# Generalized Functional Additive Mixed Models

arXiv: https://arxiv.org/abs/1506.05384 · HTML: https://mlsanity.com/paper/1506.05384/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2015.

## Built on by (most cited first, 3 of 3)

- [Neural Networks for Scalar Input and Functional Output](https://mlsanity.com/paper/2208.05776/) (2022)
- [Functional additive models on manifolds of planar shapes and forms](https://mlsanity.com/paper/2109.02624/) (2021)
- [Enhancing Functional Data Analysis with Sequential Neural Networks: Advantages and Comparative Study](https://mlsanity.com/paper/2311.01875/) (2023)

## Abstract (arXiv)

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".