically assume Gaussian errors, limiting their ability to jointly handle longitudinal repeated measurements and outliers. To address this, we propose the Robust Longitudinal Envelope Model (RoLEM) for dimension reduction in multivariate linear regression. RoLEM is the first to incorporate the scale-mixture matrix-normal distribution into the longitudinal envelope framework, enabling simultaneous modeling of within-subject correlation and heavy-tailed outliers. We further develop a geometric prior and MCMC proposal distribution on the Grassmann manifold to facilitate structured Bayesian inference over the parameter space. Simulation studies and real-data analyses demonstrate that RoLEM substantially improves estimation accuracy and exhibits superior robustness against both outliers and complex longitudinal correlation structures—overcoming key limitations of conventional envelope models when applied to longitudinal data with non-Gaussian errors.

Technology Category

• Machine Learning: Ensemble Methods
• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Develops robust longitudinal envelope model for multivariate regression
• Handles outliers and repeated measures with flexible correlation structures
• Introduces Bayesian inference on Grassmann manifold for envelope models

Innovation

• Bayesian robust longitudinal envelope model
• Matrix-variate normal mixture for outliers
• Grassmann manifold priors for inference