Abstract: Joint mean-covariance regression modeling with unconstrained parametrization for continuous longitudinal data has provided statisticians and practitioners with a powerful analytical device. How to develop a delineation of such a regression framework amongst discrete longitudinal responses remains an open and more challenging problem. This paper studies a novel mean-correlation regression for a family of generic discrete responses. Targeting the joint distributions of the discrete longitudinal responses, our regression approach is constructed by using a copula model whose correlation parameters are represented in hyperspherical coordinates with no constraint on their support. To overcome computational intractability in maximizing the full likelihood function of the model, we propose a computationally efficient pairwise likelihood approach. A pairwise likelihood ratio test is then constructed and validated for statistical inferences. We show that the resulting estimators of our approaches are consistent and asymptotically normal. We demonstrate the effectiveness, parsimoniousness and desirable performance of the proposed approach by analyzing three data sets and conducting extensive simulations.

Key words and phrases: Cholesky decomposition, discrete longitudinal data, hyperspherical coordinates, joint distribution, likelihood ratio test, mean-correlation regression, pairwise likelihood.