  Dependence modeling of multivariate count data has been receiving a
considerable attention in recent times. Multivariate elliptical copulas are
typically preferred in statistical literature to analyze dependence between
repeated measurements of longitudinal data since they allow for different
choices of the correlation structure. But these copulas lack in flexibility to
model dependence and inference is only feasible under parametric restrictions.
In this article, we propose the use of finite mixture of elliptical copulas in
order to capture complex and hidden temporal dependency of discrete
longitudinal data. With guaranteed model identifiability, our approach permits
to use different correlation matrices in each component of the mixture copula.
We theoretically examine the dependence properties of finite mixture of
copulas, before applying them for constructing regression models for count
longitudinal data. The inference of the proposed class of models is based on
composite likelihood approach and the finite sample performance of the
parameter estimates are investigated through extensive simulation studies. For
model validation, besides the standard techniques we extended the t-plot method
to accommodate finite mixture of elliptical copulas. Finally, our models are
applied to analyze the temporal dependency of two real world longitudinal data
sets and shown to provide improvements if compared against standard elliptical
copulas.
