GEE for multinomial responses using a local odds ratios parameterization

In this article, we propose a generalized estimating equations (GEE) approach for correlated ordinal or nominal multinomial responses using a local odds ratios parameterization. Our motivation lies upon observing that: (i) modeling the dependence between correlated multinomial responses via the local odds ratios is meaningful both for ordinal and nominal response scales and (ii) ordinary GEE methods might not ensure the joint existence of the estimates of the marginal regression parameters and of the dependence structure. To avoid (ii), we treat the so-called "working" association vector α as a "nuisance" parameter vector that defines the local odds ratios structure at the marginalized contingency tables after tabulating the responses without a covariate adjustment at each time pair. To estimate α and simultaneously approximate adequately possible underlying dependence structures, we employ the family of association models proposed by Goodman. In simulations, the parameter estimators with the proposed GEE method for a marginal cumulative probit model appear to be less biased and more efficient than those with the independence "working" model, especially for studies having time-varying covariates and strong correlation.