The Grammar of Graphics

A philosophy for data visualisation, based on the foundations formalised in Leland Wilkinson’s seminal book, now implemented in various software packages.

Presentation

• The Grammar of Graphics slides
• Source code
• An introduction to ggplot2 slides

Types of charts

Can you name the following data visualisations?

The Grammar of Graphics

The book

Figure 1: Wilkinson (2006) Figure 2.2

“The grammar of graphics determines how algebra, geometry, aesthetics, statistics, scales and coordinates interact”

Variables

Operations applied before scale transformations

• Mathematical transforms (sin, log)
• Sorting and ranking
• Aggregation
• Quantiles
• Residuals

Algebra

Let \(A := (x,y,z)\) and \(B := (a,a,b)\).

• Cross \(A\times B = ([x,a],~[y,a],~[z,b])\)
• Nest \(A/B = (x|a,~y|a,~z|b)\)
• Blend \(A+B = (x,y,z,a,a,b)\)

Scales

• Categorical
• Interval
• Time
• One-bend (log, power)
• Two-bend (arcsine, logit, probit)
• Probability

“Graphics do not care about the scales on which they are drawn”

Wilkinson (2006)

Statistics

After scale & variable transformations
Before coordinate transformations

• Regression coefficients
• Smoothers
• Binning and aggregation
• Confidence intervals
• Density estimation

Geometry

Things we can actually see

Functions	Partitions	Networks
point line area interval path schema	contour polygon	edge

Collision modifiers: stack, dodge, jitter

Coordinates

“Ordinary graphics such as intervals and polygons take on radically different appearances under different planar transformations.”

• Cartesian coordinates
• Triangular coordinates
• Polar coordinates
• Map projections
• Conformal mapping

A new graphic? Or a transformation of an existing one?

Aesthetics

Form	Surface	Motion	Sound	Text
position size shape rotation resolution	colour texture blur transparency	direction speed acceleration	tone volume rhythm voice	label

“Much of the skill in graphic design is knowing what combinations of attributes to avoid.”

Figure 2: Wilkinson (2006) Figure 10.11

Putting it all together

Demonstration using R package ggplot2 (Wickham 2010).

Let’s make a pie chart

Titanic dataset

head(Titanic)

  Class    Sex   Age Survived Freq
1   1st   Male Child       No    0
2   2nd   Male Child       No    0
3   3rd   Male Child       No   35
4  Crew   Male Child       No    0
5   1st Female Child       No    0
6   2nd Female Child       No    0

Algebra: Class × Survived × Freq

pie <- ggplot(Titanic) +
  scale_x_discrete() + scale_y_continuous() + scale_fill_discrete() +
  geom_bar(width = 1, position = "fill") +
  aes(x = "", fill = Survived, weight = Freq) +
  theme_titanic()

pie + coord_polar(theta = "y")

pie + coord_polar(theta = "y") +
  facet_grid( ~ Class)

gg <- ggplot(Titanic) +
  scale_x_discrete() + scale_y_continuous() + scale_fill_discrete() +
  geom_bar(width = 1, position = 'stack') +
  aes(x = Class, fill = Class, weight = Freq) +
  theme_titanic()

gg + coord_polar(theta = 'x') + ggtitle('Rose')

gg + coord_polar(theta = 'y') + ggtitle('Racetrack???')

Figure 3: Nightingale (1858)

Napoleon’s March

Figure 4: Minard (1869) (view larger)

gg <- ggplot(troops, aes(x = long, y = lat))
gg <- gg + geom_path(aes(size = survivors,
                         colour = direction,
                         group = group), lineend = "round")
gg <- gg + geom_text(data = cities, aes(label = city),
                     size = 3, family = "serif", fontface = "italic")

Or, with the more familiar default theme_grey():

Resources

Implementations

• Graphics Production Language (SPSS)

• ggplot2, ggvis (R)

• plotnine, Bokeh (Python)

• Gadfly (Julia)

• D3.js, Vega (JavaScript)

• Grammarphone (Spotify API)

• asciiplot

source('asciiplot.R')
asciiplot(
  df = iris,
  aes = list(x = 'Petal.Width', y = 'Petal.Length', shape = 'Species'),
  geom = 'point'
)

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Further reading

• Article: Chernoff faces in ggplot2 🌝

• Article: Using ggplot2 with Stata

• Cheatsheet: Data Visualisation with ggplot2 (by RStudio)

• Charles Annis on the “IntraOcular Trauma Test”

• Source code repository for these slides