Estimation of log-logistic Regression Parameters Using Genetic Algorithm with Practical Application

A Thesis Submitted

Council of the College of Administration and Economics at the University of Karbala, which is part of the requirements for obtaining a master’s degree in

Statistics

Written by

Hussein Khalil Obaid Mikhlif

Supervised by

Prof. Dr. Mushtaq Kareem Abdel Rahem

Abstract

In this thesis, one of the most important non-linear regression models was studied, which is the binary log-logistic model, which is used in modeling and estimating any statistical applications, and then the parameters of this model were estimated by statistical estimation methods, but when estimating its parameters, a special problem appeared to us. When the number of parameters (P+1). And if numerical methods are used to estimate its parameters, sometimes these methods do not give a better solution, because they depend directly on the primitive capabilities of the model, and accordingly we will use and employ the usual methods of estimation after improving them through the followers of one of the modern algorithms genetic algorithm) in order to suit this type A non-linear regression model for estimating its parameters. Then we compare all estimation methods. In order to choose the best methods in terms of estimation by a number of models and different sample sizes in the simulation. And based on the statistical standard (mean square error (MSE)). The comparison was made between the usual estimation methods, which included (the method of greatest possibility. And the method of chi-square minimization, the method of weighted least squares) and in the contrasts the improved estimation methods by (Genetic Algorithm), which included the method of estimating the improved maximum possible (MLE.GA) and the method of estimating the improved chi-square minimization (MCSE.GA) as well as the method of stimating the weighted least squares Enhanced (WLSE.GA). In general, it was concluded that the (WLSE) method is the best among all the usual methods for estimating the model arameters. The (MCSE.GA) method was the best among all the improved estimation methods for estimating the binary (log-logistic) model, and the reason for that is due to These two methods had the lowest (MSE) in the simulation program for all abilities compared to the rest of the methods. As for the practical side, real data was used for a sample of (90) patients with heart disease. The data was modeled and the parameters of this model were estimated and the best method was chosen, which was reached in The experimental side through the occurrence of real deaths of the injured with the model in modeling these data and extracting the main cause of death is (smoking), as well as it was found that the (WLSE) method (MCSE.GA) They are accurate in estimating the parameters of the binary (log-logistic) model.

Estimation of log-logistic Regression Parameters Using Genetic Algorithm with Practical Application

A Thesis Submitted

Council of the College of Administration and Economics at the University of Karbala, which is part of the requirements for obtaining a master’s degree in

Statistics

Written by

Hussein Khalil Obaid Mikhlif

Supervised by

Prof. Dr. Mushtaq Kareem Abdel Rahem

Abstract

In this thesis, one of the most important non-linear regression models was studied, which is the binary log-logistic model, which is used in modeling and estimating any statistical applications, and then the parameters of this model were estimated by statistical estimation methods, but when estimating its parameters, a special problem appeared to us. When the number of parameters (P+1). And if numerical methods are used to estimate its parameters, sometimes these methods do not give a better solution, because they depend directly on the primitive capabilities of the model, and accordingly we will use and employ the usual methods of estimation after improving them through the followers of one of the modern algorithms genetic algorithm) in order to suit this type A non-linear regression model for estimating its parameters. Then we compare all estimation methods. In order to choose the best methods in terms of estimation by a number of models and different sample sizes in the simulation. And based on the statistical standard (mean square error (MSE)). The comparison was made between the usual estimation methods, which included (the method of greatest possibility. And the method of chi-square minimization, the method of weighted least squares) and in the contrasts the improved estimation methods by (Genetic Algorithm), which included the method of estimating the improved maximum possible (MLE.GA) and the method of estimating the improved chi-square minimization (MCSE.GA) as well as the method of stimating the weighted least squares Enhanced (WLSE.GA). In general, it was concluded that the (WLSE) method is the best among all the usual methods for estimating the model arameters. The (MCSE.GA) method was the best among all the improved estimation methods for estimating the binary (log-logistic) model, and the reason for that is due to These two methods had the lowest (MSE) in the simulation program for all abilities compared to the rest of the methods. As for the practical side, real data was used for a sample of (90) patients with heart disease. The data was modeled and the parameters of this model were estimated and the best method was chosen, which was reached in The experimental side through the occurrence of real deaths of the injured with the model in modeling these data and extracting the main cause of death is (smoking), as well as it was found that the (WLSE) method (MCSE.GA) They are accurate in estimating the parameters of the binary (log-logistic) model.