Estimation in polytomous logistic model: Comparison of methods

Abstract

The logistic regression model is a powerful method for modeling the relationship between a categorical variable and a set of explanatory variables. In practice, however, the existence of maximum likelihood estimates is known to be dependent on the data configuration. In fact, the Maximum Likelihood Estimators (MLE) of unknown parameters exists if, and only if, there is data overlapping. The Hidden Logistic Regression (HLR) is an alternative model under which the observed response is related to the unobservable response. The Maximum Estimated Likelihood (MEL) method is also proposed, once it is immune to the complete or quasi-complete separation of data. The Principal Component Logistic Regression (PCLR) model is useful to reduce the number of dimensions of a logistic regression model with continuous covariates avoiding multicollinearity. In this paper we present an extension of the HLR and PCLR models as means for the solution of problems with polytomous responses. The main purpose is to compare the classificatory performance obtained by the models mentioned above with those of the Classical Logistic Regression (CLR) and Individualized Logistic regression (ILR) models, in the case of polytomous responses. The purpose is to propose an alternative approach for the parameter estimation problem in polytomous logistic models when the data groups are completely separated. Simulations results resulting from databases taken from the literature show that the proposed approach is feasible.