I must admit, I took this on as a challenge because I was looking for different ways to show other datasets. I have normally done something along the lines of the scatterhist 2D graphs shown in other answers, but I've wanted to try my hand at rgl for a while.
I use your function to generate the data
gibbs<-function (n, rho) {
mat <- matrix(ncol = 2, nrow = n)
x <- 0
y <- 0
mat[1, ] <- c(x, y)
for (i in 2:n) {
x <- rnorm(1, rho * y, (1 - rho^2))
y <- rnorm(1, rho * x, (1 - rho^2))
mat[i, ] <- c(x, y)
}
mat
}
bvn <- gibbs(10000, 0.98)
Setup
I use rgl for the hard lifting, but I didn't know how to get the confidence ellipse without going to car. I'm guessing there are other ways to attack this.
library(rgl) # plot3d, quads3d, lines3d, grid3d, par3d, axes3d, box3d, mtext3d
library(car) # dataEllipse
Process the data
Getting the histogram data without plotting it, I then extract the densities and normalize them into probabilities. The *max variables are to simplify future plotting.
hx <- hist(bvn[,2], plot=FALSE)
hxs <- hx$density / sum(hx$density)
hy <- hist(bvn[,1], plot=FALSE)
hys <- hy$density / sum(hy$density)
## [xy]max: so that there's no overlap in the adjoining corner
xmax <- tail(hx$breaks, n=1) + diff(tail(hx$breaks, n=2))
ymax <- tail(hy$breaks, n=1) + diff(tail(hy$breaks, n=2))
zmax <- max(hxs, hys)
Basic scatterplot on the floor
The scale should be set to whatever is appropriate based on the distributions. Admittedly, the X and Y labels aren't placed beautifully, but that shouldn't be too hard to reposition based on the data.
## the base scatterplot
plot3d(bvn[,2], bvn[,1], 0, zlim=c(0, zmax), pch='.',
xlab='X', ylab='Y', zlab='', axes=FALSE)
par3d(scale=c(1,1,3))
Histograms on the back walls
I couldn't figure out how to get them automatically plotted on a plane in the overall 3D render, so I had to make each rect manually.
## manually create each histogram
for (ii in seq_along(hx$counts)) {
quads3d(hx$breaks[ii]*c(.9,.9,.1,.1) + hx$breaks[ii+1]*c(.1,.1,.9,.9),
rep(ymax, 4),
hxs[ii]*c(0,1,1,0), color='gray80')
}
for (ii in seq_along(hy$counts)) {
quads3d(rep(xmax, 4),
hy$breaks[ii]*c(.9,.9,.1,.1) + hy$breaks[ii+1]*c(.1,.1,.9,.9),
hys[ii]*c(0,1,1,0), color='gray80')
}
Summary Lines
## I use these to ensure the lines are plotted "in front of" the
## respective dot/hist
bb <- par3d('bbox')
inset <- 0.02 # percent off of the floor/wall for lines
x1 <- bb[1] + (1-inset)*diff(bb[1:2])
y1 <- bb[3] + (1-inset)*diff(bb[3:4])
z1 <- bb[5] + inset*diff(bb[5:6])
## even with draw=FALSE, dataEllipse still pops up a dev, so I create
## a dummy dev and destroy it ... better way to do this?
dev.new()
de <- dataEllipse(bvn[,1], bvn[,2], draw=FALSE, levels=0.95)
dev.off()
## the ellipse
lines3d(de[,2], de[,1], z1, color='green', lwd=3)
## the two density curves, probability-style
denx <- density(bvn[,2])
lines3d(denx$x, rep(y1, length(denx$x)), denx$y / sum(hx$density), col='red', lwd=3)
deny <- density(bvn[,1])
lines3d(rep(x1, length(deny$x)), deny$x, deny$y / sum(hy$density), col='blue', lwd=3)
Beautifications
grid3d(c('x+', 'y+', 'z-'), n=10)
box3d()
axes3d(edges=c('x-', 'y-', 'z+'))
outset <- 1.2 # place text outside of bbox *this* percentage
mtext3d('P(X)', edge='x+', pos=c(0, ymax, outset * zmax))
mtext3d('P(Y)', edge='y+', pos=c(xmax, 0, outset * zmax))
Final Product
One bonus of using rgl is that you can spin it around with your mouse and find the best perspective. Lacking making an animation for this SO page, doing all of the above should allow you the play-time. (If you spin it, you'll be able to see that the lines are slightly in front of the histograms and slightly above the scatterplot; otherwise I found intersections, so it looked noncontinuous at places.)
In the end, I find this a bit distracting (the 2D variants sufficed): showing the z-axis implies that there is a third dimension to the data; Tufte specifically discourages this behavior (Tufte, "Envisioning Information," 1990). However, with higher dimensionality, this technique of using RGL will allow significant perspective on patterns.
(For the record, Win7 x64, tested with R-3.0.3 in 32-bit and 64-bit, rgl v0.93.996, car v2.0-19.)
以下の 2 つの曲線の下のコードから生成されたサンプルのヒストグラムを使用して、これに似たものをプロットする方法を誰かが教えてくれるかどうか知りたいです
。R または Matlab を使用しますが、できれば R を使用します。
