The r - d class estimator in generalized linear models: applications on gamma, Poisson and binomial distributed responses

In order to combat multicollinearity, the r - d class estimator was introduced in linear and binary logistic regression models. Since the generalized linear models (GLMs) are the models that include logistic regression model, Poisson regression model, etc., we introduce the iterative and first-order approximated r - d class estimator in GLMs. The sampling distribution of the class estimator at convergence is given and the test on the regression coefficients is provided. The properties of the first-order approximated r - d class estimator in GLMs are discussed, comparisons of the three constitute estimators in the sense of bias, variance and scalar mean square errors are done, and a cross-validation method and a mean square error method for the selection of the shrinkage parameter are given. Finally, a simulation study is conducted for Poisson response and two real data analyses are done for gamma and binomial response data to examine the performance of the first-order approximated r - d class estimator versus the first-order approximated maximum likelihood, Liu, PCR and ridge estimators in GLMs.