Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data

Abstract

Generalized and ‘working’ Wald and score tests for regression coefficients in the class of semiparametric marginal generalized linear models for cluster correlated data (Liang & Zeger, 1986) are proposed, and their asymptotic distribution examined. In addition, the asymptotic distribution of the naive likelihood ratio test, or deviance difference, is presented. Following Rao & Scott (1984), we propose simple adjustments to such ‘working’ tests. The asymptotic distributions of the ‘working’ tests allow us to explore theoretical bounds on the ratios of the robust variance of the regression parameter estimators and their naive variance counterparts computed assuming independent observations. In addition, the adequacy of a particular choice of working correlation structure is considered. We illustrate our results with a numerical example.