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Rick Wicklin (@RickWicklin) made a recent post to the SAS blog on An exploratory technique for visualizing the distributions of 100 variables. It’s a very succinct tutorial on both the power of boxplots and how to make them in SAS (of course). I’m not one to let R be “out-boxed”, so I threw together a quick re-creation of his example, mostly as tutorial for any nascent R folks that come across it. (As an aside, I catch Rick’s and other cool, non-R stuff via the Stats Blogs blog aggregator.)

The R implementation (syntax notwithstanding) is extremely similar. First, we’ll need some packages to assist with data reshaping and pretty plotting:

 library(reshape2) library(ggplot2)

Then, we setup a list so we can pick from the same four distributions and set the random seed to make this example reproducible:

 dists <- c(rnorm, rexp, rlnorm, runif)   set.seed(1492)

Now, we generate a data frame of the 100 variables with 1,000 observations, normalized from 0-1:

 many_vars <- data.frame(sapply(1:100, function(x) {   # generate 1,000 random samples tmp <- sample(dists, 1)[](1000)   # normalize them to be between 0 & 1 (tmp - min(tmp)) / (max(tmp) - min(tmp))   }))

The sapply iterates over the numbers 1 through 100, passing each number into a function. Each iteration samples an object from the dists list (which are actual R functions) and then calls the function, telling it to generate 1,000 samples and normalize the result to be values between 0 & 1. By default, R will generate column names that begin with X:

 str(many_vars[1:5]) # show the structure of the first 5 cols   ## 'data.frame': 1000 obs. of 5 variables: ## $X1: num 0.1768 0.4173 0.5111 0.0319 0.0644 ... ##$ X2: num 0.217 0.275 0.596 0.785 0.825 ... ## $X3: num 0.458 0.637 0.115 0.468 0.469 ... ##$ X4: num 0.5186 0.0358 0.5927 0.1138 0.1514 ... ## $X5: num 0.2855 0.0786 0.2193 0.433 0.9634 ... We’re going to plot the boxplots, sorted by the third quantile (just like in Rick’s example), so we’ll calculate their rank and then use those ranks (shortly) to order a factor varible:  ranks <- names(sort(rank(sapply(colnames(many_vars), function(x) { as.numeric(quantile(many_vars[,x], 0.75)) })))) There’s alot going on in there. We pass the column names from the many_vars data frame to a function that will return the quantile we want. Since sapply preserves the names we passed in as well as the values, we extract them (via names) after we rank and sort the named vector, giving us a character vector in the order we’ll need:  str(ranks) ## chr [1:100] "X29" "X8" "X92" "X43" "X11" "X52" "X34" ... Just like in the SAS post, we’ll need to reshape the data into long format from wide format, which we can do with melt:  many_vars_m <- melt(as.matrix(many_vars)) str(many_vars_m) ## 'data.frame': 100000 obs. of 3 variables: ##$ Var1 : int 1 2 3 4 5 6 7 8 9 10 ... ## $Var2 : Factor w/ 100 levels "X1","X2","X3",..: 1 1 1 1 1 1 1 1 1 1 ... ##$ value: num 0.1768 0.4173 0.5111 0.0319 0.0644 ...

And, now we’ll use our ordered column names to ensure that our boxplots will be presented in the right order (it would be in alpha order if not). Factor variables in R are space-efficient and allow for handy manipulations like this (amongst other things). By default, many_vars_m$Var2 was in alpha order and this call just re-orders that factor.  many_vars_m$Var2 <- factor(many_vars_m$Var2, ranks) str(many_vars_m) ## 'data.frame': 100000 obs. of 3 variables: ##$ Var1 : int 1 2 3 4 5 6 7 8 9 10 ... ## $Var2 : Factor w/ 100 levels "X29","X8","X92",..: 24 24 24 24 24 24 24 24 24 24 ... ##$ value: num 0.1768 0.4173 0.5111 0.0319 0.0644 ...

Lastly, we plot all our hard work (click/touch for larger version):

 gg <- ggplot(many_vars_m, aes(x=Var2, y=value)) gg <- gg + geom_boxplot(fill="#BDD7E7", notch=TRUE, outlier.size=1) gg <- gg + labs(x="") gg <- gg + theme_bw() gg <- gg + theme(panel.grid=element_blank()) gg <- gg + theme(axis.text.x=element_text(angle=-45, hjust=0.001, size=5)) gg Here’s the program in it’s entirety:

 library(reshape2) library(ggplot2)   dists <- c(rnorm, rexp, rlnorm, runif)   set.seed(1) many_vars <- data.frame(sapply(1:100, function(x) { tmp <- sample(dists, 1)[](1000) (tmp - min(tmp)) / (max(tmp) - min(tmp)) }))   ranks <- names(sort(rank(sapply(colnames(many_vars), function(x) { as.numeric(quantile(many_vars[,x], 0.75)) }))))   many_vars_m <- melt(as.matrix(many_vars))   many_vars_m$Var2 <- factor(many_vars_m$Var2, ranks)   gg <- ggplot(many_vars_m, aes(x=Var2, y=value)) gg <- gg + geom_boxplot(fill="steelblue", notch=TRUE, outlier.size=1) gg <- gg + labs(x="") gg <- gg + theme_bw() gg <- gg + theme(panel.grid=element_blank()) gg <- gg + theme(axis.text.x=element_text(angle=-45, hjust=0.001)) gg

I tweaked the boxplot, using a notch and making the outliers take up a fewer pixels.

I’m definitely in agreement with Rick that this is an excellent way to compare many distributions.

Bonus points for the commenter who shows code to color the bars by which distribution generated them!