RSS Matters

RSS Matters

The previous issue in this series can be found in the December, 2002 issue of Benchmarks Online: Interactive Graphics in R

Interactive Graphics in R (Part II): Kernel Density Estimation in One and Two Dimensions

By Dr. Rich Herrington, Research and Statistical Support Services Manager

This month we continue our discussion of elementary graphs in R. This month we examine histogram generation, 1-D and 2-D kernel density estimation. The GNU S language, "R" is used to implement this procedure. R is a statistical programming environment that utilizes the S and S-Plus language developed at Lucent Technologies. In the following document we illustrate the use of a GNU Web interface to the R engine on the "Kryton" server ( http://kryton.cc.unt.edu/cgi-bin/R/Rprog). This GNU Web interface is a derivative of the "Rcgi" Perl scripts available for download from the CRAN Website (http://www.cran.r-project.org), the main "R" Website. Scripts can be submitted interactively, edited, and then be re-submitted with changed parameters by selecting the hypertext link buttons that appear below the figures. For example, clicking the "Run Program" button below creates a vector of 100 random normal deviates; creates a histogram of the random numbers, and then overlays a nonparametric density estimate over the histogram. To view any text output, scroll to the bottom of the browser window. To view any graphical output, select the "Display Graphic" link. The script can be edited and resubmitted by changing the script in the form window and then selecting "Run the R Program". Selecting the browser "back page" button will return the reader to this document.

Simulating Data with a Known Covariance Matrix

Histograms and One-Dimensional Kernel Density Estimation

par(mfrow=c(2,1)) xhist <- hist(x, prob=T, ylim=c(0,.42)) lines(density(x)) seq.x<-seq(min(xhist$mids), max(xhist$mids),.01) lines(seq.x, dnorm(seq.x), col="red") legend(1.5,.4,c("Normal", "KDE"),lty=1,cex=.6, col=c(2,1)) yhist <- hist(y, prob=T, ylim=c(0,.40)) lines(density(y)) seq.y<-seq(min(yhist$mids), max(yhist$mids),.01) lines(seq.y, dnorm(seq.y), col="red") legend(1.5,.4,c("Normal", "KDE"),lty=1,cex=.6, col=c(2,1)) top <- max(c(xhist$counts, yhist$counts)) xrange <- c(-3,3) yrange <- c(-3,3) layout(matrix(c(2,0,1,3),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE) plot(x, y, xlim=xrange, ylim=yrange, xlab="", ylab="") abline(lm(y~x)) par(mar=c(0,3,1,1)) barplot(xhist$counts, axes=FALSE, ylim=c(0, top), space=0) par(mar=c(3,0,1,1)) barplot(yhist$counts, axes=FALSE, xlim=c(0, top), space=0, horiz=TRUE)

Contour and Perspective Plots: Two Dimensional Kernel Density Estimation

par(mfrow=c(2,2)) plot(x,y) f<-kde2d(x,y,n=50) contour(f$x,f$y,f$z) persp(f$x,f$y,f$z,shade=.3, theta = 120, phi = 45, expand = 0.5, col = "yellow") persp(f$x,f$y,f$z,shade=.3, theta = 300, phi = 45, expand = 0.5, col = "yellow")

Next Time

Next time we return to Part II of our series on multilevel modeling using the NLME (linear and nonlinear mixed effects) functions in R and S-Plus.

References

Krause, A. and Olson, M. (2000). The Basics of S and S-Plus, 2nd Edition. Springer Verlag: New York.