The model R squared and semi-partial R squared for the linear and
generalized linear mixed model (LMM and GLMM) are computed with confidence
limits. The R squared measure from Edwards et.al (2008)
This package computes model and semi partial R2 with confidence limits for the linear and generalized linear mixed model (LMM and GLMM). The R2 measure from Edwards et.al (2008) is extended to the GLMM using penalized quasi-likelihood (PQL) estimation (see Jaeger et al. 2016).
The R2 statistic is a well known tool that describes goodness-of-fit for a statistical model. In the linear model, R2 is interpreted as the proportion of variance in the data explained by the fixed predictors and semi-partial R2 provide standardized measures of effect size for subsets of fixed predictors. In the linear mixed model, numerous definitions of R2 exist and interpretations vary by definition. The r2glmm package computes R2 using three definitions:
Each interpretation can be used for model selection and is helpful for summarizing model goodness-of-fit. While the information criteria are useful tools for model selection, they do not quantify goodness-of-fit, making the R2 statistic an excellent tool to accompany values of AIC and BIC. Additionally, in the context of mixed models, semi-partial R2 and confidence limits are two useful and exclusive features of the r2glmm package.
The most up-to-date version of the r2glmm package is available on Github. To download the package from Github, after installing and loading the devtools package, run the following code from the R console:
Alternatively, There is a version of the package available on CRAN. To download the package from CRAN, run the following code from the R console:
The main function in this package is called r2beta. The r2beta function summarizes a mixed model by computing the model R2 statistic and semi-partial R2 statistics for each fixed predictor in the model. The r2glmm package computes R2 using three definitions. Below we list the methods, their interpretation, and an example of their application:
library(lme4)library(nlme)#>#> Attaching package: 'nlme'#> The following object is masked from 'package:lme4':#>#> lmListlibrary(r2glmm)data(Orthodont)# Compute the R2 statistic using the Kenward-Roger approach.m1 = lmer(distance ~ age*Sex + (1|Subject), data = Orthodont)m2 = lmer(distance ~ age + (1|Subject), data = Orthodont)(r2.m1 = r2beta(m1, method = 'kr', partial = T))#> Effect Rsq upper.CL lower.CL#> 1 Model 0.671 0.771 0.563#> 2 age 0.578 0.691 0.454#> 4 age:Sex 0.074 0.212 0.004#> 3 Sex 0.004 0.065 0.000(r2.m2 = r2beta(m2, method = 'kr', partial = T))#> Effect Rsq upper.CL lower.CL#> 1 Model 0.589 0.698 0.468#> 2 age 0.589 0.698 0.468
# m1 has a compound symmetric (CS) covariance structure.m1 = lme(distance ~ age*Sex, ~1|Subject, data = Orthodont)# m2 is an order 1 autoregressive (AR1) model with# gender-specific residual variance estimates.m2 = lme(distance ~ age*Sex, data=Orthodont,correlation = corAR1(form=~1|Subject),weights = varIdent(form=~1|Sex))# Compare the models(r2m1 = r2beta(m1,method='sgv'))#> Effect Rsq upper.CL lower.CL#> 1 Model 0.559 0.669 0.447#> 2 age 0.392 0.527 0.256#> 4 age:SexFemale 0.038 0.144 0.000#> 3 SexFemale 0.004 0.067 0.000(r2m2 = r2beta(m2,method='sgv'))#> Effect Rsq upper.CL lower.CL#> 1 Model 0.616 0.713 0.514#> 2 age 0.454 0.580 0.323#> 4 age:SexFemale 0.051 0.165 0.001#> 3 SexFemale 0.006 0.075 0.000
# Compute the R2 statistic using Nakagawa and Schielzeth's approach.(r2nsj = r2beta(m1, method = 'nsj', partial = TRUE))#> Effect Rsq upper.CL lower.CL#> 1 Model 0.410 0.540 0.290#> 2 age 0.261 0.398 0.137#> 4 age:SexFemale 0.021 0.105 0.000#> 3 SexFemale 0.002 0.055 0.000# Check the result with MuMIn's r.squaredGLMMr2nsj_mum = MuMIn::r.squaredGLMM(m1)all.equal(r2nsj[1,'Rsq'],as.numeric(r2nsj_mum), tolerance = 1e-3)#>  TRUE
The r2glmm package can compute Rβ2 for models fitted using the glmer function from the lme4 package. Note that this method is experimental in R and values of Rβ2 sometimes exceed 1. We recommend using the SAS macro available at https://github.com/bcjaeger/R2FixedEffectsGLMM/blob/master/Glimmix_R2_V3.sas. RΣ2 is more stable and can be computed for models fitted using either the glmer function or the glmmPQL function from the MASS package; however, minor differences in model estimation can lead to slight variation in the values of RΣ2.
library(lattice)library(MASS)cbpp$period = as.numeric(cbpp$period)# using glmer (based in lme4)gm1 <- glmer(formula=cbind(incidence, size-incidence) ~ poly(period,2) + (1|herd),data = cbpp, family = binomial)# using glmmPQL (based on nlme)pql1 <- glmmPQL(cbind(incidence, size-incidence) ~ poly(period,2),random = ~ 1|herd, family = binomial, data = cbpp)#> iteration 1#> iteration 2#> iteration 3#> iteration 4# Note minor differences in R^2_Sigmar2beta(model = gm1, method = 'sgv', data = cbpp)#> Effect Rsq upper.CL lower.CL#> 1 Model 0.191 0.420 0.048#> 2 poly(period, 2)1 0.180 0.397 0.029#> 3 poly(period, 2)2 0.016 0.161 0.000r2beta(model = pql1, method = 'sgv', data = cbpp)#> Effect Rsq upper.CL lower.CL#> 1 Model 0.210 0.438 0.059#> 2 poly(period, 2)1 0.194 0.411 0.036#> 3 poly(period, 2)2 0.025 0.182 0.000