# 9 Position scales and axes

Every plot has two position scales corresponding to the x and y aesthetics. Typically the user specifies the variables mapped to x and y explicitly, but sometimes an aesthetic is mapped to a computed variable, as happens with geom_histogram(), and does not need to be explicitly specified. For example, the following plot specifications are equivalent:

ggplot(mpg, aes(x = displ)) + geom_histogram()
ggplot(mpg, aes(x = displ, y = after_stat(count))) + geom_histogram()

Although the first example does not state the y-aesthetic mapping explicitly, it still exists and is associated with (in this case) a continuous position scale.

## 9.1 Numeric

The most common continuous position scales are the default scale_x_continuous() and scale_y_continuous() functions. In the simplest case they map linearly from the data value to a location on the plot. There are several other position scales for continuous variables—scale_x_log10(), scale_x_reverse(), etc—most of which are convenience functions used to provide easy access to common transformations:

base <- ggplot(mpg, aes(displ, hwy)) + geom_point()

base
base + scale_x_reverse()
base + scale_y_reverse()

### 9.1.2 Out of bounds values

By default, ggplot2 converts data outside the scale limits to NA. This means that changing the limits of a scale is not precisely the same as visually zooming in to a region of the plot. If your goal is to zoom in part of the plot, it is better to use the xlim and ylim arguments of coord_cartesian():

base <- ggplot(mpg, aes(drv, hwy)) +
geom_hline(yintercept = 28, colour = "red") +
geom_boxplot()

base
base + coord_cartesian(ylim = c(10, 35)) # zoom only
base + ylim(10, 35) # alters the boxplot
#> Warning: Removed 6 rows containing non-finite values (stat_boxplot).

The only difference between the left and middle plots is that that the latter is zoomed in. Some of the outlier points are not shown due to the restriction of the range, but the boxplots themselves remain identical. In contrast, in the plot on the right one of the boxplots has changed. When ylim() is used to set the scale limits, all observations with highway mileage greater than 35 are converted to NA before the stat (in this case the boxplot) is computed. This has the effect of shifting the sample median downward. You can learn more about coordinate systems in Section 15.1.

Although the default behaviour is to convert the out of bounds values to NA, you can override this by setting oob argument of the scale, a function that is applied to all observations outside the scale limits. The default scales::censor() which replaces any value outside the limits with NA. Another option is scales::squish() which squishes all values into the range. An example using a fill scale is shown below:

df <- data.frame(x = 1:6, y = 8:13)
base <- ggplot(df, aes(x, y)) +
geom_col(aes(fill = x)) +                    # bar chart
geom_vline(xintercept = 3.5, colour = "red") # for visual clarity only

base
base + scale_fill_gradient(limits = c(1, 3))
base + scale_fill_gradient(limits = c(1, 3), oob = scales::squish)

On the left the default fill colours are shown, ranging from dark blue to light blue. In the middle panel the scale limits for the fill aesthetic are reduced so that the values for the three rightmost bars are replace with NA and are mapped to a grey shade. In some cases this is desired behaviour but often it is not: the right panel addresses this by modifying the oob function appropriately.

### 9.1.3 Visual range expansion

If you have eagle eyes, you’ll have noticed that the visual range of the axes actually extends a little bit past the numeric limits that I have specified in the various examples. This ensures that the data does not overlap the axes, which is usually (but not always) desirable.

You can eliminate this this space with expand = c(0, 0). One scenario where it is usually preferable to remove this space is when using geom_raster():

ggplot(faithfuld, aes(waiting, eruptions)) +
geom_raster(aes(fill = density)) +
theme(legend.position = "none")

ggplot(faithfuld, aes(waiting, eruptions)) +
geom_raster(aes(fill = density)) +
scale_x_continuous(expand = c(0,0)) +
scale_y_continuous(expand = c(0,0)) +
theme(legend.position = "none")

### 9.1.4 Exercises

1. The following code creates two plots of the mpg dataset. Modify the code so that the legend and axes match, without using facetting!

fwd <- subset(mpg, drv == "f")
rwd <- subset(mpg, drv == "r")

ggplot(fwd, aes(displ, hwy, colour = class)) + geom_point()
ggplot(rwd, aes(displ, hwy, colour = class)) + geom_point()

2. What happens if you add two xlim() calls to the same plot? Why?

3. What does scale_x_continuous(limits = c(NA, NA)) do?

4. What does expand_limits() do and how does it work? Read the source code.

### 9.1.5 Breaks

In the examples above, I specified breaks manually, but ggplot2 also allows you to pass a function to breaks. This function should have one argument that specifies the limits of the scale (a numeric vector of length two), and it should return a numeric vector of breaks. You can write your own break function, but in many cases there is no need, thanks to the scales package (Wickham and Seidel 2020). It provides several tools that are useful for this purpose:

• scales::breaks_extended() creates automatic breaks for numeric axes.
• scales::breaks_log() creates breaks appropriate for log axes.
• scales::breaks_pretty() creates “pretty” breaks for date/times.
• scales::breaks_width() creates equally spaced breaks.

The breaks_extended() function is the standard method used in ggplot2, and accordingly the first two plots below are the same. I can alter the desired number of breaks by setting n = 2, as illustrated in the third plot. Note that breaks_extended() treats n as a suggestion rather than a strict constraint. If you need to specify exact breaks it is better to do so manually.

toy <- data.frame(
const = 1,
up = 1:4,
txt = letters[1:4],
big = (1:4)*1000,
log = c(2, 5, 10, 2000)
)
toy
#>   const up txt  big  log
#> 1     1  1   a 1000    2
#> 2     1  2   b 2000    5
#> 3     1  3   c 3000   10
#> 4     1  4   d 4000 2000
axs <- ggplot(toy, aes(big, const)) +
geom_point() +
labs(x = NULL, y = NULL)
axs
axs + scale_x_continuous(breaks = scales::breaks_extended())
axs + scale_x_continuous(breaks = scales::breaks_extended(n = 2))

Another approach that is sometimes useful is specifying a fixed width that defines the spacing between breaks. The breaks_width() function is used for this. The first example below shows how to fix the width at a specific value; the second example illustrates the use of the offset argument that shifts all the breaks by a specified amount:

axs + scale_x_continuous(breaks = scales::breaks_width(800))
axs + scale_x_continuous(breaks = scales::breaks_width(800, offset = 200))
axs + scale_x_continuous(breaks = scales::breaks_width(800, offset = -200))

Notice the difference between setting an offset of 200 and -200.

You can suppress the breaks entirely by setting them to NULL:

axs + scale_x_continuous(breaks = NULL)

### 9.1.6 Minor breaks

You can adjust the minor breaks (the unlabelled faint grid lines that appear between the major grid lines) by supplying a numeric vector of positions to the minor_breaks argument.

Minor breaks are particularly useful for log scales because they give a clear visual indicator that the scale is non-linear. To show them off, I’ll first create a vector of minor break values (on the transformed scale), using %o% to quickly generate a multiplication table and as.numeric() to flatten the table to a vector.

mb <- unique(as.numeric(1:10 %o% 10 ^ (0:3)))
mb
#>  [1]     1     2     3     4     5     6     7     8     9    10    20    30
#> [13]    40    50    60    70    80    90   100   200   300   400   500   600
#> [25]   700   800   900  1000  2000  3000  4000  5000  6000  7000  8000  9000
#> [37] 10000

The following plots illustrate the effect of setting the minor breaks:

log_base <- ggplot(toy, aes(log, const)) + geom_point()

log_base + scale_x_log10()
log_base + scale_x_log10(minor_breaks = mb)

As with breaks, you can also supply a function to minor_breaks, such as scales::minor_breaks_n() or scales::minor_breaks_width() functions that can be helpful in controlling the minor breaks.

### 9.1.7 Labels

Every break is associated with a label and these can be changed by setting the labels argument to the scale function:

axs + scale_x_continuous(breaks = c(2000, 4000), labels = c("2k", "4k"))

In the examples above I specified the vector of labels manually, but ggplot2 also allows you to pass a labelling function. A function passed to labels should accept a numeric vector of breaks as input and return a character vector of labels (the same length as the input). The scales package provides a number of tools that will automatically construct label functions for you. Some of the more useful examples for numeric data include:

• scales::label_bytes() formats numbers as kilobytes, megabytes etc.
• scales::label_comma() formats numbers as decimals with coomas added.
• scales::label_dollar() formats numbers as currency.
• scales::label_ordinal() formats numbers in rank order: 1st, 2nd, 3rd etc.
• scales::label_percent() formats numbers as percentages.
• scales::label_pvalue() formats numbers as p-values: <.05, <.01, .34, etc.

A few examples are shown below to illustrate how these functions are used:

axs + scale_y_continuous(labels = scales::label_percent())
axs + scale_y_continuous(labels = scales::label_dollar(prefix = "", suffix = "€"))

You can suppress labels with labels = NULL. This will remove the labels from the axis or legend while leaving its other properties unchanged:

axs + scale_x_continuous(labels = NULL)

### 9.1.8 Exercises

1. Recreate the following graphic:

Adjust the y axis label so that the parentheses are the right size.

2. List the three different types of object you can supply to the breaks argument. How do breaks and labels differ?

3. What label function allows you to create mathematical expressions? What label function converts 1 to 1st, 2 to 2nd, and so on?

## 9.2 Date-time

### 9.2.1 Breaks

A special case arises when an aesthetic is mapped to a date/time type: such as the base Date (for dates) and POSIXct (for date-times) classes, as well as the hms class for “time of day” values provided by the hms package (Müller 2020). If your dates are in a different format you will need to convert them using as.Date(), as.POSIXct() or hms::as_hms(). You may also find the lubridate package helpful to manipulate date/time data (Grolemund and Wickham 2011).

Assuming you have appropriately formatted data mapped to the x aesthetic, ggplot2 will use scale_x_date() as the default scale for dates and scale_x_datetime() as the default scale for date-time data. The corresponding scales for other aesthetics follow the usual naming rules. Date scales behave similarly to other continuous scales, but contain additional arguments that are allow you to work in date-friendly units. This section discusses breaks: controlling the labels for date scales is discussed in Section 9.2.4.

The date_breaks argument allows you to position breaks by date units (years, months, weeks, days, hours, minutes, and seconds). For example, date_breaks = "2 weeks" will place a major tick mark every two weeks and date_breaks = 25 years" will place them every 25 years:

date_base <- ggplot(economics, aes(date, psavert)) +
geom_line(na.rm = TRUE) +
labs(x = NULL, y = NULL)

date_base
date_base + scale_x_date(date_breaks = "25 years")

It may be useful to note that internally date_breaks = "25 years" is treated as a shortcut for breaks = scales::breaks_width("25 years"). The longer form is typically unnecessary, but it can be useful if—as discussed in Section 9.1.5—you wish to specify an offset. Suppose the goal is to plot data that span the 20th century, beginning 1 January 1900, and we wish to set breaks in 25 year intervals. Specifying date_breaks = "25 years" produces breaks in the following fashion:

century20 <- as.Date(c("1900-01-01", "1999-12-31"))
breaks <- scales::breaks_width("25 years")
breaks(century20)
#> [1] "1900-01-01" "1925-01-01" "1950-01-01" "1975-01-01" "2000-01-01"

Because the range in century20 starts on 1 January and the breaks increment in whole year values, each of the generated break dates falls on 1 January. We can shift all these breaks so that they fall on 1 February by setting offset = 31 (since there are thirty one days in January).

### 9.2.2 Minor breaks

For date/time scales, you can use the date_minor_breaks argument:

date_base + scale_x_date(
limits = as.Date(c("2003-01-01", "2003-04-01")),
date_breaks = "1 month"
)

date_base + scale_x_date(
limits = as.Date(c("2003-01-01", "2003-04-01")),
date_breaks = "1 month",
date_minor_breaks = "1 week"
)

Note that in the first plot, the minor breaks are spaced evenly between the monthly major breaks. In the second plot, the major and minor beaks follow slightly different patterns: the minor breaks are always spaced 7 days apart but the major breaks are 1 month apart. Because the months vary in length, this leads to slightly uneven spacing.

### 9.2.4 Date scale labels

Like date_breaks, date scales include a date_labels argument. It controls the display of the labels using the same formatting strings as in strptime() and format(). To display dates like 14/10/1979, for example, you would use the string "%d/%m/%Y": in this expression %d produces a numeric day of month, %m produces a numeric month, and %Y produces a four digit year. The table below provides a list of formatting strings:

String Meaning
%S second (00-59)
%M minute (00-59)
%l hour, in 12-hour clock (1-12)
%I hour, in 12-hour clock (01-12)
%p am/pm
%H hour, in 24-hour clock (00-23)
%a day of week, abbreviated (Mon-Sun)
%A day of week, full (Monday-Sunday)
%e day of month (1-31)
%d day of month (01-31)
%m month, numeric (01-12)
%b month, abbreviated (Jan-Dec)
%B month, full (January-December)
%y year, without century (00-99)
%Y year, with century (0000-9999)

One useful scenario for date label formatting is when there’s insufficient room to specify a four digit year. Using %y ensures that only the last two digits are displayed:

base <- ggplot(economics, aes(date, psavert)) +
geom_line(na.rm = TRUE) +
labs(x = NULL, y = NULL)

base + scale_x_date(date_breaks = "5 years")
base + scale_x_date(date_breaks = "5 years", date_labels = "%y")

It can be useful to include the line break character \n in a formatting string, particularly when full-length month names are included:

lim <- as.Date(c("2004-01-01", "2005-01-01"))

base + scale_x_date(limits = lim, date_labels = "%b %y")
base + scale_x_date(limits = lim, date_labels = "%B\n%Y")

In these examples I have specified the labels manually via the date_labels argument. An alternative approach is to pass a labelling function to the labels argument, in the same way I described in Section ??. The scales package provides two convenient functions that will generate date labellers for you:

• label_date() is what date_labels does for you behind the scenes, so you rarely need to call it directly.

• label_date_short() automatically constructs short labels that are sufficient to uniquely identify the dates:

base + scale_x_date(labels = scales::label_date("%b %y"))
base + scale_x_date(limits = lim, labels = scales::label_date_short())

## 9.3 Discrete

It is also possible to map discrete variables to position scales, with the default scales being scale_x_discrete() and scale_y_discrete() in this case. For example, the following two plot specifications are equivalent

ggplot(mpg, aes(x = hwy, y = class)) +
geom_point()

ggplot(mpg, aes(x = hwy, y = class)) +
geom_point() +
scale_x_continuous() +
scale_y_discrete()

Internally, ggplot2 handles discrete scales by mapping each category to an integer value and then drawing the geom at the corresponding coordinate location. To illustrate this, we can add a custom annotation (see Section 7.4) to the plot:

ggplot(mpg, aes(x = hwy, y = class)) +
geom_point() +
annotate("text", x = 5, y = 1:7, label = 1:7)

### 9.3.1 Limits

• For discrete scales, limits should be a character vector that enumerates all possible values.

### 9.3.2 Scale labels

When the data are categorical, you also have the option of using a named vector to set the labels associated with particular values. This allows you to change some labels and not others, without altering the ordering or the breaks:

base <- ggplot(toy, aes(const, txt)) +
geom_point() +
labs(x = NULL, y = NULL)

base
base + scale_y_discrete(labels = c(c = "carrot", b = "banana"))

The also contains functions relevant for other kinds of data, such as scales::label_wrap() which allows you to wrap long strings across lines.

### 9.3.3guide_axis()

Guide functions exist mostly to control plot legends, but—as legends and axes are both kinds of guide—ggplot2 also supplies a guide_axis() function for axes. Its main purpose is to provide additional controls that prevent labels from overlapping:

base <- ggplot(mpg, aes(manufacturer, hwy)) + geom_boxplot()

base + guides(x = guide_axis(n.dodge = 3))
base + guides(x = guide_axis(angle = 90))

## 9.4 Binned

A variation on discrete position scales are binned scales, where a continuous variable is sliced into multiple bins and the discretised variable is plotted. For example, if we want to modify the plot above to show the number of observations at each location, we could use geom_count() instead of geom_point() so that the size of the dots scales with the number of observations. As the left plot below illustrates, this is an improvement but is still rather cluttered. To improve this, the plot on the right uses scale_x_binned() to cut the hwy values into 10 bins before passing them to the geom:

base <- ggplot(mpg, aes(hwy, class)) + geom_count()

base
base + scale_x_binned(n.breaks = 10)

## 9.5 Limits

All scales have limits that define the domain over which the scale is defined and are usually derived from the range of the data. Here we’ll discuss why you might want to specify the limits rather than relying on the data:

1. You want to shrink the limits to focus on an interesting area of the plot.
2. You want to expand the limits to make multiple plots match up or to match the natural limits of a variable (e.g. percentages go from 0 to 100).

It’s most natural to think about the limits of position scales: they map directly to the ranges of the axes. But limits also apply to scales that have legends, like colour, size, and shape, and these limits are particularly important if you want colours to be consistent across multiple plots.

Use the limits argument to modify limits:

• For continuous scales, limits should be a numeric vector of length two. If you only want to set the upper or lower limit, you can set the other value to NA.

A minimal example is shown below. In the left panel the limits of the x scale are set to the default values (the range of the data), the middle panel expands the limits, and the right panel shrinks them:

df <- data.frame(x = 1:3, y = 1:3)
base <- ggplot(df, aes(x, y)) + geom_point()

base
base + scale_x_continuous(limits = c(0, 4))
base + scale_x_continuous(limits = c(1.5, 2.5))
#> Warning: Removed 2 rows containing missing values (geom_point).

You might be surprised that the final plot generates a warning, as there’s no missing value in the input dataset. I’ll talk about this in Section 9.1.2.

### 9.5.1 Setting multiple limits

Manually setting scale limits is a common task when you need to ensure that scales in different plots are consistent with one another. When you create a faceted plot, ggplot2 automatically does this for you:

ggplot(mpg, aes(displ, hwy, colour = fl)) +
geom_point() +
facet_wrap(vars(year))

(Colour represents the fuel type, which can be regular, ethanol, diesel, premium or compressed natural gas.)

In this plot the x and y axes have the same limits in both facets and the colours are consistent. However, it is sometimes necessary to maintain consistency across multiple plots, which has the often-undesirable property of causing each plot to set scale limits independently:

mpg_99 <- mpg %>% filter(year == 1999)
mpg_08 <- mpg %>% filter(year == 2008)

base_99 <- ggplot(mpg_99, aes(displ, hwy, colour = fl)) + geom_point()
base_08 <- ggplot(mpg_08, aes(displ, hwy, colour = fl)) + geom_point()

base_99
base_08

Each plot makes sense on its own, but visual comparison between the two is difficult. The axis limits are different, and because only regular, premium and diesel fuels are represented in the 1998 data the colours are mapped inconsistently.

base_99 +
scale_x_continuous(limits = c(1, 7)) +
scale_y_continuous(limits = c(10, 45))

base_08 +
scale_x_continuous(limits = c(1, 7)) +
scale_y_continuous(limits = c(10, 45))

In many cases setting the limits for x and y axes would be sufficient to solve the problem, but in this example we still need to ensure that the colour scale is consistent across plots.

base_99 +
scale_x_continuous(limits = c(1, 7)) +
scale_y_continuous(limits = c(10, 45)) +
scale_color_discrete(limits = c("c", "d", "e", "p", "r"))

base_08 +
scale_x_continuous(limits = c(1, 7)) +
scale_y_continuous(limits = c(10, 45)) +
scale_color_discrete(limits = c("c", "d", "e", "p", "r"))

Note that because the fuel variable fl is discrete, the limits for the colour aesthetic are a vector of possible values rather than the two end points.

Because modifying scale limits is such a common task, ggplot2 provides some convenience functions to make this easier. For position scales the xlim() and ylim() helper functions inspect their input and then specify the appropriate scale for the x and y axes respectively. The results depend on the type of scale:

• xlim(10, 20): a continuous scale from 10 to 20
• ylim(20, 10): a reversed continuous scale from 20 to 10
• xlim("a", "b", "c"): a discrete scale
• xlim(as.Date(c("2008-05-01", "2008-08-01"))): a date scale from May 1 to August 1 2008 (date scales are discussed in Section 9.2.1)

To ensure consistent axis scaling in the previous example, we can use these helper functions:

base_99 + xlim(1, 7) + ylim(10, 45)
base_08 + xlim(1, 7) + ylim(10, 45)

Another option for setting limits is the lims() function which takes name-value pairs as input, where the name specifies the aesthetic and the value specifies the limits:

base_99 + lims(x = c(1, 7), y = c(10, 45), colour = c("c", "d", "e", "p", "r"))
base_08 + lims(x = c(1, 7), y = c(10, 45), colour = c("c", "d", "e", "p", "r"))

### References

Grolemund, Garrett, and Hadley Wickham. 2011. “Dates and Times Made Easy with lubridate.” Journal of Statistical Software 40 (3): 1–25. http://www.jstatsoft.org/v40/i03/.

Müller, Kirill. 2020. Hms: Pretty Time of Day. https://CRAN.R-project.org/package=hms.

Wickham, Hadley, and Dana Seidel. 2020. Scales: Scale Functions for Visualization. https://CRAN.R-project.org/package=scales.