Some One and Two Parameter Estimators for the Multicollinear Logistic Regression Model: Theory, Simulation, and Applications

Authors

Md Ariful HoqueFollow

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

First Advisor's Name

B. M. GOLAM KIBRIA

First Advisor's Committee Title

Committee chair

Second Advisor's Name

FLORENCE GEORGE

Second Advisor's Committee Title

COMMITTEE MEMBER

Third Advisor's Name

WENSONG WU

Third Advisor's Committee Title

COMMITTEE MEMBER

Keywords

statistical methodology, statistical models, statistical theory

Date of Defense

6-16-2023

Abstract

The logistic regression model (LRM) is one of the most widely used models and plays an important role in analyzing and making predictions about binary data. The most popularly used estimation technique is the maximum likelihood estimator (MLE) in LRM. However, the MLE becomes unstable and gives misleading results in the presence of multicollinearity among the regressors. The ridge regression estimator has been used as an alternative method to solve the multicollinearity problem for both linear and non-linear regression models. The objective of this thesis is to propose some new estimators, namely Stein’s estimators for ridge regression and Kibria and Lukman estimator (KLE), and compare their performance with some existing estimators, namely maximum likelihood estimator, ridge regression estimator, Liu estimator, almost unbiased ridge and Liu estimators, adjusted Liu estimator, James stein’s estimator, Kibria and Lukman estimator, Dorugade estimator and Modified ridge estimator for the logistic regression model to solve the multicollinearity problem. The bias, covariance matrix, and mean square error matrix for each of the estimators are provided. A Monte Carlo simulation has been conducted to compare the performance of different estimators. We consider the smaller MSE value as a performance criterion. From the simulation study, it is evident that all proposed estimators performed better than the maximum likelihood estimator. Finally, real-life data is analyzed to illustrate the findings of the thesis. Some promising estimators are recommended for the practitioners.

Identifier

FIDC011154

Recommended Citation

Hoque, Md Ariful, "Some One and Two Parameter Estimators for the Multicollinear Logistic Regression Model: Theory, Simulation, and Applications" (2023). FIU Electronic Theses and Dissertations. 5421.
https://digitalcommons.fiu.edu/etd/5421