Data Visualization Using R

R graphics

R comes with two largely independent graphics subsystems

• “Traditional” graphics (package graphics)

  • Available in R from the beginning
  • Rich collection of tools
  • Not very flexible

• Grid graphics (package grid)

  • Relatively recent (2000)
  • Low-level tool, highly flexible

• Grid forms the basis of two high-level graphics systems:

  • Package lattice: based on Trellis graphics (Cleveland)
  • Package ggplot2: inspired by “Grammar of Graphics” (Wilkinson)

R graphics

It is also possible to interface with external graphics systems.

This is useful when some kind of interaction is required.

• Package rgl: Interactive 3-D plots with OpenGL

• Package plotly: Javascript-based plots in browser

• Package rggobi: Interactive and dynamic graphics using GGobi

We will see a little bit of all these.

Traditional graphics - some history

• Like the language itself, R graphics was derived from S (Bell Labs, 1970s)

• S graphics was based on the GRZ model:

  • May be described as a “painter’s model”

  • Graphic is built out of “primitives” such as line segments, polygons, text, etc.

  • Later elements are drawn on top of earlier ones

  • No provision for deleting an element once it was drawn

Consequence of the painter’s model

• Mental approach: a plot is a work-in-progress

• Always possibile to add something more

• This attitude pervades traditional graphics

An example: Anscombe’s dataset 1

plot(x = anscombe$x1, y = anscombe$y1)
abline(lm(y1 ~ x1, anscombe))

An example: Anscombe’s dataset 2

plot(y2 ~ x2, data = anscombe, pch = 16)
abline(lm(y2 ~ x2, anscombe), col = "red")

How could this plot have been created using low-level functions?

Try running this code one line at a time:

plot(anscombe$x1, anscombe$y1, type = "n", axes = FALSE, xlab = "", ylab = "")
box()
points(anscombe$x1, anscombe$y1, pch = 16)
axis(side = 1)
axis(side = 2)
title(main = "Anscombe's first dataset", xlab = "x1", ylab = "y1")
abline(lm(y1 ~ x1, anscombe), col = "red")

A more polished version

plot(anscombe$x2, anscombe$y2, type = "n", axes = FALSE, xlab = "", ylab = "")
lims <- par("usr")
rect(lims[1], lims[3], lims[2], lims[4], col = "grey80", border = NA)
abline(v = pretty(lims[1:2]), h = pretty(lims[3:4]), col = "white", lwd = 2)
axis(side = 1, col = "grey80", col.axis = "grey20")
axis(side = 2, col = "grey80", col.axis = "grey20", las = 1)
points(anscombe$x2, anscombe$y2, pch = 16)
title(main = "Anscombe's second dataset", xlab = "x2", ylab = "y2", col = "grey20")
abline(lm(y2 ~ x2, anscombe), col = "grey20")

Other high-level plots

• Generally, traditional graphics work by calling specialized high-level functions

• Some you have already learned about:
  • Histograms / density plots
  • Q-Q plots
  • Dot plots
  • Bar charts
  • Box and whisker plots

• Let’s see some more examples using the airquality dataset.

str(airquality)

'data.frame':   153 obs. of  6 variables:
 $ Ozone  : int  41 36 12 18 NA 28 23 19 8 NA ...
 $ Solar.R: int  190 118 149 313 NA NA 299 99 19 194 ...
 $ Wind   : num  7.4 8 12.6 11.5 14.3 14.9 8.6 13.8 20.1 8.6 ...
 $ Temp   : int  67 72 74 62 56 66 65 59 61 69 ...
 $ Month  : int  5 5 5 5 5 5 5 5 5 5 ...
 $ Day    : int  1 2 3 4 5 6 7 8 9 10 ...

Other high-level plots - examples

hist(airquality$Ozone)

Other high-level plots - examples

qqnorm(airquality$Ozone)

Other high-level plots - examples

airquality$fmonth <- with(airquality, factor(Month, levels = 1:12, labels = month.name))
boxplot(Ozone ~ droplevels(fmonth), data = airquality)

Comparing subsets

• The last example (box and whisker plot) is different — it allows comparison!

• Making comparisons is one of the primary goals of statistical graphics

• How can we compare other plots like scatter plots and histograms?

Juxtaposing by splitting figure region

par(mfrow = c(2, 2))
hist(airquality$Ozone)
hist(airquality$Solar.R)
hist(airquality$Wind)
hist(airquality$Temp)

Juxtaposing by splitting figure region

s <- with(airquality, split(Temp, droplevels(fmonth)))
str(s)

List of 5
 $ May      : int [1:31] 67 72 74 62 56 66 65 59 61 69 ...
 $ June     : int [1:30] 78 74 67 84 85 79 82 87 90 87 ...
 $ July     : int [1:31] 84 85 81 84 83 83 88 92 92 89 ...
 $ August   : int [1:31] 81 81 82 86 85 87 89 90 90 92 ...
 $ September: int [1:30] 91 92 93 93 87 84 80 78 75 73 ...

Juxtaposing by splitting figure region

par(mfrow = c(2, 3))
qqnorm(s$May, main = "May")
qqnorm(s$June, main = "June")
qqnorm(s$July, main = "July")
qqnorm(s$August, main = "August")
qqnorm(s$September, main = "September")

Juxtaposing by splitting figure region

par(mfrow = c(2, 3))
hist(s$May)
hist(s$June)
hist(s$July)
hist(s$August)
hist(s$September)

Juxtaposing: better comparison with common scales

par(mfrow = c(2, 3)); r <- range(airquality$Temp)
hist(s$May, xlim = r)
hist(s$June, xlim = r)
hist(s$July, xlim = r)
hist(s$August, xlim = r)
hist(s$September, xlim = r)

Juxtaposing: better comparison with common scales

par(mfrow = c(1, 4))
with(anscombe,
{
    rx <- range(x1, x2, x3, x4)
    ry <- range(y1, y2, y3, y4)
    plot(y1 ~ x1, pch = 16, xlim = rx, ylim = ry); abline(lm(y1 ~ x1), col = "magenta")
    plot(y2 ~ x2, pch = 16, xlim = rx, ylim = ry); abline(lm(y2 ~ x2), col = "magenta")
    plot(y3 ~ x3, pch = 16, xlim = rx, ylim = ry); abline(lm(y3 ~ x3), col = "magenta")
    plot(y4 ~ x4, pch = 16, xlim = rx, ylim = ry); abline(lm(y4 ~ x4), col = "magenta")
})

Superposition is better when feasible

dlist <- lapply(s, density, na.rm = TRUE)
dxrng <- range(unlist(lapply(dlist, function(d) d$x)))
dyrng <- range(unlist(lapply(dlist, function(d) d$y)))
plot(dxrng, dyrng, xlab = "Temperature", ylab = "Density")
for (i in seq_along(dlist)) lines(dlist[[i]], col = i)
legend("topright", legend = names(dlist), 
       lty = 1, col = seq_along(dlist))

Limitations of traditional graphics

• Although not very difficult, these plots are not simple either

• The results leave a lot to be desired

• Eventually led to the development of alternative systems such as lattice and ggplot2

• Let’s see some examples for comparison

Example of a lattice plot

library(lattice)
histogram(~ Ozone, data = airquality)

Example of a lattice plot

histogram(~ Ozone | fmonth, data = airquality)

Example of a ggplot2 plot

library(ggplot2)
ggplot(airquality, aes(x = Ozone)) +  stat_bin(binwidth = 20, geom = "bar")

Example of a ggplot2 plot

ggplot(airquality, aes(x = Ozone)) + facet_wrap(~ fmonth) + stat_bin(binwidth = 20, geom = "bar")

lattice and ggplot2

• Both are add-on packages

• lattice is based on Trellis graphics in S-PLUS

• ggplot2 is based on the “Grammar of Graphics”

• Two very different philosophical approaches

• We will learn about both these in a little more detail

Overview: lattice

• Package implementing high-level statistical displays

• Philosophically similar to traditional R graphics

  • Different function for different types of displays (histograms, scatter plots, etc.)

  • Customization done using low-level functions

• Extensively uses formula-data interface

• Use as much of the available space as possible

• Enable direct comparsion by superposition (grouping) when possible

• Encourage comparison when juxtaposing (conditioning):

  • use common axes, add common reference objects such as grids.

Example: Scatter plots with xyplot()

xyplot(y1 ~ x1, data = anscombe) # Basic usage is similar to plot()

Data must be in suitable form for conditioning

str(anscombe) # not OK

'data.frame':   11 obs. of  8 variables:
 $ x1: num  10 8 13 9 11 14 6 4 12 7 ...
 $ x2: num  10 8 13 9 11 14 6 4 12 7 ...
 $ x3: num  10 8 13 9 11 14 6 4 12 7 ...
 $ x4: num  8 8 8 8 8 8 8 19 8 8 ...
 $ y1: num  8.04 6.95 7.58 8.81 8.33 ...
 $ y2: num  9.14 8.14 8.74 8.77 9.26 8.1 6.13 3.1 9.13 7.26 ...
 $ y3: num  7.46 6.77 12.74 7.11 7.81 ...
 $ y4: num  6.58 5.76 7.71 8.84 8.47 7.04 5.25 12.5 5.56 7.91 ...

anscombe.long <-
    with(anscombe,
         data.frame(x = c(x1, x2, x3, x4),
                    y = c(y1, y2, y3, y4),
                    which = factor(rep(1:4, each = nrow(anscombe)))))
str(anscombe.long) # OK

'data.frame':   44 obs. of  3 variables:
 $ x    : num  10 8 13 9 11 14 6 4 12 7 ...
 $ y    : num  8.04 6.95 7.58 8.81 8.33 ...
 $ which: Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...

Example: conditioning

xyplot(y ~ x | which, data = anscombe.long, grid = TRUE)

Here x and y are “primary variables”, which is a “conditioning variable”.

Customization

• How can we add regression lines as before?

• There is not one but four lines to add

scatterWithLine <- function(x, y)
{
    panel.grid(h = -1, v = -1)
    panel.points(x, y, pch = 16)
    panel.abline(lm(y ~ x), col = "magenta")
}

Customization

xyplot(y ~ x | which, data = anscombe.long, panel = scatterWithLine)

Overview: lattice

• Whole display created in one step; “work-in-progress” model does not work

• Each high-level plot has a default display

• Variables play different roles: primary, conditioning, grouping (superposition)

• Can be customized by a user-supplied “panel” function

• In fact, many other aspects can be customized: axis annotation, strips, legends

Histogram

histogram(~ Solar.R | fmonth, data = airquality, as.table = TRUE)

Kernel density plots

densityplot(~ Ozone | fmonth, data = airquality, as.table = TRUE)

Kernel density plots (with grouping)

densityplot(~ Ozone, airquality, groups = droplevels(fmonth),
            auto.key = list(columns = 5))

Q-Q plots

qqmath(~ Ozone | fmonth, airquality, grid = TRUE, layout = c(5, 1))

Box and whisker plots

bwplot(fmonth ~ Ozone, airquality)

Multiple primary variables / different scales

bwplot(fmonth ~ Ozone + Solar.R, airquality, outer = TRUE,
       between = list(x = 1),
       scales = list(x = "free"), xlab = NULL)

Violin plots - alternative display function

bwplot(fmonth ~ Ozone + Solar.R, airquality, outer = TRUE,
       between = list(x = 1), panel = panel.violin,
       scales = list(x = "free"), xlab = NULL)

Tabular data

• Some common displays are designed for tabular data: bar chart, dot plot, pie chart

• Data are typically counts or rates obtained by cross classification by multiple factors

VADeaths # death rates by age and population group

      Rural Male Rural Female Urban Male Urban Female
50-54       11.7          8.7       15.4          8.4
55-59       18.1         11.7       24.3         13.6
60-64       26.9         20.3       37.0         19.3
65-69       41.0         30.9       54.6         35.1
70-74       66.0         54.3       71.1         50.0

VADeathsDF <- as.data.frame.table(VADeaths, responseName = "Rate")
str(VADeathsDF) # Better format for graphics functions

'data.frame':   20 obs. of  3 variables:
 $ Var1: Factor w/ 5 levels "50-54","55-59",..: 1 2 3 4 5 1 2 3 4 5 ...
 $ Var2: Factor w/ 4 levels "Rural Male","Rural Female",..: 1 1 1 1 1 2 2 2 2 2 ...
 $ Rate: num  11.7 18.1 26.9 41 66 8.7 11.7 20.3 30.9 54.3 ...

Bar chart - traditional graphics

par(mfrow = c(1, 2))
barplot(t(VADeaths))
barplot(VADeaths, beside=TRUE, horiz=TRUE,
        legend.text=TRUE, xlim = c(0, 100))

Bar chart - lattice

barchart(Rate ~ Var1 | Var2, VADeathsDF, layout = c(4, 1))

Bar chart - without misleading heights

barchart(Rate ~ Var1 | Var2, VADeathsDF, layout = c(4, 1), origin = 0,
         scales = list(x = list(rot = 45)))

Dot plot

dotplot(Rate ~ Var1 | Var2, VADeathsDF, layout = c(4, 1))

Dot plot with grouping

dotplot(Rate ~ Var1, VADeathsDF, groups = Var2, type = "o",
        auto.key = list(columns = 2, points = TRUE, lines = TRUE))

3-D scatter plots

cloud(depth ~ lat * long, data = quakes,
      zlim = rev(range(quakes$depth)),
      screen = list(z = 105, x = -70), panel.aspect = 0.75,
      xlab = "Longitude", ylab = "Latitude", zlab = "Depth")

3-D surface plots

wireframe(Freq ~ Var1 + Var2, data = as.data.frame.table(volcano),
          shade = TRUE, aspect = c(61/87, 0.5))

Summary

• Separate function for each display type

• Display can be customized

• Many other advanced features - see manual (start with package?lattice)

GGplot

• Traditional graphics and lattice are both procedural in their approach

• The “grammar of graphics” takes a declarative approach

• The user describes a plot using a layered grammar

  • A plot is composed by “adding” various components

  • Has one or more layers, each associated with a dataset

  • Rather than using predefined designs, user describes each layer

Components of the grammar

• Aesthetic mappings that map data values to some aspect of the displayed graph, e.g.,
  • coordinate positions
  • color, shape, size
  • group, etc.

Example: scatter plot

• A scatter plot needs a dataset, an x-variable, and a y-variable

p <- ggplot(airquality)
p + geom_point(aes(x = Ozone, y = Solar.R))

Example: scatter plot

• Equivalent call

p <- ggplot(airquality, aes(x = Ozone, y = Solar.R))
p + geom_point()

Example: scatter plot

• Something different (and meaningless)

p <- ggplot(airquality, aes(x = Ozone, y = Solar.R))
p + geom_bar(stat = "identity", position = "identity")

Example: scatter plot

• The grammar approach makes it easy to create nonsense

• But it also frees you from pre-defined plot types

• Let’s go through some examples

Example: histogram

p <- ggplot(airquality)
p + stat_bin(aes(x = Ozone), binwidth = 20, geom = "bar")

Example: density plot

p + stat_density(aes(x = Ozone))

Example: density plot without shading

p + stat_density(aes(x = Ozone), geom = "path")

Example: density plot with groups

p + stat_density(aes(x = Ozone, group = fmonth), position = "identity", geom = "path")

Example: density plot with colored groups

p + stat_density(aes(x = Ozone, color = fmonth), position = "identity", geom = "path")

Example: density plot with faceting (conditioning)

p + stat_density(aes(x = Ozone), geom = "path") + facet_wrap(~fmonth)

More compact calls using qplot()

• Using the full grammar everytime is unnecessary

• Most common plots can be created using qplot()

Example: scatter plot

qplot(x = Ozone, y = Solar.R, data = airquality, facets = ~ fmonth)

Example: density plot

qplot(data = airquality, x = Ozone, color = fmonth, geom = "density")

Layering to customize displays

qplot(x = x, y = y, data = anscombe.long, facets = ~ which) +
    stat_smooth(method = "lm", se = FALSE)

Layering to customize displays

qplot(x = x, y = y, data = anscombe.long, facets = ~ which) +
    stat_smooth(method = "lm", se = FALSE) +
    stat_smooth(method = "lm", formula = y ~ poly(x, 2), se = FALSE)

Dot plot

qplot(x = Var1, y = Rate, data = VADeathsDF, color = Var2) +
    geom_line(aes(x = as.numeric(Var1)))

Interactive 3-D graphics

• Traditional R graphics is usually good for static plots

• There is some support for interaction, but this is rudimentary

• A useful package for interactive 3-D plots is rgl

• Uses OpenGL to provide 3-D plots that can be rotated and zoomed

Interactive 3-D graphics using rgl

library(rgl)
with(quakes, plot3d(lat, long, -depth, col = "red", type = "s", size = 1))

Further choices for interactive graphics

Several add-on packages provide some useful interfaces:

• Package plotly and rbokeh: Javascript-based plots in browser

• Package rggobi: Interactive and dynamic graphics using GGobi (tours, brushing/linking)

Demos:

• rgl.R

• plotly.R

• rggobi.R