Comparison of some Logistic Regression Methodologies in Supervised Classification for Functional Data

Logistic regression for functional data is a statistical technique for modeling the relationship between functional predictor variables and a binary or multiclass outcome variable. The model’s basic structure remains the same as that of conventional logistic regression, where the objective is to model the probability of an event occurring as a function of the inputs, which, in this case, can be functions of continuous real variables. One of the main advantages of using functional data is that each data is observed at different points of a shared interval instead of fixed points in the interval, which can be interpreted as vectors. Logistic regression for functional data is a predictive and descriptive analysis tool in several disciplines. However, its practical application requires the use of theory related to infinite-dimensional spaces in obtaining parameter estimates, which leads to complexity in the implementation of such models. For this reason, this work provides a detailed exposition of the application of methodologies related to polynomials, Fourier series, and B-Splines in parameter estimation in functional data classification problems using logistic regression. Subsequently, a comparison is made in two problems between the methodologies mentioned above and the classical approach. The best performance is obtained by the methodology using the Fourier series; nonetheless, it is statistically equivalent to splines and the classical approach.