ABSTRACT
Similarly, ML is difficult for marginal models. The model applies to the marginal distributions of the multivariate response rather than the joint distribution to which components of a multinomial likelihood refer. A weighted least squares approach is simple but has the severe limitation of categorical predictors with nonsparse data (Koch et al. 1977). Recently, generalized estimating equations (GEE) have provided a popular way to estimate parameters in marginal models. With this approach, it is unnecessary to specify fully the joint distribution. One specifies models (such as a logit model if the response is binary) only for marginal distributions and uses a working guess for the correlation structure (Liang and Zeger, 1986). With marginal models, since the association structure is not the primary focus, it is regarded as a nuisance. Estimates of model parameters are consistent even if the correlation structure is misspecified. The GEE methodology, originally specified for univariate marginal distributions such as the binomial and Poisson, extends to multinomial categorical responses. For ordinal responses, for instance, see Lipsitz et al. (1994). The GEE approach is appealing for marginal modeling because of its relative simplicity, but it has limitations. Since the model does not specify the joint distribution, it lacks a likelihood function and hence inference relies on Wald methods. ft is unclear whether a particular choice of mean and variance function and correlation structure would be implied by any meaningful joint distribution for multinomial probabilities.
