Examining of the multicollinearity in poisson regression model

One of the most encountered problems in regression analysis is multicollinearity. In fact, in all types of regression models, explanatory variables may be related, and due to these relations between them, the reliability of the analysis results decreases. The Maximum Likelihood method, which is the standard estimation technique in the Pois son Regression model, in the presence of multicollinearity can lead to larger variances and wider confidence intervals of the estimated parameters. To solve this problem, one of the popular approach is the use of biased estimation techniques. In this study, after mentioning the counting data and the regression models used for the counting data, some biased estimation techniques that can be used in the presence of multicollinearity in the Poisson Regression model are emphasized. In the thesis study, we considered Po isson Ridge (PR) and Poisson Liu (PL) estimators, which are biased estimators using a single bias parameter, and their combination the Poisson Liu Type estimator which is the estimation with a two bias parameters. Also we used two different formulas for the bias parameters of the Poisson Liu Type estimator, and we named the estimators as PLT1 and PLT2. Performances of the considered estimators were compared according to the Mean Square Error criterion via Monte Carlo simulation. In the simulation study, for various correlation levels (low, medium and high), sample size and the number of explanatory variable the performances of biased estimation techniques were examined. After the simulation study, the parameters estimations on two real data sets using the biased estimation techniques. The data set is the Aircraft Damage data set and the data was taken from literature. The other data set is the English Premier league data set about the number of won matches for each of the 20 teams during the 2023 and 2024 football season. We compiled the second data set. The analysis results performed on the sets were found to be consistent with the simulation results. A general result of this thesis study is that when the number of explanatory variables is low, PLT1 estimator shows the best performance. When the number of explanatory variables is high, PLT2 estimator has the best performance. Key words: Poisson Regression Model, Multicollinearity, Poisson Ridge Estimator, Poisson Liu Estimator, Poisson Liu Type estimator