Generalized linear models for beta correlated binary longitudinal data

Multivariate binary longitudinal data sets are comprised of repeated observations of a vector outcome and a set of multi-dimensional covariates under each of many independent Clusters. The multivariate longitudinal data of this type exhibit two-way correlations: first, at a given point of time, the multivariate responses under a cluster are correlated; second, these correlated responses are repeatedly observed under a cluster over a period of time and the repeated responses are also correlated. One objective is to describe the marginal expectation of the outcome variable as a function of the covariates while accounting for the correlations among the repeated multi-dimensional responses for a given cluster. Based on the assumption that each pair of the multi-dimensional responses in a cluster follow the bivariate beta correlated binary distribution, this paper proposes a general class of estimating equations approach for inference on response probabilities and the scale parameter of the beta correlated binary distribution. The estimating equations have solutions which are consistent and asymptotically Gaussian. We illustrate the use of the estimating equations approach by analyzing a multivariate longitudinal data set on health care utilization by families in the city of St. John's, Canada.