Tuesday, March 18, 2008

Plotting contours


Plenty of packages allow you to plot contours of a "z" value; however, I wanted to be able to plot a specific density contour of a sample from a bivariate distribution over a plot that was a function of the x and y parameters. The example only plots the density of x and y; however, if you set plot.dens=FALSE, the contours will be added to the active display device (i.e., over an image(x,y,function(x,y){...})).

This function also lets you specify the line widths and types for each of the contours.
###########################################
## drawcontour.R

## Written by J.D. Forester, 17 March 2008
###########################################

##This function draws an approximate density contour based on
##empirical, bivariate data.


##change testit to FALSE if sourcing the file
testit=TRUE


draw.contour<-function(a,alpha=0.95,plot.dens=FALSE, line.width=2, line.type=1, limits=NULL, density.res=300,spline.smooth=-1,...){
##a is a list or matrix of x and y coordinates (e.g., a=list("x"=rnorm(100),"y"=rnorm(100)))
## if a is a list or dataframe, the components must be labeled "x" and "y"
## if a is a matrix, the first column is assumed to be x, the second y
##alpha is the contour level desired
##if plot.dens==TRUE, then the joint density of x and y are plotted,
## otherwise the contour is added to the current plot.
##density.res controls the resolution of the density plot

##A key assumption of this function is that very little probability mass lies outside the limits of
## the x and y values in "a". This is likely reasonable if the number of observations in a is large.

require(MASS)
require(ks)
if(length(line.width)!=length(alpha)){
line.width <- rep(line.width[1],length(alpha))
}

if(length(line.type)!=length(alpha)){
line.type <- rep(line.type[1],length(alpha))
}

if(is.matrix(a)){
a=list("x"=a[,1],"y"=a[,2])
}
##generate approximate density values
if(is.null(limits)){
limits=c(range(a$x),range(a$y))
}
f1<-kde2d(a$x,a$y,n=density.res,lims=limits)

##plot empirical density
if(plot.dens) image(f1,...)

if(is.null(dev.list())){
##ensure that there is a window in which to draw the contour
plot(a,type="n",xlim=limits[1:2],ylim=limits[3:4],...)
}

##estimate critical contour value
## assume that density outside of plot is very small

zdens <- rev(sort(f1$z))
Czdens <- cumsum(zdens)
Czdens <- (Czdens/Czdens[length(zdens)])
for(cont.level in 1:length(alpha)){
##This loop allows for multiple contour levels
crit.val <- zdens[max(which(Czdens<=alpha[cont.level]))]

##determine coordinates of critical contour
b.full=contourLines(f1,levels=crit.val)
for(c in 1:length(b.full)){
##This loop is used in case the density is multimodal or if the desired contour
## extends outside the plotting region
b=list("x"=as.vector(unlist(b.full[[c]][2])),"y"=as.vector(unlist(b.full[[c]][3])))

##plot desired contour
line.dat<-xspline(b,shape=spline.smooth,open=TRUE,draw=FALSE)
lines(line.dat,lty=line.type[cont.level],lwd=line.width[cont.level])
}
}
}

##############################
##Test the function
##############################

##generate data
if(testit){
n=10000
a<-list("x"=rnorm(n,400,100),"y"=rweibull(n,2,100))
draw.contour(a=a,alpha=c(0.95,0.5,0.05),line.width=c(2,1,2),line.type=c(1,2,1),plot.dens=TRUE, xlab="X", ylab="Y")
}

3 comments:

NightlordTW said...
This comment has been removed by the author.
NightlordTW said...

Thanks a lot for your code! I used it to visualize a multivariate skew normal distribution in maximum likelihood estimation

NerdFever said...

Howdy! I'm excited to see this code, but R is telling me there is no such package as ks ... Is it a change that's happened in the last few years? Am I missing something? Advice appreciated! Thanks!