Maximum Likelihood Estimation of Logistic Regression ...

Maximum Likelihood Estimation of Logistic Regression Models: Theory and Implementation Scott A. Czepiel . Abstract This article presents an overview of the Logistic Regression model for dependent variables having two or more discrete categorical levels. The Maximum Likelihood equations are derived from the probability distribution of the dependent variables and solved using the Newton- Raphson method for nonlinear systems of equations. Finally, a generic implementation of the algorithm is discussed. 1 Introduction Logistic Regression is widely used to model the outcomes of a categorical dependent variable. For categorical variables it is inappropriate to use linear Regression because the response values are not measured on a ratio scale and the error terms are not normally distributed.

Maximum Likelihood Estimation of Logistic Regression Models 5 YN i=1 (eyi K k=0 xik k)(1+e K k=0 xik k) ni (8) This is the kernel of the likelihood function to maximize. However, it is still cumbersometodi erentiate andcanbesimpli edagreat dealfurtherby taking its log. Since the logarithm is a monotonic function, any maximum of

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  Logistics, Maximum, Regression, Estimation, Likelihood, Logistic regression, Maximum likelihood estimation

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