Hypothesis Testing of Regression Parameters in Semi-Parametric Generalized Linear Models for Cluster Correlated Data

Andrea Rotnitzky, Department of Biostatistics, Harvard School of Public Health
Nicholas P. Jewell, Division of Biostatistics, School of Public Health, University of California, Berkeley

Abstract

Generalized and "working" Wald and score tests for regression coefficients in the class of semi-parametric marginal generalized linear models for cluster correlated data (Liang and 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 and Scott (12984), 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.