A thesis

Submitted to the council of the department of statistics \college of Administration &Economics\ University of Karbala as partial fulfillment of the requirements for the degree of Msc. of Statistics 

By
Ekhlas Azeez Mahal

Supervision
Asst. Prof Dr.  Enas Abd AL Hafedh Mohammed 

 Prof. Dr.  Mushtaq Kareem Abd AL Raheem 

This thesis addresses the modeling and analysis of hierarchical multilevel data using a two-level binary logistic regression model within both traditional and Bayesian frameworks, with a focus on improving parameter estimation accuracy and prediction efficiency. This thesis gains its significance from the hierarchical nature of the data used in many real-world applications, particularly in the banking sector, where observations overlap within different groups, making traditional single-level methods insufficient to accurately represent multiple sources of variation. The thesis aimed to develop a comprehensive statistical method that combines Bayesian hierarchical modeling and the Maximum A Posteriori (MAP) estimation method, utilizing the maximum entropy estimator as a prior value, to improve the accuracy of predictions and decision-making more efficiently. This proposed method was compared with the Maximum Likelihood Estimation (MLE) and the Bayesian Estimation using the MAP method (BM) in terms of statistical performance and estimation efficiency.
The theoretical aspect relied on a detailed review of the multilevel logistic regression model, traditional and Bayesian parameter estimation methods, highlighting the role of prior distributions, Bayes’ theorem, the concept of maximum entropy, and the mechanism of integrating it within BM. As for the experimental aspect, it included conducting a series of simulation experiments using the Monte Carlo method, covering various scenarios of sample sizes, number of groups, and number of explanatory variables at both levels. The performance of the adopted methods was evaluated using appropriate statistical criteria, most notably the mean squared error, McFadden’s pseudo-R-squared, and the likelihood ratio test. The proposed model was also applied to real data collected from three branches of the Rafidain Bank in Karbala Governorate, for the purpose of analyzing loan repayment behavior and predicting cases of financial default, taking into account individual effects and the effects of bank branches. The experimental and practical results showed the superiority of the BME method in terms of estimation accuracy and result stability compared to other methods, especially in cases of small samples and complex hierarchical structures.

A thesis

Submitted to the council of the department of statistics \college of Administration &Economics\ University of Karbala as partial fulfillment of the requirements for the degree of Msc. of Statistics 

By
Ekhlas Azeez Mahal

Supervision
Asst. Prof Dr.  Enas Abd AL Hafedh Mohammed 

 Prof. Dr.  Mushtaq Kareem Abd AL Raheem 

This thesis addresses the modeling and analysis of hierarchical multilevel data using a two-level binary logistic regression model within both traditional and Bayesian frameworks, with a focus on improving parameter estimation accuracy and prediction efficiency. This thesis gains its significance from the hierarchical nature of the data used in many real-world applications, particularly in the banking sector, where observations overlap within different groups, making traditional single-level methods insufficient to accurately represent multiple sources of variation. The thesis aimed to develop a comprehensive statistical method that combines Bayesian hierarchical modeling and the Maximum A Posteriori (MAP) estimation method, utilizing the maximum entropy estimator as a prior value, to improve the accuracy of predictions and decision-making more efficiently. This proposed method was compared with the Maximum Likelihood Estimation (MLE) and the Bayesian Estimation using the MAP method (BM) in terms of statistical performance and estimation efficiency.
The theoretical aspect relied on a detailed review of the multilevel logistic regression model, traditional and Bayesian parameter estimation methods, highlighting the role of prior distributions, Bayes’ theorem, the concept of maximum entropy, and the mechanism of integrating it within BM. As for the experimental aspect, it included conducting a series of simulation experiments using the Monte Carlo method, covering various scenarios of sample sizes, number of groups, and number of explanatory variables at both levels. The performance of the adopted methods was evaluated using appropriate statistical criteria, most notably the mean squared error, McFadden’s pseudo-R-squared, and the likelihood ratio test. The proposed model was also applied to real data collected from three branches of the Rafidain Bank in Karbala Governorate, for the purpose of analyzing loan repayment behavior and predicting cases of financial default, taking into account individual effects and the effects of bank branches. The experimental and practical results showed the superiority of the BME method in terms of estimation accuracy and result stability compared to other methods, especially in cases of small samples and complex hierarchical structures