An introduction to eulerr

Input

At the time of writing, it is possible to provide input to eulerr as either

• a named numeric vector with set combinations as disjoint set combinations or unions (depending on how the argument type is set),
• a matrix or data frame of logicals with columns representing sets and rows the set relationships for each observation, or
• a list of sample spaces.

library(eulerr)

# Input in the form of a named numeric vector
fit1 <- euler(c("A" = 25, "B" = 5, "C" = 5,
                "A&B" = 5, "A&C" = 5, "B&C" = 3,
                "A&B&C" = 3))

# Input as a matrix of logicals
set.seed(1)
mat <- cbind(
  A = sample(c(TRUE, TRUE, FALSE), size = 50, replace = TRUE),
  B = sample(c(TRUE, FALSE), size = 50, replace = TRUE),
  C = sample(c(TRUE, FALSE, FALSE, FALSE), size = 50, replace = TRUE)
)
fit2 <- euler(mat)

Fit

We inspect our results by printing the eulerr object

fit2

##       original fitted residuals region_error
## A           10 10.025    -0.025        0.003
## B            7  7.040    -0.040        0.003
## C            5  5.049    -0.049        0.002
## A&B         15 14.966     0.034        0.003
## A&C          1  0.563     0.437        0.010
## B&C          2  1.777     0.223        0.005
## A&B&C        5  5.071    -0.071        0.003
## 
## diag_error:  0.01 
## stress:      0.001

or directly access and plot the residuals.

# Cleveland dot plot of the residuals
dotchart(resid(fit2))
abline(v = 0, lty = 3)

Residuals for the eulerr fit.

This shows us that the A&C intersection is somewhat overrepresented in fit2. Given that these residuals are on the scale of the original values, however, the residuals are arguably of little concern.

As an alternative, we could plot the circles in another program by retrieving their coordinates and radii.

coef(fit2)

##            x           y        r
## A  0.6870886  0.08595579 3.122237
## B -0.7787031  0.70767363 3.030623
## C -1.7567943 -1.74679983 1.991497

Starting configuration

A starting configuration is obtained via a constrained version of multidimensional scaling that has been explained thoroughly elsewhere.

Optimization

The starting configuration is based solely on the two-way relationships of the sets so has to be optimized for most set relationships. We try to optimize the coordinates and radii of the solution with the objective of producing a diagram that is as accurate as possible. In this context, however, accuracy is an ambigious objective that has produced a slew of proposals. eulerr uses the sums of squares as the target loss function to minimize

\[\sum_{i=1}^{n} (y_i - \hat{y}_i) ^ 2\] where \(\hat{y}\) is the fitted disjoint areas.

Goodness-of-fit

For goodness-of-fit measures, we the stress statistic from venneuler (Wilkinson (2012))

\[\frac{\sum_{i=1}^{n} (y_i - \hat{y}_i) ^ 2}{\sum_{i=1}^{n} y_i ^ 2}\] where \(\hat{y}_i\) is an ordinary least squares estimate from the regression of the fitted areas on the original areas that is being explored during optimization.

We also provide the diagError statistic from eulerAPE (Micallef and Rodgers (2014–17AD)):

\[ \max_{i = 1, 2, \dots, n} \left| \frac{y_i}{\sum y_i} - \frac{\hat{y}_i}{\sum \hat{y}_i} \right|\] In our example, the diagError is 0.0096 and our stress is 6\times 10^{-4}, suggesting that the fit is accurate.

We can now be confident that eulerr provides a reasonable representation of our input. Were it otherwise, we would do best to stop here and look for another way to visualize our data. (I suggest the excellent UpSetR package.)

Plotting

No we get to the fun part: plotting our diagram. This is easy, as well as highly customizable, with eulerr.

plot(fit2)

# Remove fills, vary border type, and switch fontface.
plot(fit2, fill = "transparent", lty = 1:3, fontface = 4)

eulerr’s default color palette is taken from qualpalr – another package that I have developed – which uses color difference algorithms to generate distinct qualitative color palettes.