How to Make Models Add Up — A Primer on GLMMs

Abstract

Many problems in the analysis of ecological data have the format where there is an observed response that may be predicted by several covariates. Although the response can take several forms (e.g. measurements, counts, observations of presence/absence), and the covariates can also vary (e.g. be measurements themselves, or be grouped according to the treatment applied, the time or location of of sampling, etc.), most of these problems can be handled in a single framework, the Generalized Linear Mixed Model (GLMM). The framework encompasses regression, ANOVA, generalized linear models, and equivalent models with random as well as fixed effects. Here, the different parts of the GLMM are described, building from regression and ANOVA to show how the extra components — the wider range of distributions, and random effects — can be added into the same framework, and how the parameters of the fitted model can be estimated and interpreted. Being able to handle data with GLMMs helps ecologists to analyse the majority of their data.