Nonlinear Ordinal Logistic Regression Using Covariates Obtained by Radial Basis Function Neural Networks Models

Abstract

This paper proposes a nonlinear ordinal logistic regression method based on the hybridization of a linear model and radial basis function (RBF) neural network models for ordinal regression. The process for obtaining the coefficients is carried out in several steps. In the first step we use an evolutionary algorithm to determine the structure of the RBF neural network model, in a second step we transform the initial feature space (covariate space) adding the nonlinear transformations of the input variables given by the RBFs of the best individual in the final generation of the evolutionary algorithm. Finally, we apply an ordinal logistic regression in the new feature space. This methodology is tested using 8 benchmark problems from the UCI repository. The hybrid model outperforms both the linear and the nonlinear part obtaining a good compromise between them and better results in terms of accuracy and ordinal classification error.