R2s for correlated data: phylogenetic models, LMMs, and GLMMs

Many researchers want to report an R2 to measure the variance explained by a model. When the model includes correlation among data, such as phylogenetic models and mixed models, defining an R2 faces two conceptual problems. (i) It is unclear how to measure the variance explained by predictor (independent) variables when the model contains covariances. (ii) Researchers may want the R2 to include the variance explained by the covariances by asking questions such as “How much of the data is explained by phylogeny?” Here, I investigate three R2s for phylogenetic and mixed models. R2resid is an extension of the ordinary least-squares R2 that weights residuals by variances and covariances estimated by the model; it is closely related to R2glmm presented by Nakagawa and Schielzeth (2013). R2pred is based on predicting each residual from the fitted model and computing the variance between observed and predicted values. R2lik is based on the likelihood of fitted models and therefore reflects the...