GENERALIZED SCORE TEST OF HOMOGENEITY BASED ON CORRELATED RANDOM EFFECTS MODELS

We present a family of tests based on correlated random effects models which provides a synthesis and a generalization of recent work on hom ogeneity testing. In these models each subject has a particular random effect, but the random effects between subjects are correlated. We de rive the general form of the score statistic for testing that the rand om effects have a variance equal to 0. We apply this result to both pa rametric and semiparametric models. In both cases we show that under c ertain conditions the score statistic has an asymptotic normal distrib ution. We consider several applications of this theory, including over dispersion, heterogeneity between groups, spatial correlations and gen etic linkage.