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

• Published in: Statistical analysis and data mining Vol. 18; no. 1
• Main Authors: Mohammadi, Raziyeh, Kazemi, Iraj
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.02.2025; Wiley Subscription Services, Inc
• Subjects: Algorithms; Correlation; Covariance matrix; covariance structure; Data analysis; Hamiltonian functions; Hamiltonian Monte Carlo; modified Cholesky decomposition; Multivariate analysis; Outliers (statistics); Parameter estimation; Parameterization; Regression models; robust inference; Robustness; tuning parameter
• ISSN: 1932-1864; 1932-1872
• DOI: 10.1002/sam.70011

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.