Adding structure to generalized additive models, with applications in ecology

TL;DR

This paper introduces three extensions to generalized additive models (GAMs) that effectively incorporate vector-valued covariates with structure, such as temporal or spatial data, especially in ecological applications, using the R package exttt{mgcv}.

Contribution

The paper presents novel extensions to GAMs—varying-coefficient, scalar-on-function, and distributed lag models—that handle structured vector covariates without losing information.

Findings

Extensions improve handling of structured covariates in ecology

Models can be fitted using the exttt{mgcv} package in R

Enhanced interpretability of covariate effects in ecological data

Abstract

Generalized additive models (GAMs) connecting a set of scalar covariates that map 1-1 to a response are commonly employed in ecology and beyond. However, covariates are often inherently non-scalar, taking multiple values for each observation of the response. They can sometimes have a temporal structure, e.g., a time series of temperatures, or a spatial structure, e.g., multiple soil pH measurements made at nearby locations. While aggregating or selectively summarizing such covariates to yield a scalar covariate allows the use of standard GAM fitting procedures, exactly how to do so can be problematic and information is necessarily lost. Naively including all $p$ components of a vector-valued covariate as $p$ separate covariates, say, without recognizing the structure, can lead to problems of multicollinearity, data sets that are excessively wide given the sample size, and difficulty extracting the primary signal provided by the covariate. Here we introduce three useful extensions to GAMs that efficiently and effectively handle vector-valued covariates without requiring one to choose aggregations or selective summarizations. These extensions are varying-coefficient, scalar-on-function and distributed lag models. While these models have existed for some time they remain relatively underused in ecology. This article aims to show when these models can be useful and how to fit them with the popular R package \mgcv{}.