Machine learning

Function (biology)

Ecology

Programming language

Generalized linear model

Multilevel model

Set (abstract data type)

Code (set theory)

Generalized linear mixed model

Mathematics

Evolutionary biology

Biology

Hierarchical database model

Data mining

Computer science

Extension (predicate logic)

Theoretical computer science

Hierarchical generalized linear model

Additive model

Covariate

Mixed model

Generalized additive model

PeerJ

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.

Hierarchical generalized additive models in ecology: an introduction with mgcv