Varying-coefficient functional additive models

TL;DR

This paper introduces a new varying coefficient functional additive model that captures nonlinear relationships between functional predictors and scalar responses, with applications in environmental and crop yield analysis.

Contribution

It extends existing models to nonlinear settings and provides an interpretable, flexible approach for analyzing the influence of exogenous variables on responses.

Findings

Effective in capturing nonlinear relationships

Demonstrated through simulation studies

Applied successfully to crop yield data

Abstract

We extend the varying coefficient functional linear model to the nonlinear model and propose a varying coefficient functional additive model. The proposed method can represent the relationship between functional predictors and a scalar response where the response depends on an exogenous variable.It captures the nonlinear structure between variables and also provides interpretable relationship of them. The model is estimated through basis expansions and penalized likelihood method, and then the tuning parameters included at the estimation procedure are selected by a model selection criterion. Simulation studies are provided to show the effectiveness of the proposed method. We also apply it to the analysis of crop yield data and then investigate how and when the environmental factor relates to the amount of the crop yield.