Comparison of Two Methods for Estimating Parameters of the Model Binary Logistic Regression

Abstract

This paper we deal with one of the most important nonlinear regression models widely used in modeling statistical applications, which is the binary logistic regression model, and then estimating the parameters of this model using statistical estimation methods. However, while using this model we face a problem in estimating its parameters as the number of parameters is (p+1), and finding the estimation of parameters using numerical methods sometimes does not provide the best solution because it depends on primitive estimations. In this paper, some ordinary estimation methods are employed to fit the estimation of the parameters of this type of non-linear regression model, and then we compare these estimation methods. Further, the comparison includes some of the important estimation methods, which are the ordinary estimation methods that included the Weighted Least Squares Method (WLS), and the Bayes Method (BM). In order to choose the best method for estimating, by taking a number of models and different sample sizes and using the statistical standard mean error squares (MSE) for the logistic model estimations for the purpose of comparison. Among the preferred methods for estimating model parameters, and it was generally concluded that the WLS method provides the MSE of estimators compared to the other methods. On the practical side, this model was also used to model data for people with diabetes and to estimate parameters using the best methods, and it was reached by comparing patients with diabetes. A census of diabetes with those who did not have diabetes with the appropriateness of the model in modeling this type of data and extracting the main cause of diabetes incidence, which is insulin, as well as the accuracy of the methods in estimating the model parameters.