Category: Statistics

Victoria Stodden on Reproducible Research

Yesterday’s department seminar was by Victoria Stodden [see slides from Nov 9, 2015]. With some great Q&A during the talk, we only made it through about half the slides.

Dr Stodden spoke about several kinds of reproducibility important to science, and their links to different “flavors” of science. As I understood it, there are

  • empirical reproducibility: are the methods (lab-bench protocol, psych-test questionnaire, etc.) available, so that we could repeat the experiment or data-collection?
  • computational reproducibility: are the code and data available, so that we could repeat the processing and calculations?
  • statistical reproducibility: was the sample large enough that we can expect to get comparable results, if we do repeat the experiment and calculations?

Her focus is on the computational piece. As more and more research involves methodological contributions primarily in the software itself (and not explained in complete detail in the paper), it’s critical for that code to be open and reproducible.

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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:
Continue reading “Statistical Graphics and Visualization course materials” →

Chai Squares

I saw this typo for Chi Square a while back and thought it’d make a great recipe idea. Turns out I was right: these bars won a prize at my department’s World Statistics Day bake-off.

ChaiSquares

Start with Mark Bittman’s blondie recipe (copied/adapted from here), and add some of the spices that go into chai tea.

  • 8 tablespoons (1 stick, 4 ounces or 113 grams) butter, melted
  • 1 cup (218 grams or 7 3/4 ounces for light; 238 grams or 8 3/8 ounces for dark) brown sugar
  • 1 large egg
  • 1 teaspoon vanilla
  • Pinch salt
  • 1 cup (4 3/8 ounces or 125 grams) all-purpose flour
  • 1/2 teaspoon cardamom
  • 1/2 teaspoon cinnamon
  • 1/2 teaspoon ground ginger
  • 1/2 teaspoon ground cloves
  • scant 1/2 teaspoon fresh ground black pepper
  1. Preheat oven to 350°F. Butter an 8×8 pan, or line the pan with aluminum foil and grease the foil.
  2. Mix melted butter with brown sugar. Beat until smooth. Beat in egg and vanilla.
  3. Combine salt, flour, and spices. Gently stir flour mixture into butter mixture.
  4. Pour into prepared pan. Bake 20-25 minutes, or until barely set in the middle. Cool on rack before cutting them.

Enjoy!

Summary sheet of ways to map statistical uncertainty

A few years ago, a team at the Cornell Program on Applied Demographics (PAD) created a really nice demo of several ways to show statistical uncertainty on thematic maps / choropleths. They have kindly allowed me to host their large file here: PAD_MappingExample.pdf (63 MB)

Screenshot of index page from PAD mapping examples
Screenshot of index page from PAD mapping examples

Each of these maps shows a dataset with statistical estimates and their precision/uncertainty for various areas in New York state. If we use color or shading to show the estimates, like in a traditional choropleth map, how can we also show the uncertainty at the same time? The PAD examples include several variations of static maps, interaction by toggling overlays, and interaction with mouseover and sliders. Interactive map screenshots are linked to live demos on the PAD website.

I’m still fascinated by this problem. Each of these approaches has its strengths and weaknesses: Symbology Overlay uses separable dimensions, but there’s no natural order to the symbols. Pixelated Classification seems intuitively clear, but may be misleading if people (incorrectly) try to find meaning in the locations of pixels within an area. Side-by-side maps are each clear on their own, but it’s hard to see both variables at once. Dynamic Feedback gives detailed info about precision, but only for one area at a time, not all at once. And so forth. It’s an interesting challenge, and I find it really helpful to see so many potential solutions collected in one document.

The creators include Nij Tontisirin and Sutee Anantsuksomsri (both since moved on from Cornell), and Jan Vink and Joe Francis (both still there). The pixellated classification map is based on work by Nicholas Nagle.

For more about mapping uncertainty, see their paper:

Francis, J., Tontisirin, N., Anantsuksomsri, S., Vink, J., & Zhong, V. (2015). Alternative strategies for mapping ACS estimates and error of estimation. In Hoque, N. and Potter, L. B. (Eds.), Emerging Techniques in Applied Demography (pp. 247–273). Dordrecht: Springer Netherlands, DOI: 10.1007/978-94-017-8990-5_16 [preprint]

and my related posts:

See also Visualizing Attribute Uncertainty in the ACS: An Empirical Study of Decision-Making with Urban Planners. This talk by Amy Griffin is about studying how urban planners actually use statistical uncertainty on maps in their work.

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.

One more difference between statistics and [machine learning, data science, etc.]

Statisticians have always done a myriad of different things related to data collection and analysis. Many of us are surprised (even frustrated) that Data Science is even a thing. “That’s just statistics under a new name!” we cry. Others are trying to bring Data Science, Machine Learning, Data Mining, etc. into our fold, hoping that Statistics will be the “big tent” for everyone learning from data.

But I do think there is one core thing that differentiates Statisticians from these others. Having an interest in this is why you might choose to major in statistics rather than applied math, machine learning, etc. And it’s the reason you might hire a trained statistician rather than someone else fluent with data:

Statisticians use the idea of variability due to sampling to design good data collection processes, to quantify uncertainty, and to understand the statistical properties of our methods.

When applied statisticians design an experiment or a survey, they account for the inherent randomness and try to control it. They plan your study in such a way that’ll make your estimates/predictions as accurate as possible for the sample size you can afford. And when they analyze the data, alongside each estimate they report its precision, so you can decide whether you have enough evidence or whether you still need further study. For more complex models, they also worry about overfitting: can this model generalize well to the population, or is too complicated to estimate with this sample and hence is it just fitting noise?

When theoretical statisticians invent a new estimator, they study how well it’ll perform over repeated sampling, under various assumptions. They study its statistical properties first and foremost. Loosely speaking: How variable will the estimates tend to be? Will they be biased (i.e. tend to always overestimate or always underestimate)? How robust will they be to outliers? Is the estimator consistent (as the sample size grows, does the estimate tend to approach the true value)?

These are not the only important things in working with data, and they’re not the only things statisticians are trained to do. But (as far as I can tell) they are a much deeper part of the curriculum in statistics training than in any other field. Statistics is their home. Without them, you can often still be a good data analyst but a poor statistician.

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“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. See also a related post by Gregory Gundersen.]

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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Simplistic thinking in statistical inference

My friend Brian Segal, at the University of Michigan, writes in response to the journal that banned statistical inference:

If nothing else, I think BASP did a great job of starting a discussion on p-values, and more generally, the role of statistical inference in certain types of research. Stepping back a bit, I think the discussion fits into a broader question of how we deal with answers that are inherently grey, as opposed to clear cut. Hypothesis testing, combined with traditional cutoff values, is a neat way to get a yes/no answer, but many reviewers want a yes/no answer, even in the absence of hypothesis tests.

As one example, I recently helped a friend in psychology to validate concepts measured by a survey. In case you haven’t done this before, here’s a quick (and incomplete) summary of construct validation: based on substantive knowledge, group the questions in the survey into groups, each of which measures a different underlying concept, like positive attitude, or negativity. The construct validation question is then, “Do these groups of questions actually measure the concepts I believe they measure?”

In addition to making sure the groups are defensible based on their interpretation, you usually have to do a quantitative analysis to get published The standard approach is to model the data with a structural equation model (as a side note, this includes confirmatory factor analysis, which is not factor analysis!). The goodness of fit statistic is useless in this context, because the null hypothesis is not aligned with the scientific question, so people use a variety of heuristics, or fit indices, to decide if the model fits. The model is declared to either fit or not fit (and consequently the construct is either valid or not valid) depending on whether the fit index is larger or smaller than a rule-of-thumb value. This is the same mentality as hypothesis testing.

Setting aside the question of whether it makes sense to use structural equation models to validate constructs, the point I’m trying to make is that the p-value mentality is not restricted to statistical inference. Like any unsupervised learning situation, it’s very difficult to say how well the hypothesized groups measure the underlying constructs (or if they even exist). Any answer is inherently grey, and yet many researchers want a yes/no answer. In these types of cases, I think it would be great if statisticians could help other researchers come to terms not just with the limits of the statistical tools, but with the inquiry itself.

I agree with Brian that we can all do a better job of helping our collaborators to think statistically. Statistics is not just a set of arbitrary yes/no hoops to jump through in the process of publishing a paper; it’s a kind of applied epistemology. As tempting as it might be to just ban all conclusions entirely, we statisticians are well-trained in probing what can be known and how that knowledge can be justified. Give us the chance, and we’d would love to help you navigate the subtleties, limits, and grey areas in your research!