Many papers on logistic regression have only considered the logistic regression model with linear discriminant functions, but there are situations where quadratic discriminant functions are useful, and works better. However, the quadratic logistic regression model involves the estimation of a great number of unknown parameters, and this leads to computational difficulties when there are a great number of independent variables. This paper proposes to use a set of principal components of the explanatory variables, in order to reduce the dimensions in the problem, with continuous independent variables, and the computational costs for the parameter estimation in polytomous quadratic logistic regression, without loss of accuracy. Examples on datasets taken from the literature show that the quadratic logistic regression model, with principal components, is feasible and, generally, works better than the classical logistic regression model with linear discriminant functions, in terms of correct classification rates.
Polytomous logistic regression; quadratic logistic regression; principal components analysis