On the properties of GEE estimators in the presence of invariant covariates

In this paper it is shown that the use of non-singular block
invariant matrices of covariates leads to `generalized estimating
equations' estimators (GEE estimators; Liang, K.-Y.&Zeger, S.
(1986). Biometrika, 73(1), 13-22) which are identical regardless of
the `working' correlation matrix used. Moreover, they are efficient
(McCullagh, P. (1983). The Annals of Statistics, 11(1), 59-67). If
on the other hand only time invariant covariates are used the
efficiency gain in choosing the `correct' vs. an `incorrect'
correlation structure is shown to be negligible. The results of a
simple simulation study suggest that although different GEE
estimators are no more identical and are no more as efficient as an
ML estimator, the differences are still negligible if both time and
block invariant covariates are present.