This was the first time we utilized three instructors (as opposed to a main instructor and assistants which we often use for large classes) and it led to an amazing dynamic. Bob laid the theoretical foundation for Markov chain Monte Carlo (MCMC), explaining both with math and geometry, and discussed the computational considerations of performing simulation draws. Daniel led the participants through hands-on examples with Stan, covering everything from how to describe a model, to efficient computation to debugging. Andrew gave his usual, crowd dazzling performance use previous work as case studies of when and how to use Bayesian methods.
It was an intensive three days of training with an incredible amount of information. Everyone walked away knowing a lot more about Bayes, MCMC and Stan and eager to try out their new skills, and an autographed copy of Andrew’s book, BDA3.
A big help, as always was Daniel Chen who put in so much effort making the class run smoothly from securing the space, physically moving furniture and running all the technology.
The Wall Street Journal is reporting that even with all the concern around gerrymandering that in reality the upcoming redistricting probably won’t have much affect on upcoming elections. Gary King is mentioned as having written a paper “that helped demonstrate the relative impotence of partisan redistricting” yet “he favors the efforts to create a statistical method that would replace it.” I personally am always for using math and hard numbers to solve any problem whenever possible.
The article also mentioned a “conference last year in Washington, D.C., researchers proposed alternatives.” David Epstein presented a paper at that conference that Andy Gelman and I worked on.
While the article quoted one of Dr. Gelman’s papers it unfortunately did not mention him, or any of us by name. However, the accompanying blog post did mention both Dr.s Gelman and Epstein with specific quotes of them and their work.
A great way to visualize the results of a regression is to use a Coefficient Plot like the one to the right. I’ve seen people on Twitter asking how to build this and there has been an option available using Andy Gelman’scoefplot() in the arm package. Not knowing this I built my own (as seen in this post about taste testing tomatoes) and they both suffered the same problems:. Long coefficient names often got cut off by the left margin of the graph and the name of the variable was appended to all the levels of a factor. One big difference between his and mine is that his does not include the Intercept by default. Mine includes the intercept with the option of excluding it.
I managed to solve the latter problem pretty quickly using some regularexpressions. Now the levels of factors are displayed alone, without being prepended by the factor name. As for the former, I fixed that yesterday by taking advantage of ggplot by Hadley Wickham which deals with the margins better than I do.
Both of these changes made for a vast improvement over what I had avialable before. Future improvements will address the sorting of the coefficients displayed and allow users to choose their own display names for the coefficients.
The function is in this file and is called plotCoef() and is very customizable, down to the color and line thickness. I kept my old version, plotCoefBase(), in the file in case some people are adverse to using ggplot, though no one should be. I sent the code to Dr. Gelman to hopefully be incorporated into his function which I’m sure gets used by a lot more people than mine will. Examples of my old version and of Dr. Gelman’s are after the break.
The first thing to note is that there are only 16 data points, so multiple regression is not an option. We can all thank the Curse of Dimensionality for that. So I stuck to simpler methods and visualizations. If I can get the raw data from Slice, I can get a little more advanced.
For the sake of simplicity I removed the tomatoes from Eataly because their price was such an outlier that it made visualizing the data difficult. As usual, most of the graphics were made using ggplot2 by Hadley Wickham. The coefficient plots were made using a little function I wrote. Here is the code. Any suggestions for improvement are greatly appreciated, especially if you can help with increasing the left hand margin of the plot. And as always, all the work was done in R.
The most obvious relationship we want to test is Overall Quality vs. Price. As can be seen from the scatterplot below with a fitted loess curve, there is not a linear relationship between price and quality.