Supplementary Material
Example Code for Calculating R2LMM(M) and R2LMM(C)
setwd("Your working directory path") # This needs to be updated to whatever directory the data is located on
your computer
#This code includes how to calculate marginal and conditional R2 values, as well as p-values for a linear mixed
model.
NH4.DATA<-read.csv(file="NH4.DATA.csv", header=T) #This .csv files being read in needs to have Vf, Uvol, and
all potential predictors for each chamber
#Note - before proceeding with the code you should check assumptions of different tests (code not included
here)
#Load in packages necessary for the code:
library(arm)
library(lme4)
#First we will calculate the marginal and conditional Rsquared:
#We first write a function to calculate R2LMM
# Rsquare GLME code from jonlefcheck.net blog post:
#http://jonlefcheck.net/2013/03/13/r2-for-linear-mixed-effects-models/
#last accessed in Oct 2014. The code was modified from the original code included
#in Nakagawa and Schielzeth 2013.
rsquared.glme=function(modlist) {
# Iterate over each model in the list
do.call(rbind,lapply(modlist,function(i) {
# For models fit using lm
if(class(i)=="lm") {
Rsquared.mat=data.frame(Class=class(i),Family="Gaussian",
Marginal=summary(i)$r.squared,Conditional=NA,AIC=AIC(i)) }
# For general linear models fit using lme4
else if(class(i)=="lmerMod" | class(i)=="merLmerTest") {
# Get variance of fixed effects by multiplying coefficients by design matrix
VarF=var(as.vector(fixef(i) %*% t(i@pp$X)))
# Get variance of random effects by extracting variance components
VarRand=colSums(do.call(rbind,lapply(VarCorr(i),function(j) j[1])))
# Get residual variance
VarResid=attr(VarCorr(i),"sc")^2
# Calculate marginal R-squared (fixed effects/total variance)
Rm=VarF/(VarF+VarRand+VarResid)
# Calculate conditional R-squared (fixed effects+random effects/total variance)
Rc=(VarF+VarRand)/(VarF+VarRand+VarResid)
# Bind R^2s into a matrix and return with AIC values
Rsquared.mat=data.frame(Class=class(i),Family="Gaussian",Marginal=Rm,Conditional=Rc,
AIC=AIC(update(i,REML=F))) }
#For generalized linear models (family=="binomial") fit using lme4
else if(class(i)=="glmerMod" & summary(i)$family=="binomial") {
# Get variance of fixed effects by multiplying coefficients by design matrix
VarF=var(as.vector(fixef(i) %*% t(i@pp$X)))
# Get variance of random effects by extracting variance components
VarRand=colSums(do.call(rbind,lapply(VarCorr(i),function(j) j[1])))
# Get residual variance
VarResid=attr(VarCorr(i),"sc")^2
# Calculate marginal R-squared
Rm=VarF/(VarF+VarRand+pi^2/3)
# Calculate conditional R-squared (fixed effects+random effects/total variance)
Rc=(VarF+VarRand)/(VarF+VarRand+pi^2/3)
# Bind R^2s into a matrix and return with AIC values
Rsquared.mat=data.frame(Class=class(i),Family=summary(i)$family,Marginal=Rm,Conditional=Rc,AIC=AIC(i)) }
#For generalized linear models (family=="poisson") fit using lme4
else if(class(i)=="glmerMod" & summary(i)$family=="poisson") { print("GLMM fit to Poisson dist not yet
supported") }
# For model fit using nlme
else if(class(i)=="lme") {
# Get design matrix of fixed effects from model
Fmat=model.matrix(eval(i$call$fixed)[-2],i$data)
# Get variance of fixed effects by multiplying coefficients by design matrix
VarF=var(as.vector(fixef(i) %*% t(Fmat)))
# Get variance of random effects by extracting variance components
VarRand=sum(suppressWarnings(as.numeric(VarCorr(i)[rownames(VarCorr(i))!=
"Residual",1])),na.rm=T)
# Get residual variance
VarResid=as.numeric(VarCorr(i)[rownames(VarCorr(i))=="Residual",1])
# Calculate marginal R-squared (fixed effects/total variance)
Rm=VarF/(VarF+VarRand+VarResid)
# Calculate conditional R-squared (fixed effects+random effects/total variance)
Rc=(VarF+VarRand)/(VarF+VarRand+VarResid)
# Bind R^2s into a matrix and return with AIC values
Rsquared.mat=data.frame(Class=class(i),Marginal=Rm,Conditional=Rc,
AIC=AIC(update(i,method="ML")))
} else { print("Function requires models of class lm, lme, mer, or merMod")
}}))}
#Next we create a null and alternative model
nh4.null.model<-lmer(LOG.NH4.VF~1+(1|SITE), data=NH4.DATA)
nh4.lmm<-lmer(LOG.NH4.VF~LOG.WS.AREA*WS+(1|SITE), data=NH4.DATA)
#And we find the marginal and conditional R2 values for each model:
rsquared.glme(list(nh4.null.model, nh4.lmm))
#Next we use lmerTest to get P-values
#Note that the lmerTest package makes calculating LMM R2s impossible, therefore
#p-values must be calculated after R2s.
library(lmerTest)
#Re-run your LMM
nh4.lmm<-lmer(LOG.NH4.VF~(LOG.WS.AREA+WS)^2+(1|SITE), data=NH4.DATA)
#Get the p-values for the model
anova(nh4.lmm)