Hierarchical generalized additive models in ecology: an introduction with mgcv

Eric J. Pedersen; David L. Miller; Gavin L. Simpson; Noam Ross

doi:10.7717/peerj.6876

Hierarchical generalized additive models in ecology: an introduction with mgcv

Eric J. Pedersen^*, David L. Miller, Gavin L. Simpson, Noam Ross

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we discuss an extension to two popular approaches to modeling complex structures in ecological data: the generalized additive model (GAM) and the hierarchical model (HGLM). The hierarchical GAM (HGAM), allows modeling of nonlinear functional relationships between covariates and outcomes where the shape of the function itself varies between different grouping levels. We describe the theoretical connection between HGAMs, HGLMs, and GAMs, explain how to model different assumptions about the degree of intergroup variability in functional response, and show how HGAMs can be readily fitted using existing GAM software, the mgcv package in R. We also discuss computational and statistical issues with fitting these models, and demonstrate how to fit HGAMs on example data. All code and data used to generate this paper are available at: github.com/eric-pedersen/mixed-effect-gams.

Original language	English
Article number	e6876
Number of pages	42
Journal	PeerJ
Volume	7
DOIs	https://doi.org/10.7717/peerj.6876 https://doi.org/10.7717/peerj.6876
Publication status	Published - 27 May 2019

Keywords

Generalized additive models
Hierarchical models
Time series
Functional regression
Smoothing
Regression
Community ecology
Tutorial
Nonlinear estimation

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10.7717/peerj.6876Licence: CC BY
10.7717/peerj.6876

Pedersen_2019_PeerJ_mgcv_CC
Copyright © 2019 Pedersen et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ) and either DOI or URL of the article must be cited.
Final published version, 4.47 MBLicence: CC BY

Hierarchical Generalized Additive Models: an introduction with mgcv
Pedersen, E. J. (Creator), Miller, D. L. (Creator), Simpson, G. L. (Creator) & Ross, N. (Creator), Zenodo, 2019
DOI: 10.5281/zenodo.2604627
Dataset

Cite this

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title = "Hierarchical generalized additive models in ecology: an introduction with mgcv",

abstract = "In this paper, we discuss an extension to two popular approaches to modeling complex structures in ecological data: the generalized additive model (GAM) and the hierarchical model (HGLM). The hierarchical GAM (HGAM), allows modeling of nonlinear functional relationships between covariates and outcomes where the shape of the function itself varies between different grouping levels. We describe the theoretical connection between HGAMs, HGLMs, and GAMs, explain how to model different assumptions about the degree of intergroup variability in functional response, and show how HGAMs can be readily fitted using existing GAM software, the mgcv package in R. We also discuss computational and statistical issues with fitting these models, and demonstrate how to fit HGAMs on example data. All code and data used to generate this paper are available at: github.com/eric-pedersen/mixed-effect-gams.",

keywords = "Generalized additive models, Hierarchical models, Time series, Functional regression, Smoothing, Regression, Community ecology, Tutorial, Nonlinear estimation",

author = "Pedersen, {Eric J.} and Miller, {David L.} and Simpson, {Gavin L.} and Noam Ross",

note = "This work was funded by Fisheries and Oceans Canada, Natural Science and Engineering Research Council of Canada (NSERC) Discovery Grant (RGPIN-2014-04032), by OPNAV N45 and the SURTASS LFA Settlement Agreement, managed by the U.S. Navy{\textquoteright}s Living Marine Resources Program under Contract No. N39430-17-C-1982, and by the USAID PREDICT-2 Program.",

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AU - Simpson, Gavin L.

AU - Ross, Noam

N1 - This work was funded by Fisheries and Oceans Canada, Natural Science and Engineering Research Council of Canada (NSERC) Discovery Grant (RGPIN-2014-04032), by OPNAV N45 and the SURTASS LFA Settlement Agreement, managed by the U.S. Navy’s Living Marine Resources Program under Contract No. N39430-17-C-1982, and by the USAID PREDICT-2 Program.

PY - 2019/5/27

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N2 - In this paper, we discuss an extension to two popular approaches to modeling complex structures in ecological data: the generalized additive model (GAM) and the hierarchical model (HGLM). The hierarchical GAM (HGAM), allows modeling of nonlinear functional relationships between covariates and outcomes where the shape of the function itself varies between different grouping levels. We describe the theoretical connection between HGAMs, HGLMs, and GAMs, explain how to model different assumptions about the degree of intergroup variability in functional response, and show how HGAMs can be readily fitted using existing GAM software, the mgcv package in R. We also discuss computational and statistical issues with fitting these models, and demonstrate how to fit HGAMs on example data. All code and data used to generate this paper are available at: github.com/eric-pedersen/mixed-effect-gams.

AB - In this paper, we discuss an extension to two popular approaches to modeling complex structures in ecological data: the generalized additive model (GAM) and the hierarchical model (HGLM). The hierarchical GAM (HGAM), allows modeling of nonlinear functional relationships between covariates and outcomes where the shape of the function itself varies between different grouping levels. We describe the theoretical connection between HGAMs, HGLMs, and GAMs, explain how to model different assumptions about the degree of intergroup variability in functional response, and show how HGAMs can be readily fitted using existing GAM software, the mgcv package in R. We also discuss computational and statistical issues with fitting these models, and demonstrate how to fit HGAMs on example data. All code and data used to generate this paper are available at: github.com/eric-pedersen/mixed-effect-gams.

KW - Generalized additive models

KW - Hierarchical models

KW - Time series

KW - Functional regression

KW - Smoothing

KW - Regression

KW - Community ecology

KW - Tutorial

KW - Nonlinear estimation

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DO - 10.7717/peerj.6876

M3 - Article

SN - 2167-8359

VL - 7

JO - PeerJ

JF - PeerJ

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ER -

Hierarchical generalized additive models in ecology: an introduction with mgcv

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Keywords

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Hierarchical Generalized Additive Models: an introduction with mgcv

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