Iterative Stochastic Restricted \(r-k\) Class Estimator in Generalized Linear Models: Application on Logistic Regression

The purpose of this paper is to introduce the stochastic restricted \(r-k\) class estimator and the stochastic restricted principal components regression estimator in case of multicollinearity. The matrix mean square error (MSE) comparisons of these new proposed estimators with the maximum likelihood estimator are given. In case the response variable has a binomial distribution, the performance evaluation of new estimators is examined with a numerical example and simulation studies such that the scalar MSE in the numerical example and the estimated MSE and the prediction MSE in the simulation study are used as the performance evaluation criteria. The results show that when the appropriate tuning parameter value is used, the stochastic restricted \(r-k\) class estimator gives better results than the maximum likelihood, mixed and stochastic restricted principal components regression estimators in all evaluation criteria regardless of the degree of multicollinearity while it is superior to the stochastic restricted ridge estimator according to the estimated MSE criterion at all degree of multicollinearity and according to the prediction MSE criterion when the degree of multicollinearity is 0.80 and 0.90.