Robustifying Marginal Linear Models for Correlated Responses Using a Constructive Multivariate Huber Distribution

Abstract

The marginal regression model is convenient for analyzing correlated responses, including repeated measures and longitudinal data. This paper proposes a robust marginal linear model for analyzing a vector of univariate responses with correlated components by incorporating an innovative multivariate Huber distribution. It employs a flexible parameterization using modified Cholesky decomposition, provides a convenient approach for estimating the covariance matrix, and allows for subject-varying the tuning parameter. Our research introduces a method for estimating parameters by employing the exact likelihood function through the Hamiltonian Monte Carlo algorithm. To highlight the advantage of our model, we carried out a simulation experiment and reanalyzed two real-world case studies in the health and economics fields. The results indicate that our model offers a more robust analysis by assigning appropriate weights to extreme observations, thereby handling outliers more effectively than traditional models. © 2025 Wiley Periodicals LLC.