TY - JOUR T1 - Coefficient of determination <em>R</em><sup>2</sup> and intra-class correlation coefficient ICC from generalized linear mixed-effects models revisited and expanded JF - bioRxiv DO - 10.1101/095851 SP - 095851 AU - Shinichi Nakagawa AU - Holger Schielzeth Y1 - 2017/01/01 UR - http://biorxiv.org/content/early/2017/03/06/095851.abstract N2 - 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, Jensen’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. ER -