A ONE-STEP GAUSS-NEWTON ESTIMATOR FOR MODELING CATEGORICAL-DATA WITH EXTRANEOUS VARIATION

We examine data from a study of the effects of prenatal exposure to el evated levels of cadmium and zinc on mortality and physical malformati on rates of hamster fetuses. As is common in teratology studies, extra neous variation relative to Poisson and multinomial models arises from examining more than one fetus for each treated female. We establish a symptotic normal properties of a one-step Gauss-Newton estimator of th e parameters of any sufficiently smooth function that links the expect ation of each observed vector of counts to a finite set of covariates, when the data exhibit either overdispersion or underdispersion. The a symptotic properties of this estimator rely on the existence of the fi rst two moments of the observation vectors and on the consistency of i nitial estimators for parameters in the link function and for any addi tional parameters used to model extraneous variation. Various patterns of extraneous variation are accommodated by simultaneously adjusting different components of variation. Applications to logistic regression models for multicategory responses with extramultinomial variation ar e explicitly considered.