Lecture 8: The grammar of graphics

STAT598z: Intro. to computing for statistics

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Vinayak Rao

Department of Statistics, Purdue University

Grammar?

A set of rules describing how to compose a 'vocabulary' into permissible 'sentences'

The R language has its own grammar

"Grammar of Graphics" is an abstraction describing how to create rich and informative plots

'The Grammar of Graphics', Leland Wilkinson

Embodied in the ggplot package for R

'A Layered Grammar of Graphics', Hadlay Wickham, Journal of Computational and Graphical Statistics, 2010

R’s base graphics supports some plotting commands

E.g. plot(), hist(), barplot()

Extending these standard graphics to custom plots is tedious

ggplot is much more flexible, and pretty

Install like you’d install any other package:

install.packages('ggplot2') library(ggplot2)

Why a grammar?

View different graphs as sharing common structure

Grammar of graphics breaks everything down into a set of components and rules relating them.

Rather than viewing an images as a 'thing' views it as a sequence of transformations applied to data.

This abstraction avoids

• limiting yourself to what standard canned packages do
• hacking through the graphics rendering engine

The components of a graphic are orthogonal:

• changing one shouldn’t break the others
• different settings of components are valid (if not sensible)
• You can build complexity by adding more layers

The grammar represents what we do with the data

• Plotting is part of understanding rich datasets
• Having understood the structure of a graph, we might ask: what if we do this instead of that?

ggplot: R implementation of GoG

Components of ggplot ’s grammar of graphics:

One or more layers:

• Data and aesthetic mappings
• A statistical transformation
• A geometric object
• Position adjustments
• A scale for each aesthetic
• A coordinate system
• A facet specification

Plotting in base R

library('ggplot2') 
str(diamonds)  # diamonds is a dataset from ggplot

plot(diamonds$carat, diamonds$price)

diamonds_loc <- diamonds[sample(50000,10000),]

ggplot() +
  layer(
    data = diamonds,
    mapping = aes(x = carat, y = price),
    geom = "point", stat = "identity",
    position = "identity" ) +
  scale_y_continuous() + scale_x_continuous() +
  coord_cartesian()

Of course, ggplot has intelligent defaults:

ggplot(diamonds, aes(carat, price)) + geom_point()

There’s also further abbreviations via qplot

(I find this confusing)

Layers

ggplot produces an object that is rendered into a plot

This object consists of a number of layers

Each layer can get own inputs or share arguments to ggplot()

Add another layer to previous plot:

ggplot(diamonds, aes(x=carat, y = price)) + geom_point() +
geom_smooth()

Different layers and their components

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Data and aesthetic mappings:

• ggplot requires a dataframe as input
• this layer maps columns of input to aspects like x,y-coordinate, size, color etc
• reshape2 and tidyr packages useful to get data in the right format

mix2norm <- data.frame(x = c(rnorm(1000),rnorm(1000,3)),
                 grp = as.factor(rep(c(1,2),each=1000)))

ggplot(mix2norm, aes(x=x, color = grp)) +
    geom_density(adjust=1)

A statistical transformation

A summarization of the raw input

Example: binning, smoothing, boxplot, identity

Default: often identity (but see previous)

Specified via stat

ggplot(mix2norm, aes(x=x, color = grp, fill= grp)) +
geom_density(alpha=.4, adjust=1/2, size=2, stat="bin")

ggplot(mix2norm, aes(x=x, color = grp, fill= grp)) +
geom_density(alpha=.4, adjust=1/2, size=2, stat="bin") +
scale_color_manual(values = c("1" = "magenta", "2"="blue"))

A geometric object

The type of plot created

Specified via geom According to dimensionality:

• 0-dim point, text
• 1-dim line
• 2-dim polygon, interval geom_density uses ribbon

Others include geom_hist, geom_bar, geom_contour, geom_line

Can specify only geometry and not statistical transformation

ggplot(mix2norm, aes(x=x, color = grp)) +
geom_density(adjust=1/2)

Can change only statistical transformation but not geometry

ggplot(mix2norm, aes(x=x, color = grp)) +
stat_density(adjust=1/2)

Why does this look different? What are the defaults for position and geometry?

ggplot(mix2norm, aes(x=x, color = grp)) +
stat_density(adjust=1/2, geom="line")

geom_density plots an object of geometry "ribbon"

Requires to specify both a y_max and y_min

library('tibble')
my_waves <- tibble(x=seq(0,6.28,.1),y1=sin(x),y2=sin(x)^2)

ggplot(my_waves) + geom_ribbon(aes(x=x,ymax=y1,ymin=y2))

ggplot(mix2norm ) +
    stat_density(aes(x=x, ymin=0, ymax=..density..,color = grp), adjust=1/2, size=2,
                 geom = "ribbon")

Position

How different parts of a layer are positioned

• identity, dodge, jitter etc.

ggplot(mix2norm, aes(x=x, color = grp)) +
  stat_density(adjust=1/2, size=2, position = "identity",
  geom = "line")

Scaling

How each input value maps to the specified aesthetic

• Specified via scale

Continuous, logarithmic, values to shapes, what limits, what labels, what marks

ggplot(mix2norm, aes(x=x, color = grp)) +
  stat_density(adjust=1/2, size=2, position = "identity",
  geom = "line") + scale_y_log10(limits = c(1e-5,1))

Coordinates

How positions of things are mapped to positions on the screen.

Different coordinates can affect the shape of geometric objects

Cartesian, polar, map-projection

ggplot(mix2norm, aes(x=x, color = grp)) +
  stat_density(adjust=1/2, size=2, position = "identity",
  geom = "line") + coord_polar()

Facets

Allows arranging different graphs in a grid/panel

ggplot(mix2norm, aes(x=x, color = grp)) +
  stat_density(adjust=1/2, size=2, position = "identity",
  geom = "line") + facet_grid(grp~.)

More examples

my_diamonds <- diamonds[sample(50000,5000,F),]
ggplot(my_diamonds, aes(x=carat, y = price,colour=cut)) +
  geom_point() +  
  geom_line(stat= "smooth", method="loess",size=1, alpha= 0.7)

ggplot(my_diamonds, aes(x=carat, y = price,colour=cut)) +
geom_point() +
geom_line(stat= "smooth", method=lm, size=1, alpha= 0.7) +
scale_x_log10()+ scale_y_log10()

ggplot(my_diamonds, aes(x=carat, fill=cut)) +
geom_histogram(alpha=0.7, binwidth=.4, color="black",
position="dodge") + xlim(0,2)

• “Probably the best statistical graphic ever drawn, this map by Charles Joseph Minard portrays the losses suffered by Napoleon’s army in the Russian campaign of 1812. Beginning at the Polish-Russian border, the thick band shows the size of the army at each position. The path of Napoleon’s retreat from Moscow in the bitterly cold winter is depicted by the dark lower band, which is tied to temperature and time scales.” Edward Tufte, http://www.edwardtufte.com/tufte/posters

First read the data:

troops <- read.table("Data/minard-troops.txt", header=T)
cities <- read.table("Data/minard-cities.txt", header=T)
#  options(repr.plot.width=10, repr.plot.height=3)

plot_troops <- ggplot(troops, aes(long, lat)) +
  geom_path(aes(size = survivors, colour = direction,
  group = group))

plot_both <- plot_troops +
    geom_text(data = cities, aes(label = city), size = 3)
plot_both

plot_polished <- plot_both + scale_size(
   breaks = c(1, 2, 3) * 10^5, labels = (c(1, 2, 3) * 10^5)) +
   scale_colour_manual(values = c("grey50","red")) +
   xlab(NULL) + ylab(NULL) 
plot_polished

Income dataset: http://www-bcf.usc.edu/~gareth/ISL/data.html

DataIncm<-read.table("Data/Income2.csv",header=TRUE,sep=",")

plt1 <- ggplot(DataIncm, aes(x=Education, y = Income)) +
          geom_point(size=2, color="blue") +
          theme(text=element_text(size=15)); plt1

plt1 <- ggplot(DataIncm, aes(x=Seniority, y = Income)) +
          geom_point(size=2, color="blue") +
          theme(text=element_text(size=15)); plt1

ggplot doesn’t support 3d plotting, but:

plt1 <- ggplot(DataIncm, aes(x=Seniority, y = Education, size=Income)) +
          geom_point(color="blue") +
          theme(text=element_text(size=15)); plt1

ggplot(DataIncm, aes(x=Education, y=Seniority, color=Income)) +
geom_point(size=2) + theme(text=element_text(size=10)) +
scale_color_continuous(low="blue", high="orange")

Further reading

‘A Layered Grammar of Graphics’, Hadlay Wickham, Journal of Computational and Graphical Statistics, 2010

ggplot documentation: http://docs.ggplot2.org/current/

Search ‘ggplot’ on Google Images for inspiration

Play around to make your own figures