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

Abstract

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.

Keywords:

• Longitudinal data
• generalized linear model
• generalized estimating equation
• hyperspherical coordinates
• empirical likelihood

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by grants from the NSF of China (Grant Nos. U23A2064 and 12031005).