Generalized Functional Additive Mixed Models

TL;DR

This paper introduces a flexible, comprehensive framework for additive regression models tailored to non-Gaussian functional responses, accommodating complex random effects and correlation structures, with practical implementation in R software.

Contribution

It presents a novel, unified approach for generalized functional additive mixed models applicable to diverse data types and correlation structures, with an open-source R implementation.

Findings

Demonstrates good performance through extensive simulations

Successfully applied to large-scale pig feeding data

Provides a versatile tool for complex functional data analysis

Abstract

We propose a comprehensive framework for additive regression models for non-Gaussian functional responses, allowing for multiple (partially) nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data as well as linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the index of the functional response. Our implementation handles functional responses from any exponential family distribution as well as many others like Beta- or scaled non-central $t$-distributions. Development is motivated by and evaluated on an application to large-scale longitudinal feeding records of pigs. Results in extensive simulation studies as well as replications of two previously published simulation studies for generalized functional mixed models demonstrate the good performance of our proposal. The approach is implemented in well-documented open source software in the "pffr()" function in R-package "refund".