H. Jacqmingadda et D. Commenges, TESTS OF HOMOGENEITY FOR GENERALIZED LINEAR-MODELS, Journal of the American Statistical Association, 90(432), 1995, pp. 1237-1246
We propose two tests for testing homogeneity among clustered data adju
sting for the effects of covariates. The first is a score test for a g
eneralized linear model with random effect, in which the distribution
of the response variable given the random effect is entirely defined.
In contrast to the likelihood ratio test, however, the score test does
not require estimation of the parameters of a mixed-effects model nor
specification of the mixing distribution. The second test is proposed
in the framework of the generalized estimating equation (GEE) approac
h. In deriving this test, we need only the specification of the margin
al expectation and variance of the response variable and the fourth mo
ment for the overdispersion term, whereas for deriving the score test
for mixed effects models, the entire conditional distribution must be
specified. We demonstrate that the two tests are identical when the co
variance matrix assumed in the GEE approach is that of the random-effe
cts model. In both approaches, the test statistic can be decomposed in
to a pairwise correlation statistic and a statistic of overdispersion.
We performed a simulation study to compare the power of the score tes
t and of the test based on their pairwise correlation statistic only,
and also to compare their type I errors in cases where data present ov
erdispersion not due to the clustering studied. On the basis of these
results, we recommend using the pairwise correlation statistic, which
is more robust than the complete statistic to overdispersion not due t
o the clustering studied.