ggdensity

ggdensity extends ggplot2 providing more interpretable visualizations of density estimates based on highest density regions (HDRs). ggdensity offers drop-in replacements for ggplot2 functions:

• instead of ggplot2::geom_density_2d_filled(), use ggdensity::geom_hdr();
• instead of ggplot2::geom_density_2d(), use ggdensity::geom_hdr_lines().

Also included are the functions geom_hdr_fun() and geom_hdr_lines_fun() for plotting HDRs of user-specified bivariate probability density functions.

Installation

ggdensity isn’t on CRAN yet, but you can install its development version from GitHub with:

if (!requireNamespace("remotes")) install.packages("remotes")
remotes::install_github("jamesotto852/ggdensity")

Since it’s not on CRAN yet, the implementation interface may shift a bit, but we feel it’s stable enough to share with you now, so don’t expect big changes.

geom_density_2d_filled() vs. geom_hdr()

The standard way to visualize the joint distribution of two continuous variables in ggplot2 is to use ggplot2::geom_density_2d() or geom_density_2d_filled(). Here’s an example:

library("ggplot2"); theme_set(theme_bw())
library("ggdensity")

df <- data.frame("x" = rnorm(1000), "y" = rnorm(1000))
p <- ggplot(df, aes(x, y)) + coord_equal()
p + geom_density_2d_filled()

While it’s a nice looking plot, it isn’t immediately clear how we should understand it. That’s because geom_density_2d_filled() generates its contours as equidistant level sets of the estimated bivariate density, i.e. taking horizontal slices of the 3d surface at equally-spaced heights, and projecting the intersections down into the plane. So you get a general feel of where the density is high, but not much else. To interpret a contour, you would need to multiply its height by the area it bounds, which of course is very challenging to do by just looking at it.

geom_hdr() tries to get around this problem by presenting you with regions of the estimated distribution that are immediately interpretable:

p + geom_hdr()

level here tells us the probability bounded by the corresponding region, and the regions are computed to be the smallest such regions that bound that level of probability; these are called highest density regions or HDRs. By default, the plotted regions show the 50%, 80%, 95%, and 99% HDRs of the estimated density, but this can be changed with the probs argument to geom_hdr(). Notice that your take-away from the plot made with geom_density_2d_filled() is subtlely yet significantly different than that of the plot made by geom_hdr().

Visualizing subpopulations and geom_hdr_lines()

ggdensity’s functions were designed to be seamlessly consistent with the rest of the ggplot2 framework. As a consequence, pretty much everything you would expect to just work does. (Well, we hope! Let us know if that’s not true.)

For example, because geom_hdr() maps probability to the alpha aesthetic, the fill and color aesthetics are available for mapping to variables. You can use them to visualize subpopulations in your data. For example, in the penguins data from palmerpenguins you may want to look at how the relationship between bill length and flipper length changes across different species of penguins. Here’s one way you could look at that:

library("palmerpenguins")

ggplot(penguins, aes(flipper_length_mm, bill_length_mm, fill = species)) +
  geom_hdr(xlim = c(160, 240), ylim = c(30, 70)) +
  geom_point(shape = 21)

Nice, but a bit overplotted. To alleviate overplotting, we can use geom_hdr_lines():

ggplot(penguins, aes(flipper_length_mm, bill_length_mm, color = species)) +
  geom_hdr_lines(xlim = c(160, 240), ylim = c(30, 70)) +
  geom_point(size = 1)

Or you could facet the plot:

ggplot(penguins, aes(flipper_length_mm, bill_length_mm, fill = species)) +
  geom_hdr(xlim = c(160, 240), ylim = c(30, 70)) +
  geom_point(shape = 21) +
  facet_wrap(vars(species))

The main point here is that you should really think of geom_hdr() and geom_hdr_lines() as drop-in replacements for functions like geom_density_2d_filled(), geom_density2d(), and so on, and you can expect all of the rest of the ggplot2 stuff to just work.

A deeper cut illustrating ggplot2 integration

The underlying stat used by geom_hdr() creates the computed variable level that can be mapped in the standard way you map computed variables in ggplot2, with after_stat().

For example, geom_hdr() and geom_hdr_lines() map level to the alpha aesthetic by default. But you can override it like this, just be sure to override the alpha aesthetic by setting alpha = 1.

ggplot(faithful, aes(eruptions, waiting)) +
  geom_hdr(
    aes(fill = after_stat(level)), 
    alpha = 1, xlim = c(0, 8), ylim = c(30, 110)
  ) +
  scale_fill_viridis_d()

ggplot(faithful, aes(eruptions, waiting)) +
  geom_hdr_lines(
    aes(color = after_stat(level)), 
    alpha = 1, xlim = c(0, 8), ylim = c(30, 110)
  ) +
  scale_color_viridis_d()

Statistics details

In addition to trying to make the visuals clean and the functions what you would expect as a ggplot2 user, we’ve spent considerable effort in trying to ensure that the graphics you’re getting with ggdensity are statistically rigorous and provide a range of estimation options for more detailed control.

To that end, you can pass a method argument into geom_hdr() and geom_hdr_lines() that allows you to specify various nonparametric and parametric ways to estimate the underlying bivariate distribution, and we have plans for even more. Each of the estimators below offers advantages in certain contexts. For example, histogram estimators result in HDRs that obey constrained supports. Normal estimators can be helpful in providing simplified visuals that give the viewer a sense of where the distributions are, potentially at the expense of over-simplifying and removing important features of how the variables (co-)vary.

If you know your PDF

The above discussion has focused around densities that are estimated from data. But in some instances, you have the distribution in the form of a function that encodes the joint PDF. In those circumstances, you can use geom_hdr_fun() and geom_hdr_lines_fun() to make the analogous plots. These functions behave similarly to geom_function() from ggplot2, accepting the argument fun specifying the pdf to be summarized. Here’s an example:

f <- function(x, y) dnorm(x) * dgamma(y, 5, 3)

ggplot() +
  geom_hdr_fun(fun = f, xlim = c(-4, 4), ylim = c(0, 5))

Visualizing custom parametric density estimates with geom_hdr_fun()

In addition to all of the methods of density estimation available with geom_hdr(), one of the perks of having geom_hdr_fun() is that it allows you to plot parametric densities that you estimate outside the ggdensity framework. The basic idea is that you fit your distribution outside ggdensity calls with your method of choice, say maximum likelihood, and then plug the maximum likelihood estimate into the density formula to obtain a function to plug into geom_hdr_fun().

Here’s an example of how you can do that that assuming that the underlying data are independent and exponentially distributed with unknown rates.

set.seed(123)
th <- c(3, 5)
df <- data.frame("x" = rexp(1000, th[1]), "y" = rexp(1000, th[2]))

# construct the likelihood function
l <- function(th) {
  log_liks <- apply(df, 1, function(xy) {
    dexp(xy[1], rate = th[1], log = TRUE) +
    dexp(xy[2], rate = th[2], log = TRUE)
  })
  sum(log_liks)
}

# compute the mle
(th_hat <- optim(c(2, 2), l, control = list(fnscale = -1))$par)
#> [1] 2.912736 5.032125

# construct the parametric density estimate
f <- function(x, y, th) dexp(x, th[1]) * dexp(y, th[2])

# pass estimated density into geom_hdr_fun()
ggplot(df, aes(x, y)) +
  geom_hdr_fun(fun = f, args = list(th = th_hat)) +
  geom_point(shape = 21, fill = "lightgreen", alpha = .25) +
  coord_equal()

Stay tuned!

We have a number of neat new features cooking. Check back soon!