A novel generalized additive scalar-on-function regression model for partially observed multidimensional functional data: An application to air quality classification

TL;DR

This paper introduces a generalized additive scalar-on-function regression model capable of handling partially observed multidimensional functional data without imputation, demonstrated through simulations and an air quality classification case study.

Contribution

It presents a novel regression approach that accommodates incomplete functional data of varying dimensions using basis expansions and penalized likelihood estimation.

Findings

Effective handling of incomplete functional data demonstrated in simulations.

Accurate discrimination of air pollution levels in a real-world case study.

Model flexibility with basis choice not restricted to B-splines.

Abstract

In this work we propose a generalized additive functional regression model for partially observed functional data. Our approach accommodates functional predictors of varying dimensions without requiring imputation of missing observations. Both the functional coefficients and covariates are represented using basis function expansions, with B-splines used in this study, though the method is not restricted to any specific basis choice. Model coefficients are estimated via penalized likelihood, leveraging the mixed model representation of penalized splines for efficient computation and smoothing parameter estimation.The performance of the proposed approach is assessed through two simulation studies: one involving two one-dimensional functional covariates, and another using a two-dimensional functional covariate. Finally, we demonstrate the practical utility of our method in an application to air-pollution classification in Dimapur, India, where images are treated as observations of a two-dimensional functional variable. This case study highlights the models ability to effectively handle incomplete functional data and to accurately discriminate between pollution levels.