Lattice: Introduction

Deepayan Sarkar

R graphics

R has a reputation for being a good system for graphics
This is mainly based on its ability to produce good publication-quality statistical plots
This course is about one specific graphics system in R called lattice

R graphics

R actually has two largely independent graphics subsystems
- Traditional graphics
  - Available in R from the beginning
  - Rich collection of tools
  - Not very flexible
- Grid graphics
  - Relatively recent (2000)
  - Low-level tool, highly flexible

Grid graphics, lattice and ggplot2

Grid graphics is not usually used directly by the user
But it forms the basis of two high-level graphics systems:
- lattice: based on Trellis graphics (Cleveland)
- ggplot2: inspired by “Grammar of Graphics” (Wilkinson)

These represent two very different philosophical approaches to graphics
lattice is in many ways a natural successor to traditional graphics
ggplot2 represents a completely different declarative approach

An example: Anscombe’s quartet

I will try to illustrate this with an example
Anscombe (1973) introduced four artificial bivariate datasets to emphasize the importance of graphics
The datasets all had the same means, standard deviations, and correlation

str(anscombe)

'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 ...

An example: Anscombe’s quartet

sapply(anscombe, mean)

      x1       x2       x3       x4       y1       y2       y3       y4 
9.000000 9.000000 9.000000 9.000000 7.500909 7.500909 7.500000 7.500909

sapply(anscombe, sd)

      x1       x2       x3       x4       y1       y2       y3       y4 
3.316625 3.316625 3.316625 3.316625 2.031568 2.031657 2.030424 2.030579

with(anscombe, c(cor(x1, y1), cor(x2, y2), cor(x3, y3), cor(x4, y4)))

[1] 0.8164205 0.8162365 0.8162867 0.8165214

How can we plot all four datasets together?

Anscombe’s quartet using traditional graphics

Traditional graphics thinks of this as four different data sets
The function to create scatter plots is plot()
Multiple plots can be put in the same figure using par(mfrow = ...)
Several ways of specifying variable names inside dataset:

plot(anscombe$x1, anscombe$y1)     # ugly and error-prone

with(anscombe, plot(x1, y1))       # temporarily attach dataset

plot(y1 ~ x1, data = anscombe)     # formula-data interface (also used in modeling)

Anscombe’s quartet using traditional graphics

par(mfrow = c(1, 4))
plot(y1 ~ x1, data = anscombe, pch = 16)
plot(y2 ~ x2, data = anscombe, pch = 16)
plot(y3 ~ x3, data = anscombe, pch = 16)
plot(y4 ~ x4, data = anscombe, pch = 16)

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Anscombe’s quartet using traditional graphics

xrng <- with(anscombe, range(x1, x2, x3, x4))
yrng <- with(anscombe, range(y1, y2, y3, y4))   ## common axis limits
par(mfrow = c(1, 4))
plot(y1 ~ x1, data = anscombe, pch = 16, xlim = xrng, ylim = yrng)
plot(y2 ~ x2, data = anscombe, pch = 16, xlim = xrng, ylim = yrng)
plot(y3 ~ x3, data = anscombe, pch = 16, xlim = xrng, ylim = yrng)
plot(y4 ~ x4, data = anscombe, pch = 16, xlim = xrng, ylim = yrng)

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Anscombe’s quartet using lattice and ggplot2

Both lattice and ggplot2 are capable of producing a single plot with all four datasets
But this requires the dataset to be in the “long format” (one row per data point)

anscombe.long <- 
    with(anscombe, data.frame(x = c(x1, x2, x3, x4), 
                              y = c(y1, y2, y3, y4),
                              which = rep(c("1", "2", "3", "4"), each = 11)))
str(anscombe.long)

'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 ...

Anscombe’s quartet using lattice

library(package = "lattice")
xyplot(y ~ x | which, data = anscombe.long, layout = c(4, 1), pch = 16)

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Anscombe’s quartet using ggplot2

library(package = "ggplot2")
ggplot(data = anscombe.long) + geom_point(aes(x = x, y = y)) + facet_grid( ~ which)

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Anscombe’s quartet using lattice and ggplot2

The approaches share many common features
Both Capable of plotting subsets of data (indexed by categorical variables)
- This idea is known by several names: small multiples, conditioning, facetting
Both makes efficient use of available space (common scales, common axes)
Different visual appearance, but that is superficial (different default themes)

Anscombe’s quartet using lattice and ggplot2

However, the way in which we specify the display is very different
- lattice uses an extension of the formula-data interface (with function xyplot() instead of plot())
- ggplot2 specifies type of rendering (geom) and mapping of variables to coordinates (aesthetics)

The differences become clearer if we try to customize the display further
A natural modification in this example is to add a linear regression line to each scatter plot

Anscombe’s quartet with regression lines

xrng <- with(anscombe, range(x1, x2, x3, x4))
yrng <- with(anscombe, range(y1, y2, y3, y4))
par(mfrow = c(1, 4))
plot(y1 ~ x1, anscombe, pch = 16, xlim = xrng, ylim = yrng)
abline(lm(y1 ~ x1, anscombe))  ## lm() fits regression line, abline() adds the line to current plot
plot(y2 ~ x2, anscombe, pch = 16, xlim = xrng, ylim = yrng) 
abline(lm(y2 ~ x2, anscombe))
plot(y3 ~ x3, anscombe, pch = 16, xlim = xrng, ylim = yrng)
abline(lm(y3 ~ x3, anscombe))
plot(y4 ~ x4, anscombe, pch = 16, xlim = xrng, ylim = yrng)
abline(lm(y4 ~ x4, anscombe))

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Anscombe’s quartet with regression lines

The traditional graphics approach is to add the line after the plot is drawn
In general, a plot is never finished, you can always add more points, lines, text, …

This is possible because there is only one plot !
lattice and ggplot2 need alternative solutions
The ggplot2 solution is to allow plots to have multiple layers
The lattice solution is to allow user to fully specify the procedure used to display data

Regression lines: the ggplot2 solution

Plot with points only

ggplot(data = anscombe.long) + facet_grid( ~ which) + geom_point(aes(x = x, y = y))

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Regression lines: the ggplot2 solution

Plot with regression line only

ggplot(data = anscombe.long) + facet_grid( ~ which) + 
                          geom_smooth(aes(x = x, y = y), method = "lm", se = FALSE)

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Regression lines: the ggplot2 solution

Plot with both points and regression lines

ggplot(data = anscombe.long) + facet_grid( ~ which) + geom_point(aes(x = x, y = y)) + 
                          geom_smooth(aes(x = x, y = y), method = "lm", se = FALSE)

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Regression lines: the lattice solution

The lattice solution is actually very similar to the traditional graphics solution
Basically, we want to do the following for each data subset x, y:
- Draw points at (x, y)
- Draw the linear regression line through x, y
For lattice, we need to encapsulate this procedure into a function

displayFunction <- function(x, y) {
    panel.grid(h = -1, v = -1)               ## add a reference grid
    panel.points(x, y, pch = 16)             ## draw the points
    panel.abline(lm(y ~ x), col = "grey50")  ## draw linear regression line
}

This function is then supplied to the xyplot() function as the panel argument

Regression lines: the lattice solution

Plot with points only

xyplot(y ~ x | which, data = anscombe.long, layout = c(4, 1), panel = panel.points, pch = 16)

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Regression lines: the lattice solution

Plot with grid, points, and regression line

xyplot(y ~ x | which, data = anscombe.long, layout = c(4, 1), panel = displayFunction)

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Regression lines: the lattice solution

lattice also supports a layering mechanism inspired by ggplot2

library(package = "latticeExtra")
xyplot(y ~ x | which, data = anscombe.long, layout = c(4, 1), pch = 16) + 
                      layer_(panel.grid(h = -1, v = -1)) + layer(panel.abline(lm(y ~ x)))

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Regression lines: the lattice solution

Common customizations like these are also supported directly through optional arguments

library(package = "latticeExtra")
xyplot(y ~ x | which, data = anscombe.long, layout = c(4, 1), pch = 16, 
       grid = TRUE, type = c("p", "r"))

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Plan

Day 1
- Background and basic usage of lattice high-level functions
- Themes and annotation: customizing graphical parameters, legends, axes, labels
Day 2
- Customization of panel display using panel functions and layers
- Exercises: Recreate some regression diagnostic plots
- Discuss audience problems

References

Anscombe, Francis J. 1973. “Graphs in Statistical Analysis.” The American Statistician 27 (1). Taylor & Francis Group:17–21.