Illustration of the concept of conditioning on a random variable

conditioning.R

library("scatterplot3d")
library("MASS")

path <- "/Users/jakewestfall/Desktop/"

# simulate data from gaussian copula
covmat <- matrix(.9, nrow=3, ncol=3)
diag(covmat) <- 1
dat <- pnorm(mvrnorm(n=3000, mu=c(0,0,0), Sigma=covmat))
# pairs(dat)

# set up the plot params
png(paste0(path, "3d.png"), height=8, width=16,
    units="in", res=200, pointsize=20)
layout(cbind(1,2))

# scatterplot3d -----------------------------------------------------------

# draw the points under the plane
s3d <- scatterplot3d(
  dat[dat[,3] < .8,], pch=20, color=rgb(0, 0, 0, .4),
  xlim=0:1, ylim=0:1, zlim=0:1,
  xlab="X", ylab="", zlab="Y",
  main="Draws from joint distribution\nP(X, Y, Z)"
)

# draw the plane
s3d$plane3d(
  Intercept = .8, x.coef = 0, y.coef = 0,
  lty = 1, lwd = 0.25, draw_polygon = TRUE, draw_lines = FALSE,
  polygon_args = list(col = scales::alpha("cornsilk2", 0.5), lty = 1, lwd = 0.5)
)

# draw the points above the plane
s3d$points3d(dat[dat[,3] > .8,], pch=20, col=rgb(0, 0, 0, .4))

# Add rotated axis label
p2 <- s3d$xyz.convert(x = 1.3, y = .2, z = 0)
text(p2$x, p2$y, "Z", adj = 0.5, srt = 40, xpd = TRUE)


# 2D ----------------------------------------------------------------------

# scatterplot3d messes with the margins, so set them back...
par(mar=c(5,4,4,2))

# simulate even more data from the same copula
bigdat = pnorm(mvrnorm(n=1000000, mu=c(0,0,0), Sigma=covmat))

# empty plot
plot(x=0:1, y=0:1, cex=0, mgp=2:0, ylab="Z", xlab="X",
     main="Draws from conditional distribution\nP(X, Z | Y = 0.8)")

# background color
rect(xleft=-1, xright=2, ybottom=-1, ytop=2, col=scales::alpha("cornsilk2", 0.5))

# add the points
points(x=bigdat[abs(bigdat[,1] - .8) < .0005, 2],
       y=bigdat[abs(bigdat[,1] - .8) < .0005, 3],
       pch=19, col=rgb(0, 0, 0, .4))

dev.off()