| Abstract: |
"The binary logistic regression (BLR) model is used as an alternative to the commonly used linear regression model when the response variable is binary. As in the linear regression model, there can be a relationship between the predictor variables in a BLR, especially when they are continuous, thus giving rise to the problem of multicollinearity. The efficiency of maximum likelihood estimator (MLE) is low in estimating the parameters of BLR when there is multicollinearity alternatively, the ridge estimator (RR), the Liu estimator (LE), the Liu-type estimator (LTE) and The Modified Ridge-Type estimator (MRTE) were developed to replace MLE. However, in this study, we compared all estimators by the mean squares errors (MSE) to get the best estimator that mitigates the effect of multicollinearity.
The main objective of this thesis is to provide a clear path for what one should do when faced with the multicollinearity problem, particularly in the logistic regression model (LRM), where the response variable may not be normally distributed, as it is supposed to be in the linear regression analysis. The issue of multicollinearity, which is well-known to affect the maximum likelihood estimator by a factor of two, may lead to inaccurate maximum probability estimations, which creates ambiguity when analyzing effects. On the response variable, explanatory variables. In the logistic regression model, some approaches for detecting multicollinearity are presented.
To overcome this problem, biased estimation is commonly applied solution to the problem caused by multicollinearity. The ridge, Liu, Liu-type, and modified Ridge-Type estimators are the four often used biased estimators that are the subject of this work in order to address the problem of multicollinearity in particular. The logistic regression model summaries a review of these biased estimators. The main focus of this thesis is on logistic regression models for
count and categorical data. Aspects of computation are explored, and methods for calculating estimators of interest and the LRM are demonstrated in detail.
Results studies have been proven that Liu is better than MRTE in some cases, and MRTE is better than Liu in others, but all the obtained estimates are ultimately better than the maximum-likelihood method in the case of multicollinearity.
This thesis is organized as follows: Chapter one presents the definition of logistic regression model, its hypotheses and types, definition of multicollinearity problem, its consequences, diagnostics, and remedy methods in logistic regression model. Chapter two presents the previous studies on the multicollinearity problem, the previous studies on the ridge regression estimator, the previous studies on the Liu estimator, the previous studies on the Liu-type estimator, and the previous studies on the modified Ridge-type regression estimator. Chapter three presents the method of maximum likelihood for estimating the parameters of the logistic regression model, methods of dealing with the problem of multicollinearity, and other methods of dealing with the problem multicollinearity. Chapter four presents the Simulation definition and simulation model design to compare the proposed estimators as closely as possible with different levels of linear correlation between explanatory variables in the presence of different sample sizes, simulation results, relative efficiency of comparison estimates, and practicality.
Appendix A contains tables of simulation results, Appendix B shows some graphs summarizing the performance of the selected estimators.
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