Exploring alternative ways to visualise the random effect means and intercepts in a hierarchical linear model of the rats data from Gelfand et al. (1990).
This poster was presented at the 2017 Bayes on the Beach workshop.
You may need to check for fonts on your system for LaTeX and you'll need JAGS installed to fit the model.
The results at the conference for each plot were
| Plot | Like | Meh | Dislike | Total |
|---|---|---|---|---|
| Caterpillar | 12 | 11 | 3 | 26 |
| STAN | 18 | 7 | 2 | 27 |
| Transparent density | 10 | 10 | 2 | 26 |
| Cumulative density | 3 | 9 | 11 | 23 |
| Faceted density | 1 | 7 | 19 | 27 |
Comments about the caterpillar (raterpillar?) plot were that it's a common way they see it presented but they don't normally sort by one of the parameter levels' medians. One coauthor indicated that they hated the ordering as it implies a pattern that isn't "real" and that it misled them into thinking they were looking at posterior predictions of the rats' growth. The STAN-style visualisation was most popular, with a five number summary deemed more informative and reading bars horizontally rather than vertically was easier on the eyes as people scan left to right more easily than up and down. Another coauthor indicated that they wanted to know the overall mean, the posterior mean of β00 and β10 for context to indicate whether a given rat was higher or lower than the mean and this annotation was added to the plot.
Transparent densities were described as being pretty and informative, as the more dark the grey in the plot the more rats have interecepts/slopes in that region. The use of colour was suggested by one coauthor. The majority opinion, with only a few dissenting coauthors, was that this would scale well to 100 rats as we'd be focussing on the distribution of the distributions overall. One coauthor indicated that the transparent shading was actually misleading, as it gave more visual attention to overlapping tails when it was the means and variances of the parameters that were the important values. This dissenting coauthor indicated a preference for the cumulative density plots, as the curves are approximately parallel and do not produce any interference patterns. This graph was least popular, with many coauthors indicating that a lack of experience with cumulative densities and difficulty interpreting them were obstacles to being able to extract any meaningful information.
The overwhelming majority of coauthors described the faceted densities as awful (with one coauthor going as far to say that they would produce it for themselves on a large sheet to look at but would never publish such a graph), as all small multiples show an approximately normal distribution and the values on the x axis are the only avenue for contrast but that these were too small. One coauthor indicated that a table of small figures is less interpretable than a table of many numbers (means and credible intervals for all 30 rats' intercepts and slopes provides 180 numbers). Two coauthors indicated that there are times when this style is useful - namely detecting one parameter which is different to the others, whether skewed or bimodal (and a bimodal small multiple was added to the plot on the poster). Coauthors also indicated that using a common x axis would help understand where each rat's parameters lay in the parameter space. Another coauthor extended this idea to showing all density plots behind each small multiple and then that small multiple's density with a darker line in order to show not just where the parameter lays in the parameter space but also in reference to the other rats.
Alternative visualisations were suggested, such as putting jittered dots representing the MCMC samples behind the median and credible intervals to help show bimodality and tail behaviour. Another coauthor suggested that small multiples of posterior predictions would allow for an understanding of where the aberrant rats (fast or slow growers) lay in the pack. The data, model and visualisation code are all available on this repository.