Pretest and shrinkage estimation of the regression parameter vector of the marginal model with multinomial responses

Generalized Estimating Equations (GEE) approach has become a popular method that is applied for correlated categorical multinomial responses data in clinical trials and other biomedical experiments. GEEs estimates of the marginal regression parameter vector are consistent. In this article, we propose the pretest, shrinkage, and positive shrinkage estimators for the regression vector of the marginal model with multinomial responses. The array of estimators are compared analytically via their asymptotic quadratic risks, and numerically via their simulated relative efficiencies. We apply the proposed estimation technique to two real data examples and employed a bootstrapping approach to computing the bootstrapping mean squared error of the estimators.