Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical Research (FSSR) - Department of Statistics and Econometrics

The concept of multicollinearity for generalized linear models (GLMs) is discussed and compared to that for standard linear model. Several approaches for detecting multicollinearity are presented and shown to lead to the same diagnostic procedure. These are analyzed for the logistic, Poisson, negative binomial (NB), zero inflated Poisson (ZIP), and zero inflated negative binomial (ZINB) models. Estimation methods using maximum likelihood (ML), ridge, Liu, and Liu-type are presented. The Liu-type (two parameter) estimator is developed as suitable supplement to the ML estimator in case of sever multicollinearity. Simulation study and empirical applications are conducted to evaluate the Liu-type estimator in practice. It is then observed that for the optimal value of the shrinkage parameter along with a particular choice of the ridge parameter, the Liu-type estimator outperforms the ML estimator in terms of mean squared error (MSE) and mean absolute error (MAE) criteria. A Liu-type estimator is introduced for both ZIP and ZINB models. This is done through a simulation experiment and real dataset in which the optimal value of the shrinkage parameter is used

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