Comparison of Two Covariance Structures in the Analysis of Clustered Polytomous Data using Generalized Estimating Equations

Arguably, the use of model-based matrices as working covariance matrices in the analysis of clustered polytomous data by generalized estimating equations has the potential for greater efficiency. However, a failure to ensure that the estimated parameter values for the model-based matrices do indeed produce covariance matrices that are actually positive definite during the iterative process creates a serious risk of nonconvergence of estimators. This paper explores the performances of two classes of covariance matrices as possible working matrices for the analysis of clustered multinomial data. One class of matrices corresponds to the conventional standardizing of each multinomial observation involved, component by component. The other class results from standardizing the multinomial observation as a unit. While the two classes of matrices are found to provide similar efficiencies, independent of the choice of the working correlation matrix, they differ noticeably in the degree to which nonconvergence of the estimators occurs when random samples from a large set of data are repeatedly analyzed.