Coordinate systems and axes

Author

Claus O. Wilke

Introduction

In this worksheet, we will discuss how to change and customize scales and coordinate systems.

First we need to load the required R packages. Please wait a moment until the live R session is fully set up and all packages are loaded.

Next we set up the data.

We will be working with three different datasets, boxoffice, temperatures, and tx_counties. You have already seen the first two previously.

The boxoffice dataset contains box-office gross results for Dec. 22-24, 2017.

The temperatures dataset contains the average temperature for each day of the year for four different locations.

The tx_counties dataset holds information about how many people lived in Texas counties in 2010. The column popratio is the ratio of the number of inhabitants to the median across all counties, and the column index simply counts the counties from most populous to least populous.

Scale customizations

We can modify the appearance of the x and y axis with scale functions. All scale functions have name of the form scale_aesthetic_type(), where aesthetic stands for an aesthetic to which we’re mapping data (e.g., x, y, color, fill, etc), and type stands for the specific type of the scale. What scale types are available depends on both the aesthetic and the data.

Here, we only consider position scales, which are scales for the x and y aesthetics. The most commonly used scales types for position scales are continuous for continuous data and discrete for discrete data, yielding the scale functions scale_x_continuous(), scale_y_continuous(), scale_x_discrete(), and scale_y_discrete(). But there are others, such as date, time, or binned. You can look them up here: https://ggplot2.tidyverse.org/reference/index.html#section-scales

Position scale functions are used to modify both the appearance of the axis (axis title, axis labels, number and location of breaks, etc.) and the mapping from data to position (including the range of data values considered, i.e., axis limits, and whether the data should be transformed, as is the case in log scales).

Let’s start with this plot of the boxoffice data:

We can use scale functions to modify the axis titles, by setting the name argument. For example, scale_x_continuous(name = "the x value") would set the axis title to “the x value” in a continuous scale along the x axis.

Use the appropriate scale functions to modify both axis titles in the above plot. Think about which axes (if any) are continuous and which are discrete.

We can also use scale functions to set axis limits, via the limits argument. For continuous scales, the limits argument takes a vector of two numbers representing the lower and upper limit. For example, limits = c(0, 80) would indicate an axis that runs from 0 to 80. For discrete scales, the limits argument takes a vector of all the categories that should be shown, in the order in which they should be shown.

Try this out by setting a limit from 0 to 80 on the x axis.

Hint

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross (million USD)",
    limits = ___
  ) +
  scale_y_discrete(name = NULL)

Solution

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross (million USD)",
    limits = c(0, 80)
  ) +
  scale_y_discrete(name = NULL)

What happens if you set the axis limits such that not all data points can be shown, for example an upper limit of 65 rather than 80? Do you understand why?

(Hint: Scale limits are applied before the plot is drawn, and data points outside the scale limits are discarded. If this is not what you want, there’s an alternative way of setting limits. See the very end of this worksheet under “Coords”.)

Next, we can use the breaks and labels arguments to customize which axis ticks are shown and how they are labeled. In general, you need exactly as many breaks as labels. If you define only breaks but not labels then labels are automatically generated from the breaks.

Building on the code from the previous example, set breaks at 0, 25, 50, and 75, and format the labels such that they can be read as currency. For example, write $25M instead of just 25.

Hint

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross",
    limits = c(0, 80),
    breaks = ___,
    labels = ___
  ) +
  scale_y_discrete(name = NULL)

Solution

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross",
    limits = c(0, 80),
    breaks = c(0, 25, 50, 75),
    labels = c("0", "$25M", "$50M", "$75M")
  ) +
  scale_y_discrete(name = NULL)

When looking at the resulting plot, you may notice that the x axis extends beyond the limits you have set. This happens because by default ggplot scales expand the axis range by a small amount. You can set the axis expansion via the expand parameter. Setting the expansion can be a bit tricky, because we can set expansion at either end of a scale and we can define both additive and multiplicative expansion. (Additive expansion adds a fixed value, whereas multiplicative expansion adds a multiple of the scale range. ggplot uses additive expansion for discrete scales and multiplicative expansion for continuous scales, but you can use either for either scale.)

The simplest way to define expansions is with the expansion() function, which takes arguments mult for multiplicative expansion and add for additive expansion. Either takes a vector of two values, indicating expansion at the lower and upper end, respectively. Thus, expansion(mult = c(0, 0.1)) indicates multiplicative expansion of 0% at the lower end and 10% at the upper end, whereas expansion(add = c(2, 2)) indicates additive expansion of 2 units at either end of the scale.

Try this yourself. Use the expand argument to remove the gap to the left of 0 on the x axis.

Hint

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross",
    limits = c(0, 80),
    breaks = c(0, 25, 50, 75),
    labels = c("0", "$25M", "$50M", "$75M"),
    expand = expansion(___)
  ) +
  scale_y_discrete(name = NULL)

Solution

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross",
    limits = c(0, 80),
    breaks = c(0, 25, 50, 75),
    labels = c("0", "$25M", "$50M", "$75M"),
    expand = expansion(mult = c(0, 0.06))
  ) +
  scale_y_discrete(name = NULL)

Try different settings for the expand argument. Try both multiplicative and additive expansions. Apply different expansions to the y axis as well.

Logarithmic scales

Scales can also transform the data before plotting. For example, log scales such as scale_x_log10() and scale_y_log10() log-transform the data. To try this out, we’ll be working with the tx_counties dataset:

Modify this plot so the y axis uses a log scale.

Now customize the log scale by setting name, limits, breaks, and labels. These work exactly as they did in scale_x_continuous().

Solution

ggplot(tx_counties) +
  aes(x = index, y = popratio) +
  geom_point() +
  scale_y_log10(
    name = "population number / median",
    limits = c(0.003, 300),
    breaks = c(0.01, 1, 100),
    labels = c("0.01", "1", "100")
  )

Coords

While scales determine how data values are mapped and represented along one dimension, e.g. the x or the y axis, coordinate systems define how these dimensions are projected onto the 2d plot surface. The default coordinate system is the Cartesian coordinate system, which uses orthogonal x and y axes. In the following example, I have added the coord explicitly, but this is not normally necessary.

We can however add a different coord, for example coord_polar() to use a polar coordinate system. Try this out.

In the polar coordinate system, the y axis (here, temperature) is mapped onto the radius, and the x axis (here, day of year) is mapped onto the angle. You can use scale_x_continuous() and scale_y_continuous() to modify the radial and angular axes. For example, you may want to change the temperature limits from 0 to 105 so the temperature curve for Chicago doesn’t hit the exact center of the plot. Try this out.

There are other useful coords. For example, coord_fixed() is a Cartesian coordinate system with fixed aspect ratio. This is useful when we plot variables along the x and y axes that are measured in the same units. In this case, we want the two axes to be coordinated, such that one step along x has the same meaning as one step along y.

To demonstrate this, we reshape the temperatures dataset into wide format, and then plot temperatures in San Diego versus temperatures in Houston.

(A side remark: Do you know why we write `San Diego` and not "San Diego" or 'San Diego' inside the aes() function? If you don’t, see if you can find out.)

The units along both the x and the y axis are temperatures, but a 10 degree difference in Houston is shown as a shorter distance than a 10 degree difference in San Diego. To address this problem, add coord_fixed() to the above plot.

This plot is technically correct but it doesn’t look good, because breaks are spaced differently along the two axes. Also, the plot looks strangely narrow and tall. We can fix both issues by manually setting breaks and limits for both axes. Try this out.

Hint

ggplot(temps_wide, aes(`San Diego`, Houston)) +
  geom_point() +
  coord_fixed() +
  scale_x_continuous(
    limits = ___,
    breaks = ___
  ) +
  scale_y_continuous(
    limits = ___,
    breaks = ___
  )

Solution

ggplot(temps_wide, aes(`San Diego`, Houston)) +
  geom_point() +
  coord_fixed() +
  scale_x_continuous(
    limits = c(45, 85),
    breaks = c(40, 50, 60, 70, 80)
  ) +
  scale_y_continuous(
    limits = c(48, 88),
    breaks = c(50, 60, 70, 80)
  )

Finally, as the last example of what can be done with coords, we go back to the problem of setting limits on the box-office bar plot. Instead of setting limits with scale functions, we can also set them via the arguments xlim and ylim inside the coord, for example here coord_cartesian(). (This would be a good reason to explicity add coord_cartesian() to a plot.) When we set limits in the coord ggplot does not discard any data points. Instead it simply zooms in or out according to the limits set. Try this out by setting the x limits from 10 to 65 in the box-office plot.

Note: It is normally not a good idea to start a bar plot at a value other than 0. This exercise was solely meant to demonstrate how limits in coords differ from limits in scales.