On the Estimation and Properties of Logistic Regression Parameters

Abstract

Logistic regression is widely used as a popular model for the analysis of binary data with the areas of applications including physical, biomedical and behavioral sciences. In this study, the logistic regression model, as well as the maximum likelihood procedure for the estimation of its parameters, are introduced in detail. The study has been necessited with the fact that authors looked at the simulation studies of the logistic models but did not test sensitivity of the normal plots. Thefundamental assumption underlying classical results on the properties of MLE is that the stochastic law which determines the behaviour of the phenomenon investigated is known to lie within a specified parameter family of probability distribution (the mode!). This study focuses on investigating the asymptotic properties of maximum likelihood estimators for logistic regression models. More precisely, we show that the maximum likelihood estimators converge under conditions of fixed number of predictor variables to the real value of the parameters as the number of observations tends to infinity. We also show that the parameters estimates are normal in distribution by plotting the quantile plots and undertaking the Kolmogorov -Smirnov an the Shapiro- Wilks test for normality, where the result shows that the null hypothesis is to reject at 0.05% and conclude that parameters camefrom a normal distribution