Functional PLS logit regression model

Abstract

Functional logistic regression has been developed to forecast a binary response variable from a functional predictor. In order to fit this model, it is usual to assume that the functional observations and the parameter function of the model belong to a same finite space generated by a basis of functions. This consideration turns the functional model into a multiple logit model whose design matrix is the product of the matrix of sample paths basic coefficients and the matrix of the inner products between basic functions. The likelihood estimation of the parameter function of this model is very inaccurate due to the high dependence structure of the so obtained design matrix (multicollinearity). In order to solve this drawback several approaches have been proposed. These employ standard multivariate data analysis methods on the design matrix. This is the case of the functional principal component logistic regression model. As an alternative a functional partial least squares logit regression model is proposed, that has as covariates a set of partial least squares components of the design matrix of the multiple logit model associated to the functional one.