  Generalized estimating equations (GEE) are of great importance in analyzing
clustered data without full specification of multivariate distributions. A
recent approach jointly models the mean, variance, and correlation coefficients
of clustered data through three sets of regressions (Luo and Pan, 2022). We
observe that these estimating equations, however, are a special case of those
of Yan and Fine (2004) which further allows the variance to depend on the mean
through a variance function. The proposed variance estimators may be incorrect
for the variance and correlation parameters because of a subtle dependence
induced by the nested structure of the estimating equations. We characterize
model settings where their variance estimation is invalid and show the variance
estimators in Yan and Fine (2004) correctly account for such dependence. 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.
