Formula Interface for ggplot2

Daniel Kaplan and Randall Pruim

January, 2018

Formula-driven graphics

There are several excellent graphics packages provided for R. The ggformula package currently builds on one of them, ggplot2, but provides a very different user interface for creating plots. The interface is based on formulas (much like the lattice interface) and the use of the chaining operator (%>%) to build more complex graphics from simpler components.

The ggformula graphics were designed with several user groups in mind:

The basic formula template

The basic template for creating a plot with ggformula is

gf_plottype(formula, data = mydata)


For example, in a bivariate plot, formula will take the form y ~ x, where y is the name of a variable to be plotted on the y-axis and x is the name of a variable to be plotted on the x-axis. (It is also possible to use expressions that can be evaluated using variables in the data frame as well.)

Here is a simple example:

gf_point(mpg ~ hp, data = mtcars)

Selecting the glyph type

The “kind of graphic” is specified by the name of the graphics function. All of the ggformula data graphics functions have names starting with gf_, which is intended to remind the user that they are formula-based interfaces to ggplot2: g for ggplot2 and f for “formula.” Commonly used functions include

The function names generally match a corresponding function name from ggplot2, although

Each of the gf_ functions can create the coordinate axes and fill it in one operation. (In ggplot2 nomenclature, gf_ functions create a frame and add a layer, all in one operation.) This is what happens for the first gf_ function in a chain. For subsequent gf_ functions, new layers are added, each one “on top of” the previous layers.


Each of the marks in the plot is a glyph. Every glyph has graphical attributes (called aesthetics in ggplot2) that tell where and how to draw the glyph. In the above plot, the obvious attributes are x- and y-position:
We’ve told R to put mpg along the y-axis and hp along the x-asis, as is clear from the plot.

But each point also has other attributes, including color, shape, size, stroke, fill, and alpha (transparency). We didn’t specify those in our example, so gf_point() uses some default values for those – in this case smallish black filled-in circles.

Specifying attributes

In the gf_ functions, you specify the non-position graphical attributes using an extension of the basic formula. Attributes can be set to a constant value (e.g, set the color to “blue”; set the size to 2) or they can be mapped to a variable in the data or some expression involving the variables (e.g., map the color to sex, so sex determines the color groupings)

Attributes are set or mapped using additional arguments.

  • adding an argument of the form attribute = value sets attribute to value.
  • adding an argument of the form attribute = ~ expression maps attribute to expression

where attribute is one of color, shape, etc., value is a constant (e.g. "red" or 0.5, as appropriate), and expression may be some more general expression that can be computed using the variables in data (although often is is better to create a new variable in the data and to use that variable instead of an on-the-fly calculation within the plot).

The following plot, for instance,

  • We use cyl to determine the color and carb to determine the size of each dot. Color and size are mapped to cyl and carb. A legend is provided to show us how the mapping is being done. (Later, we can use scales to control precisely how the mapping is done – which colors and sizes are used to represent which values of cyl and carb.)

  • We also set the transparency to 50%. The gives the same value of alpha to all glyphs in this layer.

gf_point(mpg ~ hp, color = ~ cyl, size = ~ carb, alpha = 0.50, data = mtcars) 

On-the-fly calculations

ggformula allows for on-the-fly calculations of attributes, although the default labeling of the plot is often better if we create a new variable in our data frame. In the examples below, since there are only three values for carb, it is easier to read the graph if we tell R to treat cyl as a categorical variable by converting to a factor (or to a string). Except for the labeling of the legend, these two plots are the same.

gf_point(mpg ~ hp,  color = ~ factor(cyl), size = ~ carb, alpha = 0.75, data = mtcars)
gf_point(mpg ~ hp,  color = ~ cylinders, size = ~ carb, alpha = 0.75, 
         data = mtcars %>% mutate(cylinders = factor(cyl)))

“One-variable” plots

For some plots, we only have to specify the x-position because the y-position is calculated from the x-values. Histograms, densityplots, and frequency polygons are examples. To illustrate, we’ll use density plots, but the same ideas apply to gf_histogram(), and gf_freqpolygon() as well. Note that in the one-variable density graphics, the variable whose density is to be calculated goes to the right of the tilde, in the position reserved for the x-axis variable.

data(Runners, package = "mosaicModel")
Runners <- Runners %>% filter( !
gf_density( ~ net, data = Runners)
gf_density( ~ net,  fill = ~ sex,  alpha = 0.5, data = Runners)
# gf_dens() is similar, but there is no line at bottom/sides, and it is not "fillable"
gf_dens( ~ net, color = ~ sex, alpha = 0.7, data = Runners)    

Several of the plotting functions include additional arguments that do not modify attributes of individual glyphs but control some other aspect of the plot. In this case, adjust can be used to increase or decrease the amount of smoothing.

# less smoothing
gf_dens( ~ net, color = ~ sex, alpha = 0.7, data = Runners, adjust = 0.25)  
# more smoothing
gf_dens( ~ net, color = ~ sex, alpha = 0.7, data = Runners, adjust = 4)     


When the fill or color or group aesthetics are mapped to a variable, the default behavior is to lay the group-wise densities on top of one another. Other behavior is also available by using position in the formula. Using the value "stack" causes the densities to be laid one on top of another, so that the overall height of the stack is the density across all groups. The value "fill" produces a conditional probability graphic.

gf_density( ~ net, fill = ~ sex, color = NA, position = "stack", data = Runners)
gf_density( ~ net, fill = ~ sex, color = NA, position = "fill", data = Runners, adjust = 2)

Similar commands can be constructed with gf_histogram() and gf_freqpoly(), but note that color, not fill, is the active attribute for frequency polygons. It’s also rarely good to overlay histograms on top of one another – better to use a density plot or a frequency polygon for that application.


The ggplot2 system allows you to make subplots — called “facets” — based on the values of one or two categorical variables. This is done by chaining with gf_facet_grid() or gf_facet_wrap(). These functions use formulas to specify which variable(s) are to be used for faceting.

gf_density_2d(net ~ age, data = Runners) %>% gf_facet_grid( ~ sex)
# the dot here is a bit strange, but required to make a valid formula
gf_density_2d(net ~ age, data = Runners) %>% gf_facet_grid( sex ~ .)
gf_density_2d(net ~ age, data = Runners) %>% gf_facet_wrap( ~ year)
gf_density_2d(net ~ age, data = Runners) %>% gf_facet_grid(start_position ~ sex)

An alternative syntax uses | to separate the faceting information from the main part of the formula.
Here is another example using our weather data. The redundant use of the y and color attributes for temperature makes it easier to compare across facets.

gf_ribbon(low_temp + high_temp ~ date | city ~ year, data = Weather, alpha = 0.3) 

gf_linerange(low_temp + high_temp ~ date | city ~ year, color = ~ avg_temp, data = Weather) %>%
  gf_refine(scale_colour_gradientn(colors = rev(rainbow(5))))

In this case, we should either not facet by year, or allows the x-scale to be freely adjusted in each column so that we don’t have so much unnecessary white space. We can do the latter using the scales argument to gf_facet_grid().

gf_ribbon(low_temp + high_temp ~ date | city ~ ., data = Weather, alpha = 0.3) 

gf_linerange(low_temp + high_temp ~ date, color = ~ avg_temp, data = Weather) %>%
  gf_refine(scale_colour_gradientn(colors = rev(rainbow(5)))) %>%
  gf_facet_grid(city ~ year, scales = "free_x")

More 2-variable plots

Using jitter and transparency to handle overlapping cases

Sometimes you have so many points in a scatter plot that they obscure one another. The ggplot2 system provides two easy ways to deal with this: translucency and jittering.

Use alpha = 0.5 to make the points semi-translucent. If there are many points overlapping at one point, a much smaller value of alpha, say alpha = 0.01. We’ve already seen this above.

Using gf_jitter() in place of gf_point() will move the plotted points to reduce overlap. Jitter and transparency can be used together as well.

gf_point(age ~ sex, alpha = 0.05, data = Runners)
gf_jitter(age ~ sex, alpha = 0.05, data = Runners)

Box and Whisker plots

Box and whisker plots show the distribution of a quantitative variable as a function of a categorical variable. The formula used in gf_boxplot() should have the quantitative variable to the left of the tilde. (To make horizontal boxplots using ggplot2 you have to make vertical boxplots and then flip the coordinates with coord_flip().)

gf_boxplot(net ~ sex, color = "red", data = Runners)
gf_boxplot(net ~ sex, color = ~ start_position, data = Runners)