Hidden Mappings
in the
Grammar of Graphics

Paul Murrell

ggplot(pets) +
    geom_col(aes(x=millions, y=country, fill=pet), position="dodge") +
    ggtitle("Global Pet Ownership")

This is a side-by-side bar plot produced by {ggplot2}
which is based on the Grammar of Graphics.

ggplot(pets) +
    geom_col(aes(x=millions, y=country, fill=pet), position="dodge") +
    scale_x_continuous(guide=guide_axis()) +
    scale_y_discrete(guide=guide_axis()) +
    scale_colour_discrete(guide=guide_legend()) +
    ggtitle("Global Pet Ownership")

In the Grammar of Graphics, the plot is described 
as a set of **mappings**, via **scales**, 
from **data** to the **aesthetics** of **geoms**.

The variable `millions` maps to the length of the bars.
The variable `country` maps to the vertical position 
of the bars.
The variable `pet` maps to the fill colour of the bars.

Reading the plot requires axes and legends
(which the Grammar of Graphics calls **guides**)
to explain the scales.

The axis labels and plot title are also guides 
(annotations) that explain the meaning of the
data values.

ggplot(pets) +
    geom_point(aes(x=millions, y=country, colour=pet)) +
    ggtitle("Global Pet Ownership")

This plot demonstrates the power of the 
Grammar of Graphics.

We can produce a dot plot with almost exactly the
same {ggplot2} code, just by changing the geom.

PART I
Text Mappings

The Grammar of Graphics is rightly lauded for the
fact that it reduces the cornucopia of possible
data visualisations
to a small set of composable components.

But we are going to contend that it could be made
even simpler.

And the mechanism by which the grammar of graphics
could be made simpler is by broadening the role
of mappings.

ggplot(pets) +
    geom_col(aes(x=millions, y=country, fill=pet), position="dodge")

According to the Grammar of Graphics, 
these are the mappings for the bar plot:
- millions maps to bar length
- country maps to bar position (vertical)
- pet maps to bar fill colour

These mappings support simple questions ...
that some bars are different
- different colour
- different vertical position
that some bars are the same
- same colour
that some value is larger for some bars
that some value is twice as large for some bars
- different lengths

But these mappings are not enough to support all questions
- what does length represent?
- what does colour represent?

If we add grid lines (part of the x-axis),
we can answer some questions more easily
that some value is 2x, 3x, 4x, etc as large 

But what are the grid lines really?
The grid lines are mappings like the bars
- millions maps to line horizontal position 

If we add the x-axis labels, we can answer some more questions
- EXACT data values from text (0, 20, 40, 60, 80)
- size of bars
- twice, three times, four times
- size of differences

But what are the x-axis labels really?
The text labels are also mappings
- millions maps to text horizontal position 
- millions maps to text shape

ggplot(pets) +
    geom_vline(aes(xintercept=x), data=data.frame(x=seq(0, 80, 20))) +
    geom_text(aes(label=x, x=x), y=-Inf, vjust=1,
              data=data.frame(x=seq(0, 80, 20))) +
    geom_col(aes(x=millions, y=country, fill=pet), position="dodge")

We can even draw the x-axis as explicit **mappings**
from **data** to the **aesthetics** of **geoms**.

The crucial idea is that we can decode data values from
text labels

The x-axis is not a different sort of component from the bars;
the grid lines and text are just **mappings** from 
data values to aesthetics of geoms.

What is special is that we can decode **data values** 
from text, which unlocks important questions.

If we add the y-axis labels, can we answer more questions?
- what are the identities of the bars?

The y-axis labels are also mappings
- country maps to text vertical position 
- country maps to text shape
  BUT NOT to text shapes that can be decoded to countries
  (easily, in all cases)

What this shows is that mapping to different text shapes 
is not necessarily enough to be able to decode data values.

In this case, the mapping to text shape is very much like the
mapping to bar vertical position - we just get differences,
not data values.

Just to further emphasise this point, this plot has 
added a text shape legend that explains the different
text shapes.

NOTE that the text legend is still just a set of mappings
- country to text position in space
- country to (two-letter) text shape
- country to (full name) text shape

If we add full country names as the y-axis labels 
we can answer more questions
- the country for each (pair of) bars

The y-axis labels are still mappings
- country maps to text vertical position 
- country maps to text shape
  (this time that can be decoded to data values)

Again, the crucial part is that we can decode **data values**
from the text shape

If we add the legend, we can answer more questions
- the pet type for each colour

Still just more mappings
- pet type to rectangle colour
- pet type to rectangle position in space
- pet type to text shape
- pet type to text position in space

Again, the crucial part is that we can decode **data values**
from the text shape

If we add the axis title and plot title,
we can answer more questions
- the counts are in millions
- we are looking at numbers of pets owned
  (rather than, e.g., wild animal populations)

We are still mapping information to text shape,
but the information is **metadata** rather than data values

Again, the crucial part is that we can decode **data values**
from the text shape
BUT with the added point that we can decode **complex**
information from text shapes

The plot is described as a set of **mappings**, 
via **scales**, from **data** to the 
**aesthetics** of **geoms**.

This is traditionally only applied to the data symbols
(in this case bars)
- millions maps to the length of the bars.
- country maps to the vertical position of the bars.
- pet maps to the fill colour of the bars.

BUT the guides are actually also just more mappings 
of data values to aesthetics of geoms.
- millions maps to the horizontal position of lines
- millions maps to the shape of x-axis text

The special thing about a text geom is that it is 
self-explanatory and **absolute**.
All other geoms are interpreted **relative** to
each other or relative to the text geoms.

NOTE that Wilkinson acknowledged the special nature 
of a text label:
"It provides, in essence, a guide to a guide."

We are just saying that text is a guide to itself.
There is no such thing as guides; 
it is mappings all the way down.

PART II
CRAP Mappings

Having proposed a simplication of the 
Grammar of Graphics,
we now turn to an **extension** of the 
Grammar of Graphics.

One area where the Grammar of Graphics
is silent is the overall arrangement of the 
elements of a data visualisation, what we might
call issues of **graphic design**

We propose expanding the Grammar of Graphics
idea of **mappings**to encompass some of the 
basic ideas of graphic design.

CRAP Design

The CRAP acronym comes from four basic principles 
for graphic design that were popularised by 
Naomi Robbins 

CONTRAST means that elements should be obviously the same
or obviously different, not ambiguously similar.

REPETITION means the elements that are related should
appear the same (colour, size, etc)

ALIGNMENT means that every element should be aligned
with some other element.

PROXIMITY means that elements that are related should
be close to each other.

CRAP Data Visualisation

How do these CRAP design principles apply to 
data visualisation?

And can we incorporate them as just more 
examples of Grammar of Graphics **mappings**?

We will explore this idea by attempting to 
improve upon the original {ggplot2} plot

Contrast

We can think of CONTRAST as a mapping
of IMPORTANCE

In this version of the plot, there is 
greater contrast between elements of the plot 
that deserve more of our attention and
less important elements.

Importance maps to
- bars more colourful
- title larger and bolder
- axes lighter

Contrast

We can even create a guide to explain the importance mapping

Repetition

We can think of REPETITION as using
CONSISTENT **mappings**

Obviously we should have consistent colours between
the legend and the main plot, 
BUT in this version of the plot there are several
other consistent mappings
- consistent vertical position
- consistent size
- consistent horizontal position

Alignment

We can think of ALIGNMENT as a mapping of
STRUCTURE

In this version of the plot, every element
is aligned with another *related* element.

Structure maps to 
- common vertical position
- common horizontal position

Alignment

Alignment

Proximity

We can also think of PROXIMITY as mapping
STRUCTURE

In this version of the plot, the 
title is separate from the main plot 
which is separate from the legend 

Structure maps to
- vertical position

Proximity

Proximity guide

CRAP mappings

This is the original plot for comparison

CRAP mappings

Final result for comparison

Summary

• There are more mappings (and fewer guides) in a {ggplot2} plot than you might have thought.
• Mapping data values to text is an important mapping.
• Mapping metadata to text is an important mapping.
• Consistency in mappings is important.
• Mapping structure and importance are important mappings.

Acknowledgements

• “The Grammar of Graphics” (2nd Edition)
  Leland Wilkinson
• “The Non-Designer’s Design Book” (4th Edition)
  Robin Williams
• healthforanimals.org

Questions

• What does this have to do with R Graphics and {grid}?

{ggplot2} does not treat all of these things as mappings,
so we cannot control, for example, guides with as much
freedom as we can control data symbols.
Taking control of some mappings can only be done with {grid}.