The Grammar of Graphics

(Section 8.1)

Graph Concepts

It’s hard to succinctly describe how ggplot2 works because it embodies a deep philosophy of visualisation.

—Hadley Wickham (author of the ggplot2 package)

Key Graphics Vocabulary

• The Frame
• Glyphs
• Aesthetics
• Scales
• Guides

At first we focus on these key concepts. Then we will learn how to translate these concepts into code.

The Frame

What is a Frame?

Frame

The relationship between position and the data being plotted.

• The frame provides the space in which we will draw glyphs.
• The frame determines what position means.
• We work with 2D-graphs, so often we specify the frame with two variables.
• But often we need only one variable. (R will know what to do with the other dimension.)

Example: m111survey

library(bcscr)
?m111survey

data("m111survey", package = "bcscr")

  height    sex fastest  GPA
1     76   male     119 3.56
2     74   male     110 2.50
3     64 female      85 3.80
4     62 female     100 3.50
5     72   male      95 3.20

m111survey

Research Question: What’s the relationship between fastest and GPA?

Define the frame with two variables: fastest and GPA.

ggplot(data = m111survey,
       mapping = aes(x = fastest, y = GPA))

The Result: Just a Frame!

No glyphs have been plotted yet!

Glyphs

What is a Glyph?

Glyph

The basic graphical unit that corresponds to a case in the data table.

• You can see glyphs.
• Each glyph is formed from at least one case.
• The location of each glyph is determined by the variable(s) that defined the frame.

Example: m111survey Scatter Plot

In the m111survey graph, let’s represent each student (case) with a point.

The points are the glyphs.

• This time each glyph goes with one exactly one case.
• The x-coordinate is determined by the value of fastest for the case.
• The y-coordinate is determined by the value of GPA for the case.

ggplot(m111survey, aes(x = fastest, y = GPA)) +
  geom_point()

The Result: a Scatter Plot

Aesthetics

An aesthetic is a perceptible property of a glyph that varies from case to case.

We already know two aesthetics:

• location in the x-direction
• location in the y-direction

Some other possible aesthetics are:

• size
• color
• shape

Example: m111survey

Let’s use the color of each point to indicate the sex of the student.

We are mapping the aesthetic “color” to the variable sex.

ggplot(m111survey, aes(x = fastest, y = GPA)) +
  geom_point(aes(color = sex))

The Result

Another Aesthetic: Size

Let’s also map the aesthetic “size” to the variable height.

ggplot(m111survey, aes(x = fastest, y = GPA)) +
  geom_point(aes(color = sex, size = height))

The Result

Scales and Guides

Scales

Scale

The relationship between the value of a variable and the graphical attribute to be displayed for that value.

Example: we mapped color to sex. R chose to set the value “female” to a reddish color, and the value “male” to a turquoise-blue color. That choice was the choice of a scale. (You can make R use a different scale if you like.)

Every aesthetic mapping involves a scale. R has default scales ready to use, if you don’t choose you own.

Example: Your Own Color Scale

ggplot(m111survey, aes(x = fastest, y = GPA)) +
  geom_point(aes(color = sex)) +
  scale_color_manual(values = c("pink", "red"))

This scale maps:

• “female” to pink
• “male” to red

The Result

Guides

Guide

An indication, for the human viewer, of the scale being used in an aesthetic mapping.

A guide takes you backwards: from the perceptual property to the data value it represents.

Examples of Guides

• Labels and tick-marks along the x-axis show you the scale for the x location aesthetic.
• Labels and tick-marks along the y-axis show you the scale for the y location aesthetic (if one is defined).
• Legends show guides for aesthetics such as color, size and shape.

Summary (for this plot)

• The glyphs are points.
  • This time each glyph represents one and only one case.
• The frame is:
  • x = fastest
  • y = GPA
• Other aesthetics are:
  • color = sex
• There are scales for the three aesthetic mappings above.
• The legend, axis labels, tick marks and hash-lines are the guides.

More Examples

Bar Glyphs

A bar graph of sex in m111survey:

ggplot(m111survey, aes(x = sex)) + geom_bar()

Note:

• We used only one variable to define the frame. (R will guess what to do with the y-axis.)
• The glyphs will be bars.

The Result

Some New things

• This time, each glyph corresponded to more than one case.
  • All the female students helped determine the bar over “female” on the x-axis.
  • All the male students helped determine the bar over “male” on the x-axis.
• R determined the height of the bars by counting up the number of students in each group.
• It guessed to do this because we did not map the y-aesthetic, and we asked for bars.
• The choice to count was the choice of a statistic.
• Sometimes one can ask R to use a statistic other than its default.

Sex and Feeling about Weight

Let’s map the aesthetic “fill” to weight_feel:

ggplot(m111survey, aes(x = sex)) +
  geom_bar(aes(fill = weight_feel))

The Result

Practice

• How many glyphs are in the sex-and-weight bar graph?
• What aesthetics got mapped to what variables?
• What guides do you see?

Histograms

Question:

How are the fastest speeds driven distributed, for students in the m111survey data?

Let’s investigate with a histogram.

Histogram of the fastest speed ever driven.

In the Histogram

• The glyphs are rectangles. Each rectangle represents the cases in an interval of speed.
• The frame is:
  • x-location maps to fastest.
  • y-location is not part of the frame. (It represents a statistic: the height of a rectangle gives the number of cases that it represents.)
• There are no other aesthetics. (The burlywood fill is constant.)
• The scale for x-location maps \(x\) to fastest in linear fashion
• The x-axis has guides found for numerical variables.

Layering

• Many graphs have more than one type of glyph.
• This is called layering.

We can layer the histogram with a rug of jittered speeds.

Histogram of the fastest speed ever driven.

Density-Curve Glyphs

• Density curves also describe the distribution of a numerical variable.
• They are a good alternative to histograms.

Density plot of the fastest speed ever driven.

Numerical and Categorical Variable

Question:

Is there a relationship between seating preference and the fastest speed ever driven?

Density plot of the fastest speed ever driven.

In This Plot

• Frame is x-location (mapped to fastest)
• Another aesthetic was color (mapped to seat)
• Glyphs are the density curves (representing the cases for each value of seat)
• What guides do you see?

Violin Plots

These are a good alternative to density plots, especially when studying the relationship between a numerical variable and a categorical variable.

Violin plot of the fastest speed ever driven.

Box-and-Whisker Glyphs

These are useful in about the same range of circumstances as violin plots.

What the Plots Mean

In a list of values:

• the first quartile \(Q_1\) is a number that has about 25% of the values less than it
• the third quartile \(Q_3\) is a number that has about 75% of the values less than it
• \(Q_1 - Q_3\) is called the interquartile range (IQR).
• the median is a number that has about 50% of the data below it

\(Q_3 - Q_1\) is called the interquartile range (IQR).

Box-and-Whisker I

When there are no outliers:

• lower whisker goes from minimum value to \(Q_1\) (extends along lowest 25% of the values)
• box from \(Q_1\) to \(Q_3\) shows middle 50% of the values
• the median is the line inside the box
• upper whisker goes from \(Q_3\) to the maximum value (extends along highest 25% of the values)

Box-and-Whisker II

• If a value is bigger than \(Q_3 + 1.5 \times IQR\) then it is plotted individually as an outlier.
• Then the upper whisker goes from \(Q_3\) to the highest value that is not an outlier.
• If a value is less than \(Q_1 - 1.5 \times IQR\) then it is plotted individually as an outlier.
• Then the lower whisker goes from \(Q_1\) to the lowest value that is not an outlier.

Illustration of a simple box plot.

Choropleth Maps

• choropleth: from the Greeks words “choros” (region) and “plethos” (a multitude)
• A choropleth graph is a graph in which the frame is provided by some sort of map with regions that might be:
  • countries
  • cities in the U.S.
  • counties in the U.S.
  • any other type of regions

Choropleth map of state populations in the U.S.

Facets

Making Facets

• Sometimes it is useful to split out your graphs into separate plots.
• This enables you to incorporate more variables into your study.

Question:

How does fastest speed drive relate to sex and to seating preference?

Violin plots of the fastest speed ever driven, by sex and seating preference.

In This Plot:

• Frame: x-location mapped to sex, y-location mapped to fastest.
• Glyphs are of two types: violins and jittered points.
• Other aesthetics: none.
• Facet-ing by seat.