**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** is available on CRAN and can be installed with `install.packages("ggdensity")`

. You can also install its development version from GitHub with:

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

##
`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()`

`probs`

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 `probs`

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 `probs`

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(probs)),
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(probs)),
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()
```