The mountainplot
package provide an extension to the lattice
package that allows for the construction of mountain plots, which are also known as folded empirical cumulative distribution plots.
library("knitr") opts_chunk$set(fig.align="center", fig.width=6, fig.height=6) options(width=90)
Load the package and use the singer
data from the lattice
package. Combine the first and second parts of each voice part
into a new variable called section
.
library("mountainplot") data(singer, package = "lattice") parts <- within(singer, { section <- voice.part section <- gsub(" 1", "", section) section <- gsub(" 2", "", section) section <- factor(section) }) # Change levels to logical ordering parts$section <- factor(parts$section, levels=c("Bass","Tenor","Alto","Soprano"))
A mountainplot, or folded empirical cumulative distribution function, is similar to an ordinary empirical CDF, but once the cumulative probability reaches 0.50, the CDF is inverted, decreasing back down instead of continuing upward.
Here is an example of the traditional empirical CDFs.
require(latticeExtra) # for ecdfplot ecdfplot(~height|section, data = parts, groups=voice.part, type='l', layout=c(1,4), main="Empirical CDF", auto.key=list(columns=2), as.table=TRUE)
Here is a view of the same data shown with a mountain plot.
mountainplot(~height|section, data = parts, groups=voice.part, type='l', layout=c(1,4), main="Folded Empirical CDF", auto.key=list(columns=4), as.table=TRUE)
@monti1995folded suggests that a mountain plot is helpful with exploring data and makes it easier to:
Additionally, the area under the curve is equal to the mean absolute deviation (MAD) @xue2011pfolded.
@huh1995exploring developed at the same time the concept of the flipped empirical distribution function. The following code creates a mountainplot of Hand's diabetic mice data, which can be compared to Huh's version.
dmice <- data.frame( albumen=c(156,282,197,297,116,127,119,29,253,122,349,110,143,64,26,86,122,455,655,14, 391,46,469,86,174,133,13,499,168,62,127,276,176,146,108,276,50,73, 82,100,98,150,243,68,228,131,73,18,20,100,72,133,465,40,46,34, 44), group=c(rep('normal',20), rep('alloxan', 18), rep('insulin', 19)) ) mountainplot(~albumen, data=dmice, group=group, auto.key=list(columns=3), main="Diabetic mice", xlab="Nitrogen-bound bovine serum albumen")
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