Supplementary material from "The coefficient of determination R 2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded"

However, estimating R 2 for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R 2 that we called R 2 GLMM for Poisson and binomial GLMMs, but not for other distributional families.

Similarly, we earlier discussed how to estimate intra-class correlation coefficients ICC using Poisson and binomial GLMMs. In this paper, we expand our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs.