@article {Nakagawa095851, author = {Shinichi Nakagawa and Holger Schielzeth}, title = {Coefficient of determination R2 and intra-class correlation coefficient ICC from generalized linear mixed-effects models revisited and expanded}, elocation-id = {095851}, year = {2017}, doi = {10.1101/095851}, publisher = {Cold Spring Harbor Laboratory}, abstract = {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{\textquoteright}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.}, URL = {https://www.biorxiv.org/content/early/2017/03/06/095851}, eprint = {https://www.biorxiv.org/content/early/2017/03/06/095851.full.pdf}, journal = {bioRxiv} }