How to scale density plots (for several variables)

Question

I have a melted data set which also includes data generated from normal distribution. I want to plot empirical density function of my data against normal distribution but the scales of the two produced density plots are different. I could find this post for two separate data sets:

Normalising the x scales of overlaying density plots in ggplot

but I couldn't figure out how to apply it to melted data. Suppose I have a data frame like this:

df<-data.frame(type=rep(c('A','B'),each=100),x=rnorm(200,1,2)/10,y=rnorm(200))
df.m<-melt(df)

using the code below:

qplot(value,data=df.m,col=variable,geom='density',facets=~type)

produces this graph:

How can I make the two densities comparable given the fact that normal distribution is the reference plot? (I prefer to use qplot instead of ggplot)

UPDATE: I want to produce something like this (i.e. in terms of plot-comparison) but with ggplot2:

plot(density(rnorm(200,1,2)/10),col='red',main=NA) #my data
par(new=T)
plot(density(rnorm(200)),axes=F,main=NA,xlab=NA,ylab=NA) # reference data

which generates this:

Answer 1

df<-data.frame(type=rep(c('A','B'),each=100),x = rnorm(200,1,2)/10, y = rnorm(200))
df.m<-melt(df)

require(data.table)
DT <- data.table(df.m)

Insert a new column with the scaled value into DT. Then plot.

This is the image code:

DT <- DT[, scaled := scale(value), by = "variable"]
str(DT)

ggplot(DT) +
  geom_density(aes(x = scaled, color = variable)) +
  facet_grid(. ~ type)

qplot(data = DT, x = scaled, color = variable,
      facets = ~ type, geom = "density")

# Using fill (inside aes) and alpha outside(so you don't get a legend for it)
ggplot(DT) +
  geom_density(aes(x = scaled, fill = variable), alpha = 0.2) +
  facet_grid(. ~ type)

qplot(data = DT, x = scaled, fill = variable, geom = "density", alpha = 0.2, facets = ~type)

# Histogram
ggplot(DT, aes(x = scaled, fill = variable)) +
  geom_histogram(binwidth=.2, alpha=.5, position="identity") +
  facet_grid(. ~ type, scales = "free")

qplot(data = DT, x = scaled, fill = variable, alpha = 0.2, facets = ~type)

Answer 2

Is this what you had in mind?

There's a built-in variable, ..scaled.. that does this automatically.

set.seed(1)
df<-data.frame(type=rep(c('A','B'),each=100),x=rnorm(200,1,2)/10,y=rnorm(200))
df.m<-melt(df)
ggplot(df.m) + 
  stat_density(aes(x=value, y=..scaled..,color=variable), position="dodge", geom="line")