Add 2D conditional distributions (in a third dimension) to 2D scatterplot in R

Question

Can anyone think of a way to add, to a 2D scatterplot, a third dimension that houses distinct distributions for Y|X=120, Y|X=140, and Y|X=160? I'm trying to include theoretical standard normals for starters (but would eventually like to include the empirical distributions).

For reference, here's a ggplot2 depiction of the 2D scatterplot

df <- data.frame(x = c(replicate(5, 120), replicate(7, 140), replicate(6, 160)),
                 y = c(c(79, 84, 90, 94, 98), c(80, 93, 95, 103, 108, 113, 115),
                       c(102, 107, 110, 116, 118, 125)))

library(dplyr)
df <- df %>% group_by(x) %>% mutate(gp.mn = mean(y))

library(ggplot2)
( ggplot(df, aes(x = x)) + geom_point(aes(y = y)) + geom_line(aes(y = gp.mn)))

I'm essentially trying to replicate an image I created in .tpx:

I'm not tied to any particular 3D package, but plot3Drgl can be used to generate a 2D plot similar to the one above:

library(plot3Drgl)
scatter2Drgl(df$x, df$y, xlab = "x", ylab = "y")
scatter2Drgl(df$x, df$gp.mn, type = "l", add = TRUE, lwd = 4)

My hope was to use the 2D plot as a building block for a pseudo-3D rgl plot, however, incorporating the distributions into a third dimension (rgl or otherwise) is eluding me. Any thoughts?

Answer 1

Maybe this will help. (I've never been very happy with he ggplot paradigm so I'm showing a base graphics version that someone can translate.) I also thought adding the group means to the df-object confused things so I'm only using the oritignal df.

 aggregate(y~x,df, FUN=function(y) c(mn=mean(y),sd=sd(y))  )
#--------
    x       y.mn       y.sd
1 120  89.000000   7.615773
2 140 101.000000  12.476645
3 160 113.000000   8.294577
#----------
png(); plot(df, xlim=c(110,170) )
lines( x= 120 - 100*dnorm(seq(89-2*7.6,89+2+7.6,length=25), 89, 7.6), 
       y= seq(89-2*7.6,89+2+7.6,length=25) )
lines( x=140 - 100*dnorm(seq(101-2*12.5,101+2*12.5,length=25), 101, 12.5), 
       y- seq(89-2*7.6,101+2+12.5,length=25) );dev.off()

The basic strategy is to reverse the argument order (and expand the distribution value by multiplying by a factor on the scale of the plotted points) and then "translate" the distributions so they are adjacent to the points they are derived from.