Using ggplot2: Create faceted scatterplot with scaled and moved density - r

Question

I would like to plot some data as a scatter plot using facet_wrap, while superimposing some information such as a linear regression and the density.
I managed to do all that, but the density values are out of proportion with respect to my points, which is a normal thing since these points are far away. Nevertheless, I'd like to scale and move my density curve so that it is clearly visible; I don't care about it's real values but more about its shape.
Here is an exaggerated minimum working example of what I have:
set.seed(48151623)
mydf <- data.frame(x1=rnorm(mean=5,n=100),x2=rnorm(n=100,mean=10),x3=rnorm(n=100,mean=20,sd=3))
mydf$var <- mydf$x1 + mydf$x2 * mydf$x3
mydf.wide <- melt(mydf,id.vars='var',measure.vars=c(1:3))
ggplot(data=mydf.wide,aes(x=value,y=var)) +
geom_point(colour='red') +
geom_smooth(method='lm') +
stat_density(aes(x=value,y=..scaled..),position='identity',geom='line') +
facet_wrap(~variable,scale='free_x')
Which results in:
What I would like resembles to this ugly hack:
stat_density(aes(x=value,y=..scaled..*100+200),position='identity',geom='line')
Ideally, I would use y=..scaled..* diff(range(value)) + min(value) but when I do this I get an error saying that 'value' was not found. I suspect the problem is related to the faceting, but I would prefer to keep my facets.
How can I scale and move the density curve in this case?

Answer 1

I suggest to make two plots and combine them with grid.arrange:
p1 <- ggplot(data=mydf.wide,aes(x=value,y=var)) +
geom_point(colour='red') +
geom_smooth(method='lm') +
facet_wrap(~variable,scale='free_x') +
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank(),
plot.margin = unit(c(1, 1, 0, 0.5), "lines"))
p2 <- ggplot(data=mydf.wide,aes(x=value,y=var)) +
stat_density(aes(x=value,y=..scaled..),position='identity',geom='line') +
facet_wrap(~variable,scale='free_x') +
theme(strip.background=element_blank(),
strip.text=element_blank(),
plot.margin = unit(c(-1, 1, 0.5, 0.35), "lines"))
library(gridExtra)
grid.arrange(p1, p2, heights = c(2,1))

Answer 2

I'm not sure if this completely answers your question, but it was too long to put in a comment, so... In response to your second chunk of code in your question, since you've already defined x=value, you can use x instead of value in your definition of y.
stat_density(aes(x=value,y=..scaled..*diff(range(x)) +
min(x)),position='identity',geom='line')
This seems to fix your error and produces the following plot:
The only problem is, of course, if you have data with low y-values, then you're still going to overlap your density curves with your scatterplot. But, if this isn't the case, I personally think this is a fairly informative figure, as long as you can communicate effectively that the y axis values aren't important in interpreting the density curves--only the shapes of the curves are important.

Answer 3

I appreciate the answers of everyone, which led me to better understand ggplot underlying mechanisms. I also realize how awkward my requirement is; ggplot is not going to solve my problem.
I managed to do what I wanted not by using ggplot stat_density but to directly calculate my densities in another data frame:
set.seed(48151623)
mydf <- data.frame(x1=rnorm(mean=5,n=100),x2=rnorm(n=100,mean=10),x3=rnorm(n=100,mean=20,sd=3))
mydf$var <- mydf$x1 + mydf$x2 * mydf$x3
mydf.wide <- melt(mydf,id.vars='var',measure.vars=c(1:3))
mydf.densities <- do.call('rbind',lapply(unique(mydf.wide$variable), function(var) {
tmp <- mydf.wide[which(mydf.wide$variable==var),c('var','value')]
dfit <- density(tmp$value,cut=0)
scaledy <-dfit$y/max(dfit$y) * diff(range(tmp$var)) + min(tmp$var)
data.frame(x=dfit$x,y=scaledy,variable=rep(var,length(dfit$x)))
}))
ggplot(data=mydf.wide,aes(x=value,y=var)) +
geom_point(colour='red') +
geom_smooth(method='lm') +
geom_line(aes(x=x,y=y),data=mydf.densities) +
facet_wrap(~variable,scale='free_x')
(I know that the construction of mydf.densities is a bit obfuscated, but I will work on that later).
I'm giving out the bounty to the most voted solution at the end of the day, for your troubles.