Department of Statistics, Fox School of Business
“Mean-Correlation Regression For Discrete Longitudinal Responses”
Joint mean-covariance regression modelling with unconstrained parameterization has provided statisticians and practitioners a powerful analytical device for characterizing covariations between continuous longitudinal responses. How to develop a delineation of such an unconstrained regression framework amongst categorical or discrete longitudinal responses, however, remains an open and challenging problem. This paper studies, for the first time, a novel mean-correlation regression for a family of generic discrete responses. Targeting at the joint distributions of the discrete longitudinal responses, our regression approach is constructed by using an innovative copula model whose correlation parameters are represented by unconstrained hyperspherical coordinates. To overcome the computational intractability in maximizing the full likelihood of the discrete responses in practice, we develop a computationally efficient pairwise likelihood approach for estimation. We show that the resulting estimators of the proposed approaches are consistent and asympotically normal. A pairwise likelihood ratio test is further proposed for statistical inference. We demonstrate the effectiveness, parsimoniousness and desirable performance of the proposed approach by analyzing three discrete longitudinal data sets and conducting extensive simulations.
This is a joint work with Chenlei Leng and Weiping Zhang.