Jg. Morel et Kj. Koehler, A ONE-STEP GAUSS-NEWTON ESTIMATOR FOR MODELING CATEGORICAL-DATA WITH EXTRANEOUS VARIATION, Applied Statistics, 44(2), 1995, pp. 187-200
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.