Principal component estimation of functional logistic regression: discussion of two different approaches

Abstract

Over the last few years many methods have been developed for analyzing functional data with different objectives. The purpose of this paper is to predict a binary response variable in terms of a functional variable whose sample information is given by a set of curves measured without error. In order to solve this problem we formulate a functional logistic regression model and propose its estimation by approximating the sample paths in a finite dimensional space generated by a basis. Then, the problem is reduced to a multiple logistic regression model with highly correlated covariates. In order to reduce dimension and to avoid multicollinearity, two different approaches of functional principal component analysis of the sample paths are proposed. Finally, a simulation study for evaluating the estimating performance of the proposed principal component approaches is developed.

Keywords:

• Functional data analysis
• Logistic regression
• Principal components

Acknowledgements

This research has been funded by BFM2000-1466 project from the Spanish Ministry of Science and Technology. The authors thanks an anonymous referee for helpful comments and suggestions that have contributed to improve the final version of this paper.