New Methods for Solving Maximum Likelihood Estimating Equations of Logistic and Probit Regression Models

Several iterative methods are available in literature for solving the Maximum Likelihood Estimating Equations (MLEEs) of logistic and probit regression models. Generalized Self Consistency (GSC) method is such an existing iterative method. We introduce a new idea using the paired observations and combine it with the GSC method for both logistic and probit regression models and propose several new methods for solving MLEEs. For probit regression model, we introduce a linear approximation method for finding the exact solution of MLEEs. We illustrate the proposed methods with a real data as well as a simulated data and compare their performances with the existing methods. We investigate some theoretical properties of our estimates. We also present a meaningful method of choosing the initial values of parameters for the iterative methods