Joint Modeling of Mean-Covariance Structures Based on Partial Autocorrelation for Longitudinal Data

In this paper, we propose a joint mean-variance-correlation modeling approach for longitudinal studies. By applying partial autocorrelations, we obtain an unconstrained parametrization for the correlation matrix that automatically guarantees its positive definiteness, and develop a regression approach to model the correlation matrix of the longitudinal measurements by exploiting the parametrization. The proposed modeling framework is parsimonious, interpretable, and flexible for analyzing longitudinal data. Real data example and simulation support the effectiveness of the proposed approach.