Bayesian estimation in generalized linear models for longitudinal data with hyperspherical coordinates

• Published in: Statistics (Berlin, DDR) Vol. 58; no. 2; pp. 302 - 315
• Main Authors: Geng, Shuli, Zhang, Lixin
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.03.2024; Taylor & Francis Ltd
• Subjects: Bayesian analysis; Correlation analysis; Data analysis; Empirical analysis; empirical likelihood; Estimation; generalized estimating equation; generalized linear model; hyperspherical coordinates; Linear equations; Longitudinal data; Longitudinal studies; Markov chains; Maximum likelihood method; Normal distribution; Statistical models
• ISSN: 0233-1888; 1029-4910
• DOI: 10.1080/02331888.2024.2332711

Under the framework of generalized linear models (GLM), the generalized estimating equation (GEE) method is typically applied for longitudinal data analysis. However, there are a series of problems due to the misspecification of the within-subject correlation structure, especially in Bayesian estimation. To handle these difficulties, in this paper, we construct a class of generalized estimating equations for longitudinal data with hyperspherical coordinates (HPC) and propose a Bayesian approach established through empirical likelihood (EL). Additionally, an efficient Markov chain Monte Carlo (MCMC) procedure is developed for the required computation of the posterior distribution. As proved by the simulation studies and an application to a real longitudinal data set, our method not only performs better than traditional empirical likelihood estimation and Bayesian estimation with partial autocorrelations (PAC) but also is suitable for non-Gaussian data.