Simulating an interaction effect in a lmer() model in R - r

Question

Is there an R package with a function that can:
(1) simulate the different values of an interaction variable,
(2) plot a graph that demonstrates the effect of the interaction on Y for different values of the terms in interaction, and
(3) works well with the models fitted with the lmer() function of the lme4 package?
I have looked in arm, ez, coefplot2, and fanovaGraph packages, but could not find what I was looking for.

Answer 1

I'm not sure about a package, but you can simulate data varying the terms in the interaction, and then graph it. Here is an example for a treatment by wave (i.e. longitudinal) interaction and the syntax to plot. I think the story behind the example is a treatment to improve oral reading fluency in school age children. The term of the interaction is modified by changing the function value for bX.
library(arm)
sim1 <- function (b0=50, bGrowth=4.672,bX=15, b01=.770413, b11=.005, Vint=771, Vslope=2.24, Verror=40.34) {
#observation ID
oID<-rep(1:231)
#participant ID
ID<-rep(1:77, each=3)
tmp2<-sample(0:1,77,replace=TRUE,prob=c(.5,.5))
ITT<-tmp2[ID]
#longitudinal wave: for example 0, 4, and 7 months after treatment
wave <-rep(c(0,4,7), 77)
bvaset<-rnorm(77, 0, 11.58)
bva<-bvaset[ID]
#random effect intercept
S.in <- rnorm(77, 0, sqrt(Vint))
#random effect for slope
S.sl<-rnorm(77, 0, sqrt(Vslope))
#observation level error
eps <- rnorm(3*77, 0, sqrt(Verror))
#Create Outcome as product of specified model
ORFset <- b0 + b01*bva+ bGrowth*wave +bX*ITT*wave+ S.in[ID]+S.sl[ID]*wave+eps[oID]
#if else statement to elimiante ORF values below 0
ORF<-ifelse(ORFset<0,0,ORFset)
#Put into a data frame
mydata <- data.frame( oID,ID,ITT, wave,ORF,bva,S.in[ID],S.sl[ID],eps)
#run the model
fit1<-lmer(ORF~1+wave+ITT+wave:ITT+(1+wave|ID),data=mydata)
fit1
#grab variance components
vc<-VarCorr(fit1)
#Select Tau and Sigma to select in the out object
varcomps=c(unlist(lapply(vc,diag)),attr(vc,"sc")^2)
#Produce object to output
out<-c(coef(summary(fit1))[4,"t value"],coef(summary(fit1))[4,"Estimate"],as.numeric(varcomps[2]),varcomps[3])
#outputs T Value, Estimate of Effect, Tau, Sigma Squared
out
mydata
}
mydata<-sim1(b0=50, bGrowth=4.672, bX=1.25, b01=.770413, b11=.005, Vint=771, Vslope=2.24, Verror=40.34)
xyplot(ORF~wave,groups=interaction(ITT),data=mydata,type=c("a","p","g"))

Answer 2

Try plotLMER.fnc() from the languageR package, or the effects package.

Answer 3

The merTools package has some functionality to make this easier, though it only applies to working with lmer and glmer objects. Here's how you might do it:
library(merTools)
# fit an interaction model
m1 <- lmer(y ~ studage * service + (1|d) + (1|s), data = InstEval)
# select an average observation from the model frame
examp <- draw(m1, "average")
# create a modified data.frame by changing one value
simCase <- wiggle(examp, var = "service", values = c(0, 1))
# modify again for the studage variable
simCase <- wiggle(simCase, var = "studage", values = c(2, 4, 6, 8))
After this, we have our simulated data which looks like:
simCase
y studage service d s
1 3.205745 2 0 761 564
2 3.205745 2 1 761 564
3 3.205745 4 0 761 564
4 3.205745 4 1 761 564
5 3.205745 6 0 761 564
6 3.205745 6 1 761 564
7 3.205745 8 0 761 564
8 3.205745 8 1 761 564
Next, we need to generate prediction intervals, which we can do with merTools::predictInterval (or without intervals you could use lme4::predict)
preds <- predictInterval(m1, level = 0.9, newdata = simCase)
Now we get a preds object, which is a 3 column data.frame:
preds
fit lwr upr
1 3.312390 1.2948130 5.251558
2 3.263301 1.1996693 5.362962
3 3.412936 1.3096006 5.244776
4 3.027135 1.1138965 4.972449
5 3.263416 0.6324732 5.257844
6 3.370330 0.9802323 5.073362
7 3.410260 1.3721760 5.280458
8 2.947482 1.3958538 5.136692
We can then put it all together to plot:
library(ggplot2)
plotdf <- cbind(simCase, preds)
ggplot(plotdf, aes(x = service, y = fit, ymin = lwr, ymax = upr)) +
geom_pointrange() + facet_wrap(~studage) + theme_bw()
Unfortunately the data here results in a rather uninteresting, but easy to interpret plot.