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 journalArticlepeer-review

514 Citations (Scopus)
14 Downloads (Pure)


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 languageEnglish
Article numbere6876
Number of pages42
Publication statusPublished - 27 May 2019


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


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