The qqmath function makes great caterpillar plots of random effects using the output from the lmer package. That is, qqmath is great at plotting the intercepts from a hierarchical model with their errors around the point estimate. An example of the lmer and qqmath functions are below using the built-in data in the lme4 package called Dyestuff. The code will produce the hierarchical model and a nice plot using the ggmath function.
library("lme4")
data(package = "lme4")
# Dyestuff
# a balanced one-way classiï¬cation of Yield
# from samples produced from six Batches
summary(Dyestuff)
# Batch is an example of a random effect
# Fit 1-way random effects linear model
fit1 <- lmer(Yield ~ 1 + (1|Batch), Dyestuff)
summary(fit1)
coef(fit1) #intercept for each level in Batch
# qqplot of the random effects with their variances
qqmath(ranef(fit1, postVar = TRUE), strip = FALSE)$Batch
The last line of code produces a really nice plot of each intercept with the error around each estimate. But formatting the qqmath function seems to be very difficult, and I've been struggling to format the plot. I've come up with a few questions that I cannot answer, and that I think others could also benefit from if they are using the lmer/qqmath combination:
So far, adding any additional option in the qqmath function produce errors where I would not get errors if it was a standard plot, so I'm at a loss.
Also, if you feel there is a better package/function for plotting intercepts from lmer output, I'd love to hear it! (for example, can you do points 1-3 using dotplot?)
EDIT: I'm also open to an alternative dotplot if it can be reasonably formatted. I just like the look of a ggmath plot, so I'm starting with a question about that.
Didzis' answer is great! Just to wrap it up a little bit, I put it into its own function that behaves a lot like qqmath.ranef.mer()
and dotplot.ranef.mer()
. In addition to Didzis' answer, it also handles models with multiple correlated random effects (like qqmath()
and dotplot()
do). Comparison to qqmath()
:
require(lme4) ## for lmer(), sleepstudy
require(lattice) ## for dotplot()
fit <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
ggCaterpillar(ranef(fit, condVar=TRUE)) ## using ggplot2
qqmath(ranef(fit, condVar=TRUE)) ## for comparison
Comparison to dotplot()
:
ggCaterpillar(ranef(fit, condVar=TRUE), QQ=FALSE)
dotplot(ranef(fit, condVar=TRUE))
Sometimes, it might be useful to have different scales for the random effects - something which dotplot()
enforces. When I tried to relax this, I had to change the facetting (see this answer).
ggCaterpillar(ranef(fit, condVar=TRUE), QQ=FALSE, likeDotplot=FALSE)
## re = object of class ranef.mer
ggCaterpillar <- function(re, QQ=TRUE, likeDotplot=TRUE) {
require(ggplot2)
f <- function(x) {
pv <- attr(x, "postVar")
cols <- 1:(dim(pv)[1])
se <- unlist(lapply(cols, function(i) sqrt(pv[i, i, ])))
ord <- unlist(lapply(x, order)) + rep((0:(ncol(x) - 1)) * nrow(x), each=nrow(x))
pDf <- data.frame(y=unlist(x)[ord],
ci=1.96*se[ord],
nQQ=rep(qnorm(ppoints(nrow(x))), ncol(x)),
ID=factor(rep(rownames(x), ncol(x))[ord], levels=rownames(x)[ord]),
ind=gl(ncol(x), nrow(x), labels=names(x)))
if(QQ) { ## normal QQ-plot
p <- ggplot(pDf, aes(nQQ, y))
p <- p + facet_wrap(~ ind, scales="free")
p <- p + xlab("Standard normal quantiles") + ylab("Random effect quantiles")
} else { ## caterpillar dotplot
p <- ggplot(pDf, aes(ID, y)) + coord_flip()
if(likeDotplot) { ## imitate dotplot() -> same scales for random effects
p <- p + facet_wrap(~ ind)
} else { ## different scales for random effects
p <- p + facet_grid(ind ~ ., scales="free_y")
}
p <- p + xlab("Levels") + ylab("Random effects")
}
p <- p + theme(legend.position="none")
p <- p + geom_hline(yintercept=0)
p <- p + geom_errorbar(aes(ymin=y-ci, ymax=y+ci), width=0, colour="black")
p <- p + geom_point(aes(size=1.2), colour="blue")
return(p)
}
lapply(re, f)
}