On GEE for Mean-Variance-Correlation Models: Variance Estimation and Model Selection

Abstract

Generalized estimating equations (GEE) are of great importance in analyzing clustered data without full specification of multivariate distributions. A recent approach by Luo and Pan jointly models the mean, variance, and correlation coefficients of clustered data through three sets of regressions. We note that it represents a specific case of the more general estimating equations proposed by Yan and Fine which further allow the variance to depend on the mean through a variance function. In certain scenarios, the proposed variance estimators for the variance and correlation parameters in Luo and Pan may face challenges due to the subtle dependence induced by the nested structure of the estimating equations. We characterize specific model settings where their variance estimation approach may encounter limitations and illustrate how the variance estimators in Yan and Fine can correctly account for such dependencies. In addition, we introduce a novel model selection criterion that enables the simultaneous selection of the mean-scale-correlation model. The sandwich variance estimator and the proposed model selection criterion are tested by several simulation studies and real data analysis, which validate its effectiveness in variance estimation and model selection. Our work also extends the R package geepack with the flexibility to apply different working covariance matrices for the variance and correlation structures.