A Joint Modelling Approach For Analyzing Longitudinal Zero-Inflated Count Data

Modeling the mean and covariance parsimoniously remains an open problem for analyzing longitudinal zero-inflated count data, mainly due to the lack of suitable mul-tivariate joint distributions that broadly incorporate the correlations between measure-ments from the same subject. In this paper, we propose a novel approach by using cop-ula in mean-correlation regression analysis for longitudinal zero-inflated data, solving both problems of generally specifying joint distributions and parsimoniously modeling correlations with no constraint. We then study the use of hyperspherical coordinates to parametrize the correlation matrix in the copula in terms of a set of angles, effectively a new set of constraint-free parameters on their support. Aided by this property, we pro-pose separated mean, correlation, and dispersion regression models to understand these three key quantities, which can also handle irregularly and possibly subject-specified times points. We show that the resulting estimators of the proposed approach are consis-tent and asymptotically normal. Data example and simulation support the effectiveness of the proposed approach.