Category Archives: R

PSA: R’s rnorm() and mvrnorm() use different spreads

Quick public service announcement for my fellow R nerds:

R has two commonly-used random-Normal generators: rnorm and MASS::mvrnorm. I was foolish and assumed that their parameterizations were equivalent when you’re generating univariate data. But nope:

  • Base R can generate univariate draws with rnorm(n, mean, sd), which uses the standard deviation for the spread.
  • The MASS package has a multivariate equivalent, mvrnorm(n, mu, Sigma), which uses the variance-covariance matrix for the spread. In the univariate case, Sigma is the variance.

I was using mvrnorm to generate a univariate random variable, but giving it the standard deviation instead of the variance. It took me two weeks of debugging to find this problem.

Dear reader, I hope this cautionary tale reminds you to check R function arguments carefully!

Data sanity checks: Data Proofer (and R analogues?)

I just heard about Data Proofer (h/t Nathan Yau), a test suite of sanity-checks for your CSV dataset.

It checks a few basic things you’d really want to know but might forget to check yourself, like whether any rows are exact duplicates, or whether any columns are totally empty.
There are things I always forget to check until they cause a bug, like whether geographic coordinates are within -180 to 180 degrees latitude or longitude.
And there are things I never think to check, though I should, like whether there are exactly 65k rows (probably an error exporting from Excel) or whether integers are exactly at certain common cutoff/overflow values.
I like the idea of automating this. It certainly wouldn’t absolved me of the need to think critically about a new dataset—but it might flag some things I wouldn’t have caught otherwise.

(They also do some statistical checks for outliers; but being a statistician, this is one thing I do remember to do myself. (I’d like to think) I do it more carefully than any simple automated check.)

Does an R package like this exist already? The closest thing in spirit that I’ve seen is testdat, though I haven’t played with that yet. If not, maybe testdat could add some more of Data Proofer’s checks. It’d become an even more valuable tool to run whenever you load or import any tabular dataset for the first time.

Why bother with magrittr

I’ve seen R users swooning over the magrittr package for a while now, but I couldn’t make heads or tails of all these scary %>% symbols. Finally I had time for a closer look, and it seems potentially handy indeed. Here’s the idea and a simple toy example.

So, it can be confusing and messy to write (and read) functions from the inside out. This is especially true when functions take multiple arguments. Instead, magrittr lets you write (and read) functions from left to right.

Say you need to compute the LogSumExp function \log\left(\sum_{i=1}^n\exp(x_i)\right), and you’d like your code to specify the logarithm base explicitly.

In base R, you might write
log(sum(exp(MyData)), exp(1))
But this is a bit of a mess to read. It takes a lot of parentheses-matching to see that the exp(1) is an argument to log and not to one of the other functions.

Instead, with magrittr, you program from left to right:
MyData %>% exp %>% sum %>% log(exp(1))
The pipe operator %>% takes output from the left and uses it as the first argument of input on the right. Now it’s very clear that the exp(1) is an argument to log.

There’s a lot more you can do with magrittr, but code with fewer nested parentheses is already a good selling point for me.

Apart from cleaning up your nested functions, this approach to programming might be helpful if you write a lot of JavaScript code, for example if you make D3.js visualizations. R’s magrittr pipe is similar in spirit to JavaScript’s method chaining, so it might make context-switching a little easier.

Statistical Graphics and Visualization course materials

I’ve just finished teaching the Fall 2015 session of 36-721, Statistical Graphics and Visualization. Again, it is a half-semester course designed primarily for students in the MSP program (Masters of Statistical Practice) in the CMU statistics department. I’m pleased that we also had a large number of students from other departments taking this as an elective.

For software we used mostly R (base graphics, ggplot2, and Shiny). But we also spent some time on Tableau, Inkscape, D3, and GGobi.

We covered a LOT of ground. At each point I tried to hammer home the importance of legible, comprehensible graphics that respect human visual perception.

Pie chart with remake

Remaking pie charts is a rite of passage for statistical graphics students

My course materials are below. Not all the slides are designed to stand alone, but I have no time to remake them right now. I’ll post some reflections separately.

Download all materials as a ZIP file (38 MB), or browse individual files:
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About to teach Statistical Graphics and Visualization course at CMU

I’m pretty excited for tomorrow: I’ll begin teaching the Fall 2015 offering of 36-721, Statistical Graphics and Visualization. This is a half-semester course designed primarily for students in our MSP program (Masters in Statistical Practice).

A large part of the focus will be on useful principles and frameworks: human visual perception, the Grammar of Graphics, graphic design and interaction design, and more current dataviz research. As for tools, besides base R and ggplot2, I’ll introduce a bit of Tableau, D3.js, and Inkscape/Illustrator. For assessments, I’m trying a variant of “specs grading”, with a heavy use of rubrics, hoping to make my expectations clear and my TA’s grading easier.

Di Cook, LDA and CART classification boundaries on Flea Beetles dataset

Classifier diagnostics from Cook & Swayne’s book

My initial course materials are up on my department webpage.
Here are the

  • syllabus (pdf),
  • first lecture (pdf created with Rmd), and
  • first homework (pdf) with dataset (csv).

(I’ll probably just use Blackboard during the semester, but I may post the final materials here again.)

It’s been a pleasant challenge to plan a course that can satisfy statisticians (slice and dice data quickly to support detailed analyses! examine residuals and other model diagnostics! work with data formats from rectangular CSVs through shapefiles to social networks!) … while also passing on lessons from the data journalism and design communities (take design and the user experience seriously! use layout, typography, and interaction sensibly!). I’m also trying to put into practice all the advice from teaching seminars I’ve taken at CMU’s Eberly Center.

Also, in preparation, this summer I finally enjoyed reading more of the classic visualization books on my list.

  • Cleveland’s The Elements of Graphing Data and Robbins’ Creating More Effective Graphs are chock full of advice on making clear graphics that harness human visual perception correctly.
  • Ware’s Information Visualization adds to this the latest research findings and a ton of useful detail.
  • Cleveland’s Visualizing Data and Cook & Swayne’s Interactive and Dynamic Graphics for Data Analysis are a treasure trove of practical data analysis advice. Cleveland’s many case studies show how graphics are a critical part of exploratory data analysis (EDA) and model-checking. In several cases, his analysis demonstrates that previously-published findings used an inappropriate model and reached poor conclusions due to what he calls rote data analysis (RDA). Cook & Swayne do similar work with more modern statistical methods, including the first time I’ve seen graphical diagnostics for many machine learning tools. There’s also a great section on visualizing missing data. The title is misleading: you don’t need R and GGobi to learn a lot from their book.
  • Monmonier’s How to Lie with Maps refers to dated technology, but the concepts are great. It’s still useful to know just how maps are made, and how different projections work and why it matters. Much of cartographic work sounds analogous to statistical work: making simplifications in order to convey a point more clearly, worrying about data quality and provenance (different areas on the map might have been updated by different folks at different times), setting national standards that are imperfect but necessary… The section on “data maps” is critical for any statistician working with spatial data, and the chapter on bureaucratic mapping agencies will sound familiar to my Census Bureau colleagues.

I hope to post longer notes on each book sometime later.

“Don’t invert that matrix” – why and how

The first time I read John Cook’s advice “Don’t invert that matrix,” I wasn’t sure how to follow it. I was familiar with manipulating matrices analytically (with pencil and paper) for statistical derivations, but not with implementation details in software. For reference, here are some simple examples in MATLAB and R, showing what to avoid and what to do instead.

[Edit: R code examples and results have been revised based on Nicholas Nagle’s comment below and advice from Ryan Tibshirani.]

If possible, John says, you should just ask your scientific computing software to directly solve the linear system Ax = b. This is often faster and more numerically accurate than computing the matrix inverse of A and then computing x = A^{-1}b.

We’ll chug through a computation example below, to illustrate the difference between these two methods. But first, let’s start with some context: a common statistical situation where you may think you need matrix inversion, even though you really don’t.

[One more edit: I’ve been guilty of inverting matrices directly, and it’s never caused a problem in my one-off data analyses. As Ben Klemens comments below, this may be overkill for most statisticians. But if you’re writing a package, which many people will use on datasets of varying sizes and structures, it may well be worth the extra effort to use solve or QR instead of inverting a matrix if you can help it.]

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Two principled approaches to data visualization

Yesterday I spoke at Stat Bytes, our student-run statistical computing seminar.

My goal was to introduce two principled frameworks for thinking about data visualization: human visual perception and the Grammar of Graphics.
(We also covered some relevant R packages: RColorBrewer, directlabels, and a gentle intro to ggplot2.)

These are not the only “right” approaches, nor do they guarantee your graphics will be good. They are just useful tools to have in your arsenal.

Example plot with direct labels and ColorBrewer colors, made in ggplot2.

Example plot with direct labels and ColorBrewer colors, made in ggplot2.

The talk was also a teaser for my upcoming fall course, 36-721: Statistical Graphics and Visualization [draft syllabus pdf].

Here are my

The talk was quite interactive, so the slides aren’t designed to stand alone. Open the slides and follow along using my notes below.
(Answers are intentionally in white text, so you have a chance to think for yourself before you highlight the text to read them.)

If you want a deeper introduction to dataviz, including human visual perception, Alberto Cairo’s The Functional Art [website, amazon] is a great place to start.
For a more thorough intro to ggplot2, see creator Hadley Wickham’s own presentations at the bottom of this page.

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DotCity: a game written in R? and other statistical computer games?

A while back I recommended Nathan Uyttendaele’s beginner’s guide to speeding up R code.

I’ve just heard about Nathan’s computer game project, DotCity. It sounds like a statistician’s minimalist take on SimCity, with a special focus on demographic shifts in your population of dots (baby booms, aging, etc.). Furthermore, he’s planning to program the internals using R.

This is where scatterplot points go to live and play when they're not on duty.

This is where scatterplot points go to live and play when they’re not on duty.

Consider backing the game on Kickstarter (through July 8th). I’m supporting it not just to play the game itself, but to see what Nathan learns from the development process. How do you even begin to write a game in R? Will gamers need to have R installed locally to play it, or will it be running online on something like an RStudio server?

Meanwhile, do you know of any other statistics-themed computer games?

  • I missed the boat on backing Timmy’s Journey, but happily it seems that development is going ahead.
  • SpaceChem is a puzzle game about factory line optimization (and not, actually, about chemistry). Perhaps someone can imagine how to take it a step further and gamify statistical process control à la Shewhart and Deming.
  • It’s not exactly stats, but working with data in textfiles is an important related skill. The Command Line Murders is a detective noir game for teaching this skill to journalists.
  • The command line approach reminds me of Zork and other old text adventure / interactive fiction games. Perhaps, using a similar approach to the step-by-step interaction of swirl (“Learn R, in R”), someone could make an I.F. game about data analysis. Instead of OPEN DOOR, ASK TROLL ABOUT SWORD, TAKE AMULET, you would type commands like READ TABLE, ASK SCIENTIST ABOUT DATA DICTIONARY, PLOT RESIDUALS… all in the service of some broader story/puzzle context, not just an analysis by itself.
  • Kim Asendorf wrote a fictional “short story” told through a series of data visualizations. (See also FlowingData’s overview.) The same medium could be used for a puzzle/mystery/adventure game.

Reader Morghulis

TL;DR: Memento mori. After reading too much Seneca, I’m meditating on death like a statistician, by counting how many of GRRM’s readers did not even survive to see the HBO show (much less the end of the book series). Rough answer: around 40,000.
No disrespect meant to Martin, his readers, or their families—it’s just a thought exercise that intrigued me, and I figured it may interest other people.
Also, we’ve blogged about GoT and statistics before.

In the Spring a young man’s fancy lightly turns to actuarial tables.

That’s right: Spring is the time of year when the next bloody season of Game of Thrones airs. This means the internet is awash with death counts from the show and survival predictions for the characters still alive.

All the deaths in 'A Song of Ice and Fire'

Others, more pessimistically, wonder about the health of George R. R. Martin, author of the A Song of Ice and Fire (ASOIAF) book series (on which Game of Thrones is based). Some worried readers compare Martin to Robert Jordan, who passed away after writing the 11th Wheel of Time book, leaving 3 more books to be finished posthumously. Martin’s trilogy has become 5 books so far and is supposed to end at 7, unless it’s 8… so who really knows how long it’ll take.

(Understandably, Martin responds emphatically to these concerns. And after all, Martin and Jordan are completely different aging white American men who love beards and hats and are known for writing phone-book-sized fantasy novels that started out as intended trilogies but got out of hand. So, basically no similarities whatsoever.)

But besides the author and his characters, there’s another set of deaths to consider. The books will get finished eventually. But how many readers will have passed away waiting for that ending? Let’s take a look.

Caveat: the inputs are uncertain, the process is handwavy, and the outputs are certainly wrong. This is all purely for fun (depressing as it may be).


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Small Area Estimation 101: old materials posted

I never got around to polishing my Small Area Estimation (SAE) “101” tutorial materials that I promised a while ago. So here they are, though still unedited and not as clean / self-explanatory as I’d like.

The slides introduce a few variants of the simplest area-level (Fay-Herriot) model, analyzing the same dataset in a few different ways. The slides also explain some basic concepts behind Bayesian inference and MCMC, since the target audience wasn’t expected to be familiar with these topics.

  • Part 1: the basic Frequentist area-level model; how to estimate it; model checking (pdf)
  • Part 2: overview of Bayes and MCMC; model checking; how to estimate the basic Bayesian area-level model (pdf)
  • All slides, data, and code (ZIP)

The code for all the Frequentist analyses is in SAS. There’s R code too, but only for a WinBUGS example of a Bayesian analysis (also repeated in SAS). One day I’ll redo the whole thing in R, but it’s not at the top of the list right now.

Frequentist examples:

  • “ByHand” where we compute the Prasad-Rao estimator of the model error variance (just for illustrative purposes since all the steps are explicit and simpler to follow; but not something I’d usually recommend in practice)
  • “ProcMixed” where we use mixed modeling to estimate the model error variance at the same time as everything else (a better way to go in practice; but the details get swept up under the hood)

Bayesian examples:

  • “ProcMCMC” and “ProcMCMC_alt” where we use SAS to fit essentially the same model parameterized in a few different ways, some of whose chains converge better than others
  • “R_WinBUGS” where we do the same but using R to call WinBUGS instead of using SAS

The example data comes from Mukhopadhyay and McDowell, “Small Area Estimation for Survey Data Analysis using SAS Software” [pdf].

If you get the code to run, I’d appreciate hearing that it still works 🙂

My SAE resources page still includes a broader set of tutorials/textbooks/examples.