## Electronic Journal of Statistics

### Generalized functional additive mixed models

#### 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 and shifted $t$-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.

#### Article information

Source
Electron. J. Statist., Volume 10, Number 1 (2016), 1455-1492.

Dates
First available in Project Euclid: 31 May 2016

https://projecteuclid.org/euclid.ejs/1464710238

Digital Object Identifier
doi:10.1214/16-EJS1145

Mathematical Reviews number (MathSciNet)
MR3507370

Zentralblatt MATH identifier
1341.62242

#### Citation

Scheipl, Fabian; Gertheiss, Jan; Greven, Sonja. Generalized functional additive mixed models. Electron. J. Statist. 10 (2016), no. 1, 1455--1492. doi:10.1214/16-EJS1145. https://projecteuclid.org/euclid.ejs/1464710238

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#### Supplemental materials

• Code to reproduce results for Section 4. Contains code for the simulations and replication studies in Section 4 as well an R Markdown document with graphs of typical results for the Binomial data in Section 4.1.