PT - JOURNAL ARTICLE
AU - Shinichi Nakagawa
AU - Holger Schielzeth
TI - Coefficient of determination <em>R</em><sup>2</sup> and intra-class correlation coefficient ICC from generalized linear mixed-effects models revisited and expanded
AID - 10.1101/095851
DP - 2017 Jan 01
TA - bioRxiv
PG - 095851
4099 - http://biorxiv.org/content/early/2017/03/06/095851.short
4100 - http://biorxiv.org/content/early/2017/03/06/095851.full
AB - The coefficient of determination R2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R2 for (generalized) linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R2 that we called R2GLMM 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, but not for other distributional families. In this article, we expand our methods to all the other non-Gaussian distributions such as negative binomial and gamma GLMMs. While expanding our approach, we highlight two useful concepts, Jensenâ€™s inequality and the delta method, both of which help us in understanding the properties of GLMMs. We illustrate the implementation of our extension by worked examples in the R environment although our method can be used regardless of statistical environments.