40  Density contours

This graph is largely complete and just needs final proof reading.


This graph requires:

✅ a categorical variable

✅ two numeric (continuous) variables

40.1 Description

Density contours (or 2-D density plots) are helpful for displaying differences in values between two numeric (continuous) variables.

In topographical maps, contour lines are drawn around areas of equal elevation above sea-level. In density contours, the contour lines are drawn around the areas our data occupy (essentially replacing sea-level as ‘an area without any x or y values.’)

Specifically, the contour lines outline areas on the graph with differing point densities, and semi-transparent colors (gradient) can be added to further highlight the separate regions.

40.2 Set up

PACKAGES:

Install packages.

show/hide 
install.packages("palmerpenguins")
library(palmerpenguins)
library(ggplot2)

DATA:

Artwork by allison horst

We’ll use the penguins data from the palmerpenguins package, but remove the missing values from bill_length_mm, flipper_length_mm, and species.

show/hide 
peng_dnsty_2d <- palmerpenguins::penguins |>
  dplyr::filter(!is.na(bill_length_mm) &
    !is.na(flipper_length_mm) &
    !is.na(species)) |>
  dplyr::mutate(species = factor(species))
glimpse(peng_dnsty_2d)
#> Rows: 342
#> Columns: 8
#> $ species           <fct> Adelie, Adelie, Adelie…
#> $ island            <fct> Torgersen, Torgersen, …
#> $ bill_length_mm    <dbl> 39.1, 39.5, 40.3, 36.7…
#> $ bill_depth_mm     <dbl> 18.7, 17.4, 18.0, 19.3…
#> $ flipper_length_mm <int> 181, 186, 195, 193, 19…
#> $ body_mass_g       <int> 3750, 3800, 3250, 3450…
#> $ sex               <fct> male, female, female, …
#> $ year              <int> 2007, 2007, 2007, 2007…

40.3 Grammar

CODE:

  • Create labels with labs()

  • Initialize the graph with ggplot() and provide data

  • Create two values for extending the range of the x and y axis (x_min/x_max and y_min/y_max)

  • Map bill_length_mm to x and flipper_length_mm to y

  • Add the expand_limits() function, assigning our stored values to x and y

  • Add the geom_density_2d()

show/hide 
# labels
labs_dnsty_2d <- labs(
  title = "Bill Length vs. Flipper Length",
  x = "Bill Length (mm)",
  y = "Flipper length (mm)"
)

# x limits
x_min <- min(peng_dnsty_2d$bill_length_mm) - 5
x_max <- max(peng_dnsty_2d$bill_length_mm) + 5
# y limits
y_min <- min(peng_dnsty_2d$flipper_length_mm) - 10
y_max <- max(peng_dnsty_2d$flipper_length_mm) + 10

ggp2_dnsty_2d <- ggplot(
  data = peng_dnsty_2d,
  mapping = aes(
    x = bill_length_mm,
    y = flipper_length_mm
  )
) +
  # use our stored values
  expand_limits(
    x = c(x_min, x_max),
    y = c(y_min, y_max)
  ) +
  geom_density_2d()
# plot
ggp2_dnsty_2d +
  labs_dnsty_2d

GRAPH:

40.4 More info

We’re going to break down how to create the density contour layer-by-layer using the stat_density_2d() function (which allows us to access some of the inner-workings of geom_density_2d())

40.4.1 Base

  • Create a new set of labels

  • Initialize the graph with ggplot() and provide data

  • Build a base layer:

    • Map bill_length_mm to x and flipper_length_mm to y

    • Expand the x and y values with expand_limits() (using the values we created above)

show/hide 
labs_sdens_2d <- labs(
  title = "Bill Length vs. Flipper Length",
  x = "Bill Length (mm)",
  y = "Flipper length (mm)",
  color = "Species"
)
# base
base_sdens_2d <- ggplot(
  data = peng_dnsty_2d,
  mapping = aes(
    x = bill_length_mm,
    y = flipper_length_mm
  )
) +
  expand_limits(
    x = c(x_min, x_max),
    y = c(y_min, y_max)
  )
base_sdens_2d +
  labs_sdens_2d

40.4.2 Stat

Add the stat_density_2d() layer:

  • Inside aes(), use after_stat() to map level to fill (from Help, “Evaluation after stat transformation will have access to the variables calculated by the stat, not the original mapped values.”)

  • Set the geom to "polygon"

  • Change the color to black (#000000)

  • adjust the linewidth to 0.35

show/hide 
stat_sdens_2d <- base_sdens_2d +
  stat_density_2d(
    aes(fill = after_stat(level)),
    geom = "polygon",
    color = "#000000",
    linewidth = 0.35
  )
stat_sdens_2d +
  labs_sdens_2d

40.4.3 Fill

Where did levels come from?

You probably noticed the stat_density_2d() produced a legend with level, and a series of values for the color gradient. These numbers are difficult to interpret directly, but you can think of them as ‘elevation changes’ in point density. Read more here on SO.

Now that we have a color gradient for our contour lines, we can adjust it’s the range of colors using scale_fill_gradient()

  • low is the color for the low values of level

  • high is the color for the high values of level

  • guide let’s us control the legend

We’ll set these to white ("#ffffff") and dark gray ("#404040")

show/hide 
fill_sdens_2d <- stat_sdens_2d +
  scale_fill_gradient(
    low = "#ffffff",
    high = "#404040",
    guide = "legend"
  )
fill_sdens_2d +
  labs_sdens_2d

40.4.4 Points

The dark areas in the contour lines are the areas with higher value density, but why don’t we test that by adding some data points?

  • Add a geom_point() layer

    • Inside aes(), map species to color (this will tell us if the three dark areas represent differences in the three species in the dataset)

    • Set size to 2

    • Change the alpha to 2/3

show/hide 
# geom_point()
pnts_sdens_2d <- fill_sdens_2d +
  geom_point(aes(color = species),
    size = 2,
    alpha = 2 / 3
  )
# final
pnts_sdens_2d +
  labs_sdens_2d

40.5 Even more info

In the previous plot, we used the species variable in the geom_point() layer to identify the points using color. In the section below, we’ll show more methods of displaying groups with density contour lines.

40.5.1 Groups

Re-create the labels

Initialize the graph with ggplot() and provide data

Build a geom_density_2d() layer:

  • Map bill_length_mm to x and flipper_length_mm to y

  • Expand the limits using our adjusted min/max x and y values

  • Add the geom_density_2d(), mapping species to color

Build the geom_point() layer:

  • Map species to color

  • set the alpha and remove the legend

show/hide 
labs_dnsty_2d_grp <- labs(
  title = "Bill Length vs. Flipper Length",
  x = "Bill Length (mm)",
  y = "Flipper length (mm)",
  color = "Species"
)

ggp2_dnsty_2d_grp <- ggplot(
  data = peng_dnsty_2d,
  mapping = aes(
    x = bill_length_mm,
    y = flipper_length_mm
  )
) +
  expand_limits(
    x = c(x_min, x_max),
    y = c(y_min, y_max)
  ) +
  geom_density_2d(aes(color = species))


ggp2_dnsty_2d_pnts <- ggp2_dnsty_2d_grp +
  geom_point(aes(color = species),
    alpha = 2 / 3,
    show.legend = FALSE
  )

ggp2_dnsty_2d_pnts +
  labs_dnsty_2d_grp

40.5.2 Facets

  • Re-create the labels

  • Initialize the graph with ggplot() and provide data

  • Build the base/limits:

    • Map bill_length_mm to x and flipper_length_mm to y

    • Expand the limits using our adjusted min/max x and y values

  • Build the geom_density_2d_filled() layer:

    • Add the geom_density_2d_filled(), setting linewidth to 0.30 and contour_var to "ndensity"

  • Add the scale_discrete_manual():

    • Set aesthetics to "fill"

    • Provide a set of color values (this plot needed 10 values, and I grabbed them all from color-hex.

  • Facet:

    • Add facet_wrap(), and place species in the vars()
show/hide 
labs_dnsty_2d_facet <- labs(
  title = "Bill Length vs. Flipper Length",
  subtitle = "By Species",
  x = "Bill Length (mm)",
  y = "Flipper length (mm)"
)
ggp2_dnsty_2d_facet <- ggplot(
  data = peng_dnsty_2d,
  mapping = aes(
    x = bill_length_mm,
    y = flipper_length_mm
  )
) +
  expand_limits(
    x = c(x_min, x_max),
    y = c(y_min, y_max)
  ) +
  geom_density_2d_filled(
    linewidth = 0.30,
    contour_var = "ndensity"
  ) +
  scale_discrete_manual(
    aesthetics = "fill",
    values = c(
      "#18507a", "#2986cc", "#3e92d1", "#539ed6", "#69aadb",
      "#7eb6e0", "#a9ceea", "#bedaef", "#d4e6f4", "#e9f2f9"
    )
  ) +
  facet_wrap(vars(species))

ggp2_dnsty_2d_facet +
  labs_dnsty_2d_facet

40.5.3 Fill

In the previous section, we defined the color values used in geom_density_2d_filled() with scale_discrete_manual(). Below we give an example using the default colors:

  • Re-create the labels

  • Initialize the graph with ggplot() and provide data

  • Build the base/limits:

    • Map bill_length_mm to x and flipper_length_mm to y

    • Expand the limits using our adjusted min/max x and y values

  • Add the geom_density_2d() layer

  • Add the geom_density_2d_filled(), setting alpha to 0.8

show/hide 
labs_dnsty_2d <- labs(
  title = "Bill Length vs. Flipper Length",
  x = "Bill Length (mm)",
  y = "Flipper length (mm)"
)

ggp2_dnsty_2d <- ggplot(
  data = peng_dnsty_2d,
  mapping = aes(
    x = bill_length_mm,
    y = flipper_length_mm
  )
) +
  # use our stored values
  expand_limits(
    x = c(x_min, x_max),
    y = c(y_min, y_max)
  ) +
  geom_density_2d()

ggp2_dnsty_2d_fill <- ggp2_dnsty_2d +
  geom_density_2d_filled(alpha = 0.8)

ggp2_dnsty_2d_fill +
  labs_dnsty_2d

40.5.4 Lines

We can also outline the contours by adding color to the lines using another geom_density_2d() layer:

  • Set linewidth to 0.30

  • Set color to "#ffffff"

show/hide 
ggp2_dnsty_2d_fill_lns <- ggp2_dnsty_2d_fill +
  geom_density_2d(
    linewidth = 0.30,
    color = "#ffffff"
  )
ggp2_dnsty_2d_fill_lns +
  labs_dnsty_2d