Estimation methods in generalized linear models

Multicollinearity among the explanatory variables seriously effects the maximum likelihood estimator in linear regression models which results in large estimates in absolute value and in large variance-covariance matrix. The adverse effects of multicollinearity on parameter estimation in generalized linear models (GLMs) are also explored by various authors in the case of maximum likelihood estimator. Although ridge estimator and restricted estimator were proposed as an alternative to maximum likelihood estimator in GLMs, there are a few number of methods of the alternative estimators in GLMs. In this study, restricted ridge, Liu and restricted Liu estimators are introduced to combat multicollinearity in GLMs and mean squared error comparisons are done in the context of first-order approximated estimators. The performance of these estimators is examined in detail for the gamma and Poisson response models. The results are illustrated by conducting numerical examples and simulation studies.