# 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

### 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)?

Partitioning explained variance to fixed effects by comparing r squared (R2) between linear mixed models

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

## References

Jaeger et al 2017.  An R2 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/