{"id":3010,"date":"2014-09-10T09:59:17","date_gmt":"2014-09-10T14:59:17","guid":{"rendered":"http:\/\/rud.is\/b\/?p=3010"},"modified":"2018-03-07T16:44:24","modified_gmt":"2018-03-07T21:44:24","slug":"r-version-of-an-exploratory-technique-for-visualizing-the-distributions-of-100-variables","status":"publish","type":"post","link":"https:\/\/rud.is\/b\/2014\/09\/10\/r-version-of-an-exploratory-technique-for-visualizing-the-distributions-of-100-variables\/","title":{"rendered":"R version of “An exploratory technique for visualizing the distributions of 100 variables:”"},"content":{"rendered":"

Rick Wicklin (@[RickWicklin](https:\/\/twitter.com\/RickWicklin)) made a
\nrecent post to the SAS blog on
\n[An exploratory technique for visualizing the distributions of 100
\nvariables](http:\/\/blogs.sas.com\/content\/iml\/). It’s a very succinct tutorial on both the power of
\nboxplots and how to make them in SAS (of course). I’m not one to let R
\nbe “out-boxed”, so I threw together a quick re-creation of his example,
\nmostly as tutorial for any nascent R folks that come across it. (As an
\naside, I catch Rick’s and other cool, non-R stuff via the [Stats
\nBlogs](http:\/\/www.statsblogs.com\/) blog aggregator.)<\/p>\n

The R implementation (syntax notwithstanding) is extremely similar.
\nFirst, we’ll need some packages to assist with data reshaping and pretty
\nplotting:<\/p>\n

\r\nlibrary(reshape2)\r\nlibrary(ggplot2)\r\n<\/pre>\n
Then, we setup a list so we can pick from the same four distributions
\nand set the random seed to make this example reproducible:<\/p>\n
\r\ndists <- c(rnorm, rexp, rlnorm, runif)\r\n\r\nset.seed(1492)\r\n<\/pre>\n
Now, we generate a data frame of the `100` variables with `1,000`
\nobservations, normalized from `0`-`1`:<\/p>\n
\r\nmany_vars <- data.frame(sapply(1:100, function(x) {\r\n  \r\n  # generate 1,000 random samples\r\n  tmp <- sample(dists, 1)[[1]](1000)\r\n  \r\n  # normalize them to be between 0 & 1\r\n  (tmp - min(tmp)) \/ (max(tmp) - min(tmp))\r\n  \r\n}))\r\n<\/pre>\n
The `sapply` iterates over the numbers `1` through `100`, passing each
\nnumber into a function. Each iteration samples an object from the
\n`dists` list (which are actual R functions) and then calls the function,
\ntelling it to generate `1,000` samples and normalize the result to be
\nvalues between `0` & `1`. By default, R will generate column names that
\nbegin with `X`:<\/p>\n
\r\nstr(many_vars[1:5]) # show the structure of the first 5 cols\r\n\r\n## 'data.frame':    1000 obs. of  5 variables:\r\n##  $ X1: num  0.1768 0.4173 0.5111 0.0319 0.0644 ...\r\n##  $ X2: num  0.217 0.275 0.596 0.785 0.825 ...\r\n##  $ X3: num  0.458 0.637 0.115 0.468 0.469 ...\r\n##  $ X4: num  0.5186 0.0358 0.5927 0.1138 0.1514 ...\r\n##  $ X5: num  0.2855 0.0786 0.2193 0.433 0.9634 ...\r\n<\/pre>\n
We're going to plot the boxplots, sorted by the third quantile (just
\nlike in Rick's example), so we'll calculate their rank and then use
\nthose ranks (shortly) to order a factor varible:<\/p>\n
\r\nranks <- names(sort(rank(sapply(colnames(many_vars), function(x) {\r\n  as.numeric(quantile(many_vars[,x], 0.75))\r\n}))))\r\n<\/pre>\n
There's alot going on in there. We pass the column names from the
\n`many_vars` data frame to a function that will return the quantile we
\nwant. Since `sapply` preserves the names we passed in as well as the
\nvalues, we extract them (via `names`) after we rank and sort the named
\nvector, giving us a character vector in the order we'll need:<\/p>\n
\r\nstr(ranks)\r\n\r\n##  chr [1:100] \"X29\" \"X8\" \"X92\" \"X43\" \"X11\" \"X52\" \"X34\" ...\r\n<\/pre>\n
Just like in the SAS post, we'll need to reshape the data into [long
\nformat from wide
\nformat](http:\/\/www.cookbook-r.com\/Manipulating_data\/Converting_data_between_wide_and_long_format\/),
\nwhich we can do with `melt`:<\/p>\n
\r\nmany_vars_m <- melt(as.matrix(many_vars))\r\n\r\nstr(many_vars_m)\r\n\r\n## 'data.frame':    100000 obs. of  3 variables:\r\n##  $ Var1 : int  1 2 3 4 5 6 7 8 9 10 ...\r\n##  $ Var2 : Factor w\/ 100 levels \"X1\",\"X2\",\"X3\",..: 1 1 1 1 1 1 1 1 1 1 ...\r\n##  $ value: num  0.1768 0.4173 0.5111 0.0319 0.0644 ...\r\n<\/pre>\n
And, now we'll use our ordered column names to ensure that our boxplots
\nwill be presented in the right order (it would be in alpha order if
\nnot). Factor variables in R are space-efficient and allow for handy
\nmanipulations like this (amongst other things). By default,
\n`many_vars_m$Var2` was in alpha order and this call just re-orders that
\nfactor.<\/p>\n
\r\nmany_vars_m$Var2 <- factor(many_vars_m$Var2, ranks)\r\n\r\nstr(many_vars_m)\r\n\r\n## 'data.frame':    100000 obs. of  3 variables:\r\n##  $ Var1 : int  1 2 3 4 5 6 7 8 9 10 ...\r\n##  $ Var2 : Factor w\/ 100 levels \"X29\",\"X8\",\"X92\",..: 24 24 24 24 24 24 24 24 24 24 ...\r\n##  $ value: num  0.1768 0.4173 0.5111 0.0319 0.0644 ...\r\n<\/pre>\n
Lastly, we plot all our hard work (click\/touch for larger version):<\/p>\n
\r\ngg <- ggplot(many_vars_m, aes(x=Var2, y=value))\r\ngg <- gg + geom_boxplot(fill=\"#BDD7E7\", notch=TRUE, outlier.size=1)\r\ngg <- gg + labs(x=\"\")\r\ngg <- gg + theme_bw()\r\ngg <- gg + theme(panel.grid=element_blank())\r\ngg <- gg + theme(axis.text.x=element_text(angle=-45, hjust=0.001, size=5))\r\ngg\r\n<\/pre>\n
\"unnamed-chunk-9\"<\/a><\/p>\n
Here's the program in it's entirety:<\/p>\n
\r\nlibrary(reshape2)\r\nlibrary(ggplot2)\r\n\r\ndists <- c(rnorm, rexp, rlnorm, runif)\r\n\r\nset.seed(1)\r\nmany_vars <- data.frame(sapply(1:100, function(x) {\r\n  tmp <- sample(dists, 1)[[1]](1000)\r\n  (tmp - min(tmp)) \/ (max(tmp) - min(tmp))\r\n}))\r\n\r\nranks <- names(sort(rank(sapply(colnames(many_vars), function(x) {\r\n  as.numeric(quantile(many_vars[,x], 0.75))\r\n}))))\r\n\r\nmany_vars_m <- melt(as.matrix(many_vars))\r\n\r\nmany_vars_m$Var2 <- factor(many_vars_m$Var2, ranks)\r\n\r\ngg <- ggplot(many_vars_m, aes(x=Var2, y=value))\r\ngg <- gg + geom_boxplot(fill=\"steelblue\", notch=TRUE, outlier.size=1)\r\ngg <- gg + labs(x=\"\")\r\ngg <- gg + theme_bw()\r\ngg <- gg + theme(panel.grid=element_blank())\r\ngg <- gg + theme(axis.text.x=element_text(angle=-45, hjust=0.001))\r\ngg\r\n<\/pre>\n
I tweaked the boxplot, using a
\n[notch](https:\/\/sites.google.com\/site\/davidsstatistics\/home\/notched-box-plots)
\nand making the outliers take up a fewer pixels.<\/p>\n
I'm definitely in agreement with Rick that this is an excellent way to
\ncompare many distributions.<\/p>\n
Bonus points for the commenter who shows code to color the bars by which distribution generated them!<\/p>\n","protected":false},"excerpt":{"rendered":"
Rick Wicklin (@[RickWicklin](https:\/\/twitter.com\/RickWicklin)) made a recent post to the SAS blog on [An exploratory technique for visualizing the distributions of 100 variables](http:\/\/blogs.sas.com\/content\/iml\/). 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 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":3,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"","footnotes":""},"categories":[24,677,678,673,674,91],"tags":[810],"class_list":["post-3010","post","type-post","status-publish","format-standard","hentry","category-charts-graphs","category-data-analysis-2","category-data-visualization","category-datavis-2","category-dataviz","category-r","tag-post"],"yoast_head":"\nR version of "An exploratory technique for visualizing the distributions of 100 variables:" - rud.is<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/rud.is\/b\/2014\/09\/10\/r-version-of-an-exploratory-technique-for-visualizing-the-distributions-of-100-variables\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R version of "An exploratory technique for visualizing the distributions of 100 variables:" - rud.is\" \/>\n<meta property=\"og:description\" content=\"Rick Wicklin (@[RickWicklin](https:\/\/twitter.com\/RickWicklin)) made a recent post to the SAS blog on [An exploratory technique for visualizing the distributions of 100 variables](http:\/\/blogs.sas.com\/content\/iml\/). It’s a very succinct tutorial on both the power of boxplots and how to make them in SAS (of course). 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