# R2 in Generalized Linear mixed Models

**Bolkers GLMM FAQ:** Model summaries (goodness-of-fit, decomposition of variance, etc.) http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#how-do-i-compute-a-coefficient-of-determination-r2-or-an-analogue-for-glmms

**Listserve thread:** http://thread.gmane.org/gmane.comp.lang.r.lme4.devel/3281, including a comment by Doug Bates: http://thread.gmane.org/gmane.comp.lang.r.lme4.devel/3281

**Listserve thread:** http://thread.gmane.org/gmane.comp.lang.r.lme4.devel/684

### Cross Validated

A problem that interests me: small marging $R^2$ values for otherwise interesting models: Is it worth reporting small fixed-effect R2 (marginal R2), large model R2 (conditional R2)?

Is R2 useful or dangerous? (general issues with R2)

Misc. references on R2 in GLMMs at Proportion of explained variance in a mixed-effects model

Good explanation of Nakagawa and Schielzeth (2013) at: R2 for mixed models with multiple fixed and random effects

An open question: R2 for negative binomial GLMM: R2 from a generalized linear mixed-effects models (GLMM) using a negative binomial distribution

In response to the question Calculating R2 in mixed models using Nakagawa & Schielzeth’s (2013) R2glmm method, some re-posts a response from Douglas Bates where he voices his extreme skepticism about R2 for mixed models.

A related topics: Does the variance of a sum equal the sum of the variances?

## R Packages for R2

muMIn::`r.squaredGLMM`

piecewiseSEM::rsquared

sjstats::r2

sjstats:cod “coefficient of discrimination” for logistic regression. See Tjur T (2009) Coefficients of determination in logistic regression models – a new proposal: The coefficient of discrimination. The American Statistician, 63(4): 366-372

sjstats:rsme “root mean square error”

Documentation for sjstats discusses how ICC can be used to investigate amount of variance due to clustering

## R Packages for related stuff

rptR: Repeatability estimation for Gaussian and non-Gaussian data; An introduction to repeatability estimation with rptR

## References

Jaeger et al 2017. An *R*^{2} statistic for fixed effects in the generalized linear mixed model. http://www.tandfonline.com/doi/abs/10.1080/02664763.2016.1193725?journalCode=cjas20

LaHuis et al. 2014. Explained Variance Measures for Multilevel Models. http://journals.sagepub.com/doi/abs/10.1177/1094428114541701

Tjur T (2009) Coefficients of determination in logistic regression models – a new proposal: The coefficient of discrimination. The American Statistician, 63(4): 366-372

http://www.tandfonline.com/doi/abs/10.1198/tast.2009.08210

Assessing the Fit of Regression Models

http://www.theanalysisfactor.com/assessing-the-fit-of-regression-models/