Properties of the Maximum Likelihood Estimates and Bias Reduction for Logistic Regression Model

Abstract

A frequent problem in estimating logistic regression models is a failure of the likelihood maximization algorithm to converge. Although popular and extremely well established in bias correction for maximum likelihood estimates of the parameters for logistic regression, the behaviour and properties of the maximum likelihood method are less investigated. The main aim of this paper is to examine the behaviour and properties of the parameters estimates methods with reduction technique. We will focus on a method used a modified score function to reduce the bias of the maximum likelihood estimates. We also present new and interesting examples by simulation data with different cases of sample size and percentage of the probability of outcome variable.