At the end of March, Jonah Gabry and I released bayesplot 1.5.0. The major additions to the package were visualizations using ridgelines and a new plot for PIT diagnostics from LOO validation. I don’t know what that LOO PIT thing is yet, so I’ll talk about how ridgelines have been incorporated into bayesplot instead.

Behind the scenes of mcmc_areas()

I’m going to start with a less obvious use of ridgelines.

mcmc_areas() visualizes the posterior distribution of model parameters. It helps us see where the peak values are. By default, it will plot the complete range of the distribution, shade the middle 50% of the distribution, and draw a line at the median.

For this release, I rewrote the function so that it uses the ggridges package. I had noticed that the shapes it produced had different areas. Here’s an example of how the plots have changed.

library(ggplot2)

# Temporarily install the previous version of bayesplot and 
# make an mcmc_areas() plot.
withr::with_temp_libpaths({
  versions::install.versions("bayesplot", "1.4.0", quiet = TRUE)
  
  example_data <- bayesplot::example_mcmc_draws()
  p_a <- bayesplot::mcmc_areas(example_data, pars = c("beta[1]", "beta[2]")) +
    ggtitle("Version 1.4.0") +
    bayesplot::theme_default()
})
#> package 'bayesplot' successfully unpacked and MD5 sums checked

library(bayesplot)
#> This is bayesplot version 1.5.0
#> - Plotting theme set to bayesplot::theme_default()
#> - Online documentation at mc-stan.org/bayesplot
p_b <- mcmc_areas(example_data, c("beta[1]", "beta[2]")) + 
  ggtitle("Version 1.5.0") +
  bayesplot::theme_default()

# Show the two together
cowplot::plot_grid(p_a, p_b)

In the plot on the left, the shapes have different areas. Eyeballing it, it looks like beta[2] would fit inside beta[1]. Area is width times height. These shapes have different widths because they cover different values—that makes sense. Therefore, the problem is the height—namely, the fact that the shapes have the same height. To make the areas more similar, we adjust the heights, and that’s what’s happening in the plot on the right. The distribution for beta[2] is concentrated to a more narrow range, and that feature manifests in that shape’s much higher peak.

Three plots in one

This plot is built using the ggridges packages which handles drawing the shapes at different heights. It took a bit of trickery, however, to do the annotation for the shaded 50% interval and the median. Here is a high-level overview of what’s happening.

mcmc_areas_data() tidies the MCMC samples into a dataframe suitable for plotting. It computes the density of the parameter values, and it returns the densities over three intervals: 1) an outer interval, 2) an inner interval to be shaded, and 3) a narrow “point” interval.

library(dplyr, warn.conflicts = FALSE)

d <- mcmc_areas_data(example_data, c("beta[1]", "beta[2]")) %>% 
  mutate(
    interval = factor(interval, c("outer", "inner", "point")))

d
#> # A tibble: 4,238 x 5
#>    parameter interval interval_width     x density
#>    <fct>     <fct>             <dbl> <dbl>   <dbl>
#>  1 beta[1]   inner             0.500 0.136   0.986
#>  2 beta[1]   inner             0.500 0.137   0.988
#>  3 beta[1]   inner             0.500 0.137   0.989
#>  4 beta[1]   inner             0.500 0.138   0.990
#>  5 beta[1]   inner             0.500 0.138   0.991
#>  6 beta[1]   inner             0.500 0.139   0.992
#>  7 beta[1]   inner             0.500 0.139   0.993
#>  8 beta[1]   inner             0.500 0.139   0.994
#>  9 beta[1]   inner             0.500 0.140   0.995
#> 10 beta[1]   inner             0.500 0.140   0.997
#> # ... with 4,228 more rows

Internally, mcmc_areas() uses ggridges::geom_density_ridges() to draw three different ridgeline plots.

# Separate the full range so it can be drawn on each facet.
full_range <- d %>% 
  filter(interval == "outer") %>% 
  select(-interval)

p_base <- ggplot(d) + 
  aes(x = x, y = parameter, fill = interval, height = density) + 
  # For reference include the full-range. 
  # `stat = "identity"` means that ggridges should not scale the heights
  ggridges::geom_density_ridges(
    stat = "identity", data = full_range, color = "grey80",
    size = 1, fill = NA) + 
  ggridges::geom_density_ridges(stat = "identity") + 
  scale_fill_brewer(type = "seq") + 
  guides(fill = FALSE)

p_base + 
  facet_wrap("interval")

These intervals are layered to achieve the desired look.

There’s a bit more fussing to the actual function. For example, the width of the intervals and whether a point is calculated are options that have to be handled. The tips of the topmost peaks are not cut off in those plots as well. But that’s the basic idea.

Overlapping ridgelines for related parameters

Plots with the classic, overlapping Unknown Pleasures look are supported by mcmc_areas_ridges(). I like these plots for hierarchical models where the parameters represent similar units. In fact, part of the reason Jonah approached me about contributing to bayesplot was a proof-of-concept demo I wrote to visualize hierarchical effects using ridgeline plots, back when they were popularly called “joyplots”.

Below is the “eight schools” example where there is a treatment effect for each school (thetas) and an overall average effect (mu).

m <- shinystan::eight_schools@posterior_sample

mcmc_areas_ridges(m, pars = "mu", regex_pars = "theta") +
  ggplot2::ggtitle("Treatment effect on eight schools (Rubin, 1981)")

If we really want to go for the Unknown Pleasures look, we can manually plot the densities in a white-on-black theme. Most of the work here is padding zero values onto the ridgelines so that they all have the same width.

d <- mcmc_areas_ridges_data(m, pars = "mu", regex_pars = "theta") %>% 
  filter(interval == "outer") 

zeroes <- d %>%
  # Get range of each parameter
  group_by(parameter) %>% 
  summarise(pmin = min(x), pmax = max(x)) %>% 
  mutate(
    min = min(pmin), 
    max = max(pmax),
    # On each row, make a data-frame of zeroes from absolute minimum 
    # value to this parameter's minimum value
    lower_df = purrr::map2(
      min, pmin, 
      ~ data.frame(x = seq(.x, .y, length.out = 20), density = 0)),
    # Make a dataframe of zeroes from each parameter's max to the 
    # overall max
    upper_df = purrr::map2(
      pmax, max, 
      ~ data.frame(x = seq(.x, .y, length.out = 20), density = 0)),
    # Gather the zeroes together
    df = purrr::map2(lower_df, upper_df, bind_rows)) %>% 
  select(parameter, df) %>% 
  tidyr::unnest(df)

ggplot(bind_rows(d, zeroes)) + 
  aes(x = x, y = parameter, height = density) +
  ggridges::geom_density_ridges(
    stat = "identity", fill = NA, 
    color = "grey70", scale = 5) + 
  theme_void() + 
  theme(
    plot.background = element_rect(fill = "black"), 
    plot.margin = unit(c(.25, .25, .25, .25), units = "npc"),
    axis.ticks = element_blank())

Finally, ridgelines appear in by-chain diagnostics using mcmc_dens_chains().

mcmc_dens_chains(m, pars = c("theta[1]", "theta[2]", "theta[3]"))

There really isn’t much interesting to say about this plot, except that it follows Mike DeCrescenzo’s early example of using ridgelines on Bayesian models.