Trellis graphics 1

Trellis graphics

Extremely useful approach for graphical exploratory data analysis (EDA)

Allows to examine for complicated, multiple variable relationships.

Types of plots

xyplot: scatterplot

bwplot: boxplots

stripplot: display univariate data against a numerical variable

dotplot: similar to stripplot

histogram

densityplot: kernel density estimates

barchart

piechart: (Not available in R)

splom: scatterplot matrices

contourplot: contour plot of a surface on a regular grid

levelplot: pseudo-colour plot of a surface on a rectangular grid

Trellis graphics 2

wireframe: perspective plot of a surface evaluated on a regular grid

cloud: perspective plot of a cloud of points (3D scatterplot)

Note in S-Plus, the trellis graphics functions are contained in the library, trellis. This library should be loaded automatically when starting S-Plus. However if it isn’t, give the command library(trellis). In R, the trellis graphics features are usually not automatically loaded. To load them you need to give the command library(lattice).

Trellis graphics 3

<digression>

. Fi r st ( ) and . Last ( ) functions

It is possible to configure S-Plus and R to load certain files, override defaults, etc when they start up with the use of the . Fi r st ( ) function. This is similar to the use of . cshr c/. bashr c and . l ogi n files in Unix.

Any commands that you wish to run everytime you start up S-Plus and R should go in the . Fi r st ( ) function. An example of a . Fi r st ( ) function is . Fi r st <- f unct i on( ) {

l i br ar y( l at t i ce)

opt i ons( cont r ast s=c( “ cont r . t r eat ment ” , “ cont r . pol y” ) )

}

So everytime that S-Plus/R is run from the directory containing this . Fi r st ( ) function, these two commands will be run. The opt i ons( ) command sets the default contrasts when dealing with factors in linear models.

The . Last ( ) function is similar to Unix’s . l ogout file in that it contains the commands you want run when quitting S-Plus/R.

</digression>

Trellis graphics 4

Trellis graph

dist

time

50

100

150

200

5 10 15 20 25

Usual approach

5 10 15 20 25

5010

015

020

0

dist

time

Trellis graphics 5

Trellis approach xyplot(time ~ dist, data=hills,

panel = function(x, y, ...) {

panel.xyplot(x, y, ...)

panel.lmline(x, y ,type="l")

panel.abline(ltsreg(x, y), lty=3)

}

)

Usual plotting approach attach(hills)

plot(dist, time)

abline(lm(time ~ dist))

abline(ltsreg(time ~ dist), lty=3)

detach()

Trellis graphics 6

Trellis approach

Speed of Light Data

Speed

Exp

erim

ent

No.

1

2

3

4

5

600 700 800 900 1000 1100

Usual approach

1 2 3 4 5

700

800

900

1000

Speed of Light Data

Experiment No.

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Trellis approach bwplot(Expt ~ Speed, main="Speed of Light Data", ylab="Experiment No.", data=morley,

panel = function(x, y, ...) {

panel.bwplot(x, y, ...)

panel.abline(v=734.5)

}

)

Usual plotting approach attach(morley)

plot.factor(Expt, Speed, main="Speed of Light Data", xlab="Experiment No.")

abline(h=734.5)

detach(morley)

Instead of plot.factor, the boxplot command boxplot(split(Speed,Expt), main="Speed of Light Data", xlab="Experiment No.")

could be used as well.

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Many trellis type plots can not be done using the more standard graphics commands, or are very complicated. One example is a scatter plot matrix

Scatter Plot Matrix

Fertility

4040

50

50

60

60

70

7080

8090 90

Agriculture

00

2020

40

40

40

40

60

6080 80

Examination

1010

20

20

20

2030

30

Education

00

1010

20

20

30

3040

4050 50

Catholic

00

2020

40

40

60

6080

80100 100

Infant.Mortality

1010

1515

20

2025 25

splom(~ swiss.df, aspect="fill",

panel = function(x, y, ...) {

panel.xyplot(x, y, ...); panel.loess(x, y, ...)

}

)

Trellis graphics 9

This example shows the power of panel functions, as the basic plot commands can easily be applied to multi-panel displays. In this example the scatterplot smoother loess is applied to each panel of the plot

Viscosity

Tim

e

0

50

100

150

200

250

0 50 100 150 200 250 300

Weight: 20 grams 50 grams 100 grams

sps<-trellis.par.get("superpose.symbol") sps$pch <- 1:7 trellis.par.set("superpose.symbol",sps)

xyplot(Time ~ Viscosity, data=stormer, groups = Wt, panel = panel.superpose, type="b", key = list(columns=3, text= list(paste(c("Weight: ","",""), unique(stormer$Wt), "grams")), points=Rows(sps,1:3)))

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There are an number approaches with Trellis graphics for displaying 3 dimensional information

0

1

2

3

4

5

6

1 2 3 4 5 6

-700

-750

-800

-850

-900

-950

topo.plt <- expand.grid(topo.mar)

topo.plt$pred <- as.vector(predict(topo.loess,topo.plt))

levelplot(pred ~ x*y, topo.plt,aspect=1,

at = seq(690, 960, 10), xlab="", ylab="",

panel = function(x,y,subscripts, ...) {

panel.levelplot(x,y,subscripts, ...)

panel.xyplot(topo$x, topo$y, cex=0.5, col=1)

}

)

Trellis graphics 11

x

pred

pred

700

750

800

850

900

950

wireframe(pred ~ x*y, topo.plt,aspect=c(1,0.5), drape=T,

screen=list(z=-150, x=-60),

colorkey=list(space="right", height=0.6))

Trellis graphics 12

0

1

2

3

4

5

6

0 1 2 3 4 5 6

700 725 750 775 800

800

825

850

850

875

875

875 875 900 900 925

925

950

contourplot(z ~ x * y, mat2tr(topo.lo), aspect=1,

at = seq(700, 1000, 25), xlab="", ylab="",

panel = function(x,y,subscripts, ...) {

panel.contourplot(x,y,subscripts, ...)

panel.xyplot(topo$x, topo$y, cex=0.5) } )

Note that these last two plots are from S-Plus not R (where the rest of today’s plots are from. I couldn’t get the code to work properly in R for these two plots.

Trellis graphics 13

Where Trellis plots get particularly useful is when we condition.

Scatter Plot Matrix

Comp.1

-1-1

-0.5

-0.5

0

0

0.5

0.5

1

11.5 1.5

Comp.2

-0.1-0.1

-0.05

-0.05

0

0

0.05

0.05

0.1

0.10.15 0.15

Comp.3

-0.1-0.1

-0.05

-0.05

0

0

0

0

0.05

0.050.1 0.1

Blue male Blue female Orange male Orange female

lcrabs <- log(crabs[,4:8]) lcrabs.pc <- predict(princomp(lcrabs)) crabs.grp <- c("B","b","O","o")[rep(1:4,rep(50,4))] splom(~lcrabs.pc[,1:3], groups=crabs.grp, panel = panel.superpose, key = list(text=list(c("Blue male","Blue female", "Orange male", "Orange female")), points=Rows(trellis.par.get("superpose.symbol"),1:4), columns=4))

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BlueFemale

Comp.1

Comp.2

Comp.3

OrangeFemale

Comp.1

Comp.2

Comp.3

BlueMale

Comp.1

Comp.2

Comp.3

OrangeMale

Comp.1

Comp.2

Comp.3

sex <- crabs$sex; levels(sex) <- c("Female","Male")

sp <- crabs$sp; levels(sp) <- c("Blue","Orange")

splom(~lcrabs.pc[,1:3] | sp*sex, pscales=0)

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The princomp command calculates the principle components of the data. Principle components finds linear combinations of the data, such that each is orthogonal to each other, and they maximize the variance of each. The crab data is highly correlated and the principle component analysis rotates the data to 5 uncorrelated descriptors

Scatter Plot Matrix

FL

222.2

2.2

2.4

2.4

2.6

2.6

2.6

2.62.8

2.83 33.2

3.2

RW

1.81.8 22

2.2

2.2

2.4

2.4

2.4

2.4

2.6

2.62.8

2.83 3

CL

2.82.83

3

3.2

3.2

3.4

3.43.6

3.63.8 3.8

CW

2.82.8 33

3.2

3.2

3.4

3.4

3.4

3.4

3.6

3.63.8 3.84

4

BD

22

2.5

2.5

2.5

2.53 3

Blue male Blue female Orange male Orange female

Trellis graphics 16

> summary(princomp(lcrabs))

Importance of components:

Comp.1 Comp.2 Comp.3 Comp.4

Std deviation 0.5166405 0.07465358 0.047914392 0.024804021

Prop of Variance 0.9689051 0.02023046 0.008333672 0.002233308

Cum Proportion 0.9689051 0.98913557 0.997469244 0.999702552

Comp.5

Standard deviation 0.0090521887

Proportion of Variance 0.0002974484

Cumulative Proportion 1.0000000000

> loadings(princomp(lcrabs))

Loadings:

Comp.1 Comp.2 Comp.3 Comp.4 Comp.5

FL -0.452 -0.157 0.438 0.752 0.114

RW -0.387 0.911

CL -0.453 -0.204 -0.371 -0.784

CW -0.440 -0.672 0.591

BD -0.497 -0.315 0.458 -0.652 0.136

Trellis graphics 17

Days

Primary

First form

Second form

Third form

0 20 40 60 80

FemaleAverage learner

Aboriginal

MaleAverage learner

Aboriginal

0 20 40 60 80

FemaleSlow learnerAboriginal

MaleSlow learnerAboriginal

Primary

First form

Second form

Third form

FemaleAverage learnerNon-aboriginal

MaleAverage learnerNon-aboriginal

0 20 40 60 80

FemaleSlow learner

Non-aboriginal

MaleSlow learner

Non-aboriginal

0 20 40 60 80

Quine <- quine

levels(Quine$Eth) <- c("Aboriginal","Non-aboriginal")

levels(Quine$Sex) <- c("Female","Male")

levels(Quine$Age) <- c("Primary", "First form", "Second form", "Third form")

levels(Quine$Lrn) <- c("Average learner","Slow learner")

bwplot(Age ~ Days | Sex*Lrn*Eth,data=Quine,layout=c(4,2))

Trellis graphics 18

Primary

First form

Second form

Third form

0 20 40 60 80

Eth: AboriginalSex: Female

Eth: Non-aboriginalSex: Female

Primary

First form

Second form

Third form

Eth: AboriginalSex: Male

0 20 40 60 80

Eth: Non-aboriginalSex: Male

Days of Absence

Average learner Slow learner

stripplot(Age ~ Days | Eth*Sex, data=Quine, groups=Lrn, jitter=T, panel = function(x,y, subscripts, jitter.data=F, ...) { if(jitter.data) y <- jitter(y) panel.superpose(x,y,subscripts,...) }, xlab = "Days of Absence", between = list(y=1), par.strip.text = list(cex=1.2), key = list(columns=2, text=list(levels(Quine$Lrn)), points=Rows(trellis.par.get("superpose.symbol"), 1:2)), strip = function(...) strip.default(..., strip.names=c(T,T),style=1))

Trellis graphics 19

The conditioning variables in trellis plot are treated as categorical. For continuous variables, you can have lots of categories

Temperature

Ozo

ne

0

50

100

150

60 70 80 90

wind wind

60 70 80 90

wind wind

60 70 80 90

wind wind

60 70 80 90

wind

wind wind wind wind wind wind

0

50

100

150

wind 0

50

100

150

wind wind wind wind wind wind wind

wind wind

60 70 80 90

wind wind

60 70 80 90

wind wind

60 70 80 90

0

50

100

150

wind

xyplot(ozone ~ temperature | wind, data=environmental,

ylab="Ozone",xlab="Temperature")

> length(unique(environmental$wind))

[1] 28

Trellis graphics 20

Lets split wind into different levels (shingles) and condition on that instead. Wind <- equal.count(environmental$wind, number=6, overlap=0.2)

xyplot(ozone ~ temperature | Wind, data=environmental,

ylab="Ozone",xlab="Temperature")

Temperature

Ozo

ne

0

50

100

150

60 70 80 90

Wind Wind

60 70 80 90

Wind

Wind Wind

60 70 80 90

0

50

100

150

Wind

Trellis graphics 21

> Wind

Data:

[1] 7.4 8.0 12.6 11.5 8.6 13.8 20.1 9.7 9.2 10.9 13.2 11.5 12.0 18.4 11.5 [16] 9.7 9.7 16.6 9.7 12.0 12.0 14.9 5.7 7.4 9.7 13.8 11.5 8.0 14.9 20.7

and so on

[106] 10.3 16.6 6.9 14.3 8.0 11.5

Intervals:

min max count

1 2.05 7.15 24 2 6.65 8.25 22 3 7.75 9.95 25 4 9.45 11.75 35 5 10.65 14.05 27 6 12.35 20.95 23

Ovrlap between adjacent intervals:

[1] 6 7 9 16 7

Trellis graphics 22

The shingles can also be displayed graphically with plot(Wind,aspect=0.4)

Range

Pan

el

1

2

3

4

5

6

5 10 15 20

Range

Pan

el

1

2

3

4

5

6

5 10 15 20

Trellis graphics 23

Temperature

Ozo

ne

0

50

100

150

60 70 80 90

WindRad

WindRad

60 70 80 90

WindRad

WindRad

60 70 80 90

WindRad

WindRad

WindRad

WindRad

WindRad

WindRad

WindRad

0

50

100

150

WindRad

0

50

100

150

WindRad

WindRad

WindRad

WindRad

WindRad

WindRad

WindRad

WindRad

60 70 80 90

WindRad

WindRad

60 70 80 90

WindRad

0

50

100

150

WindRad

60 70 80 90

xyplot(ozone ~ temperature | Wind * Rad, data=environmental

Temperature

Ozo

ne

0 50100150

60 70 80 90

RadWind

RadWind

60 70 80 90

RadWind

RadWind

RadWind

RadWind

RadWind

0 50100150

RadWind

0 50100150

RadWind

RadWind

RadWind

RadWind

RadWind

RadWind

RadWind

0 50100150

RadWind

0 50100150

RadWind

RadWind

RadWind

RadWind

RadWind

RadWind

60 70 80 90

RadWind

0 50100150

RadWind

60 70 80 90

Trellis graphics 24

Height (inches)

Den

sity

0.00

0.05

0.10

0.15

0.20

60 65 70 75

Bass 2 Bass 1

60 65 70 75

Tenor 2 Tenor 1

Alto 2 Alto 1

60 65 70 75

Soprano 2

0.00

0.05

0.10

0.15

0.20

Soprano 1

60 65 70 75

histogram( ~ height | voice.part, data = singer,

xlab = "Height (inches)", type = "density",

panel = function(x, ...) {

panel.histogram(x, ...)

panel.mathdensity(dmath = dnorm,

args = list(mean=mean(x),sd=sd(x)),

col=1)

}

)

Trellis graphics 25

Height (inches)

Den

sity

0.00

0.05

0.10

0.15

0.20

60 65 70 75

Bass 2 Bass 1

60 65 70 75

Tenor 2 Tenor 1

Alto 2 Alto 1

60 65 70 75

Soprano 2

0.00

0.05

0.10

0.15

0.20

Soprano 1

60 65 70 75

histogram( ~ height | voice.part, data = singer,

xlab = "Height (inches)", type = "density",

panel = function(x, ...) {

panel.histogram(x, ...)

panel.densityplot(x, darg = list(bw=1.5),

col=1)

}

)

Trellis graphics 26

Note that it is not possible to update Trellis graphics after they have been plotted. A Trellis plotting command actually creates a Trellis object which can be saved for example, speed.tr <-bwplot(Expt ~ Speed, main="Speed of Light Data", ylab="Experiment No.", data=morley)

This command creates the object but doesn’t display it. To see what it looks then give the command speed.tr

This will display the graph in the current Trellis device, which is probably to the screen.

A different Trellis device can be set with a command like trellis.device("win.metafile", file="tdev.emf", color=F)

win.metafile (R) and win.graph (S-Plus version 6 or later) create Windows metafile which are great for plugging into Microsoft Word. To see what other devices are available, see help(Devices). Then to display the graph in the new device, run the commands speed.tr

dev.off()

This is similar to using postscript or pdf with regular plotting commands.