Second-order generalized estimating equations for correlated count data

Abstract

Generalized estimating equations have been widely used in the analysis of correlated count data. Solving these equations yields consistent parameter estimates while the variance of the estimates is obtained from a sandwich estimator, thereby ensuring that, even with misspecification of the so-called working correlation matrix, one can draw valid inferences on the marginal mean parameters. That they allow misspecification of the working correlation structure, though, implies a limitation of these equations should scientific interest also be in the covariance or correlation structure. We propose herein an extension of these estimating equations such that, by incorporating the bivariate Poisson distribution, the variance-covariance matrix of the response vector can be properly modelled, which would permit inference thereon. A sandwich estimator is used for the standard errors, ensuring sound inference on the parameters estimated. Two applications are presented.