geom cloud.

Thu 21 September 2017 by Steven E. Pav

I wanted a drop-in replacement for geom_errorbar in ggplot2 that would plot a density cloud of uncertainty. The idea is that typically (well, where I work), the ymin and ymax of an errorbar are plotted at plus and minus one standard deviation. A 'cloud' where the alpha is proportional to a normal density with the same standard deviations could show the same information on a plot with a little less clutter. I found out how to do this with a very ugly function, but wanted to do it the 'right' way by spawning my own geom. So the geom_cloud.

After looking at a bunch of other ggplot2 extensions, some amount of tinkering and hair-pulling, and we have the following code. The first part just computes standard deviations which are equally spaced in normal density. This is then used to create a list of geom_ribbon with equal alpha, but the right size. A little trickery is used to get the scales right. There are three parameters: the steps, which control how many ribbons are drawn. The default value is a little conservative. A larger value, like 15, gives very smooth clouds. The se_mult is the number of standard deviations that the ymax and ymin are plotted at, defaulting to 1 here. If you plot your errorbars at 2 standard errors, change this to 2. The max_alpha is the alpha at the maximal density, i.e. around y.

# get points equally spaced in density 
equal_ses <- function(steps) {
    xend <- c(0,4)
    endpnts <- dnorm(xend)
# perhaps use ppoints instead?
    deql <- seq(from=endpnts[1],to=endpnts[2],length.out=steps+1)
    davg <- (deql[-1] + deql[-length(deql)])/2
# invert
    xeql <- unlist(lapply(davg,function(d) {
                     uniroot(f=function(x) { dnorm(x) - d },interval=xend)$root


geom_cloud <- function(mapping …
read more

Spy vs Spy vs Wald Wolfowitz.

Tue 05 September 2017 by Steven E. Pav

I turned my kids on to the great Spy vs Spy cartoon from Mad Magazine. This strip is pure gold for two young boys: Rube Goldberg plus explosions with not much dialog (one child is still too young to read). I became curious whether the one Spy had the upper hand, whether Prohias worked to keep the score 'even', and so on.

Not finding any data out there, I collected the data to the best of my ability from the Spy vs Spy Omnibus, which collects all 248 strips that appeared in Mad Magazine (plus two special issues). I think there are more strips out there by Prohias that appeared only in collected books, but have not collected them yet. I entered the data into a google spreadsheet, then converted into CSV, then into an R data package. Now you can play along at home.

On to the simplest form of my question: did Prohias alternate between Black and White Spy victories? or did he choose at random? Up until 1968 it was common for two strips to appear in one issue of Mad, with one victory per Spy. In some cases three strips appeared per issue, with the Grey Spy appearing in the third; the Black and White Spies always receive a comeuppance when she appears, and so the balance of power was maintained. After 1972, it seems that only a single strip appeared per issue, and we can examine the time series of victories.


# show that there are multiple per strip
svs %>%
    group_by(Mad_no,yrmo) %>%
                            net_victories=sum(as.numeric(white_comeuppance) - as.numeric(black_comeuppance))) %>%
    ungroup() %>%
    select(yrmo,nstrips,net_victories) %>%
    head(n=20) %>%
yrmo nstrips net_victories
1961-01 3 -1
1961-03 2 0
1961-04 2 0
1961-06 2 0
1961-07 …
read more

Calendar plots in ggplot2.

Thu 18 May 2017 by Steven E. Pav

I like the calendar 'heatmap' plots of commits you can see on github user pages, and wanted to play around with some. Of course, if I just wanted to make some plots, I could have just googled around, and then followed this recipe, or maybe used the rChartsCalmap package. Instead I set out, as an exercise, to make my own using ggplot2.

For data, I am using the daily GHCND observations data for station USC00047880, which is located in the San Rafael, CA, Civic Center. I downloaded this data as part of a project to join weather data to campground data (yes, it's been done before), directly from the NOAA FTP site, then read the fixed width file. I then processed the data, subselected to 2016 and beyond, and converted the units. I am left with a dataframe of dates, the element name, and the value, which is a temperature in Celsius. The first ten values I show here:

date element value
2016-01-01 TMAX 9.4
2016-01-01 TMIN 0.0
2016-01-02 TMAX 10.0
2016-01-02 TMIN 3.9
2016-01-03 TMAX 11.7
2016-01-03 TMIN 6.7
2016-01-04 TMAX 12.8
2016-01-04 TMIN 6.7
2016-01-05 TMAX 12.8
2016-01-05 TMIN 8.3

Here is the code to produce the heatmap itself. I first use the date field to compute the x axis labels and locations: the dates are converted essentially to 'Julian' days since January 4, 1970 (a Sunday), then divided by seven to get a 'Julian' week number. The week number containing the tenth of the month is then set as the location of the month name in the x axis labels. I add years to the January labels.

I then compute the Julian week number and day number of the week. I create a variable which alternates between …

read more

Elo and Draws.

Thu 04 May 2017 by Steven E. Pav

I still had some nagging thoughts after my recent examination of the distribution of Elo. In that blog post, I recognized that a higher probability of a draw would lead to tighter standard error around the true 'ability' of a player, as estimated by an Elo ranking. Without any data, I punted on what that probability should be. So I decided to look at some real data.

I started working in a risk role about a year ago. Compared to my previous gig, there is a much greater focus on discrete event modeling than on continuous outcomes. Logistic regression and survival analysis are the tools of the trade. However, financial risk modeling is more complex than the textbook presentation of these methods. As is chess. A loan holder might go bankrupt, stop paying, die, etc. Similarly, a chess player might win, lose or draw.

There are two main ways of approaching multiple outcome discrete models that leverage the simpler binary models: the competing hazards view, and the sequential hazards view. Briefly, risk under competing hazards would be like traversing the Fire Swamp: at any time, the spurting flames, the lightning sand or the rodents of unusual size might harm you. The risks all come at you at once. An example of a sequential hazard is undergoing surgery: you might die in surgery, and if you survive you might incur an infection and die of complications; the risks present themselves conditional on surviving other risks. (Both of these views are mostly just conveniences, and real risks are never so neatly defined.)

Returning to chess, I will consider sequential hazards. Assume two players, and let the difference in true abilities between them be denoted \(\Delta a\). As with Elo, we want the difference in abilities is such that the odds that the …

read more