TESTS OF HOMOGENEITY FOR GENERALIZED LINEAR-MODELS

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.