library(zenplots)
A zenplot
can show the same information as a pairs
plot but with two
important display differences.
First, the matrix organization of the pairs
layout is replaced by the
"zig-zag" layout of zenplot
. Second, the number of plots produced is about
half that of a pairs
plot allowing each plot in a zenplot
to be given more
visual space.
PairViz
A convenient function to produce all pairs can be found in the PairViz
package
found on cran
and installed in R
via install.packages("PairViz")
.
library(PairViz)
We will illustrate this functionality and the difference between a pairs
plot
and a zenplot
by first considering a small dataset on earthquakes having only
a few variates. The difference between the two plots becomes much more
important for data having larger numbers of variates -- we illustrate the
difference again using German data on voting patterns in two elections.
The built-in R
data set called attenu
contains measurements to estimate the
attenuating effect of distance on the ground acceleration of earthquakes in
California.
There are r ncol(attenu)
different variates used to describe the peak
acceleration of 23 California earthquakes measured at different observation
stations. The data set contains r nrow(attenu)
different peak acceleration
measurements and has some missing data. The first few cases of the data set
look like
head(attenu)
Its variates are
names(attenu)
and we are interested in all pairs of these variates.
To get these, first imagine a graph having as its nodes the variates of the data. An edge of this graph connects two nodes and hence represents a pair of variates. If interest lies in all pairs of varates, then the graph is a complete graph -- it will have an edge between every pair of nodes. An ordering of variate pairs corresponds to any path on the graph. To have an ordering of all pairs of variates, the path must visit all edges and is called an Eulerian, or Euler path. Such a path always exists for complete graphs on an odd number of nodes; when the number of nodes is even, extra edges must be added to the graph before an Eulerian can exist.
For a complete graph with n nodes, the function eseq
(for Euler sequence)
function from the PairViz
package returns an order in which the nodes
(numbered 1 to n) can be visited to produce an Euler path. It works as follows.
## Since attenu has 5 variates, the complete graph has n=5 nodes ## and an Euler sequence is given as eseq(5)
In terms of the variate names of attenu
, this is:
names(attenu)[eseq(5)]
As can be seen in the corresponding complete graph below,
library(Rgraphviz) parOptions <- par(no.readonly = TRUE) plot(mk_complete_graph(names(attenu)), "circo") par(parOptions)
this sequence traces an Eulerian path on the complete graph and so presents every variate next to every other variate somewhere in the order.
zenpath
This functionality (and more) from PairViz
has been bundled together in the
zenplots
package as a single function zenpath
. For example,
zenpath(5)
This sequence, while still Eulerian, is slightly different than that returned by
eseq(5)
. The sequence is chosen so that all pairs involving the first index
appear earliest in the sequence, then all pairs involving the second index, and
so on. We call this a "front loaded" sequence and identify it with the
zenpath
argument method = "front.loaded"
. Other possibilities are method =
"back.loaded"
and method = "balanced"
giving the following sequences:
## Back loading ensures all pairs appear latest (back) for ## high values of the indices. zenpath(5, method = "back.loaded") ## Frot loading ensures all pairs appear earliest (front) for ## low values of the indices. zenpath(5, method = "front.loaded") ## Balanced loading ensures all pairs appear in groups of all ## indices (Hamiltonian paths -> a Hamiltonian decomposition of the Eulerian) zenpath(5, method = "balanced")
The differences are easier to see when there are more nodes. Below, we show the index ordering (top to bottom) for each of these three methods when the graph has 15 nodes, here labelled"a" to "o" (to make plotting easier).
parOptions <- par(mfrow=c(1,3), mar=c(4, 2,2,0),oma=rep(0,4)) back <- zenpath(15, method = "back.loaded") balanced <- zenpath(15, method = "balanced") front <- zenpath(15, method = "front.loaded") n <- length(zenpath(15)) plot_chars <- letters[1:15] plot(back, n - 1:n,type="b", ylab="", xlab="", main="Back loaded", pch=plot_chars[back], bty="n", xaxt="n", yaxt="n") plot(balanced, n - 1:n,type="b", ylab="", xlab="", main="Balanced", pch=plot_chars[balanced], bty="n", xaxt="n", yaxt="n") plot(front, n - 1:n,type="b", ylab="", xlab="", main="Front loaded", pch=plot_chars[front], bty="n", xaxt="n", yaxt="n") par(parOptions)
Starting from the bottom (the back of the sequence), "back loading" has the last
index, "o", complete its pairing with every other index before "n" completes
all of its pairings. All of "n"'s pairings complete before those of "m", all of
"m"'s before "l", and so on until the last pairing of "a" and "b" are completed.
Note that the last indices still appear at the end of the sequence (since the
sequence begins at the top of the display and moves down). The term "back
loading" is used here in a double sense - the later (back) indices have their
pairings appear as closely together as possible towards the back of the returned
sequence. A simple reversal, that is rev(zenpath(15, method = "back.loaded"))
,
would have them appear at the beginning of the sequence. In
this case the "back loading" would only be in one sense, namely that the later
indexed (back) nodes appear first in the reversed sequence.
Analogously, "front loading" has the first (front) indices appear at the front of the sequence with their pairings appear as closely together as possible.
The "balanced" case ensures that all indices appear in each block of pairings. In the figure there are 7 blocks.
All three sequences are Eulerian, meaning all pairs appear somewhere in each sequence.
Eulerian sequences can now be used to compare a pairs
plot with a zenplot
when all pairs of variates are to be displayed.
First a pairs plot:
## We remove the space between plots and suppress the axes ## so as to give maximal space to the individual scatterplots. ## We also choose a different plotting character and reduce ## its size to better distinguish points. pairs(attenu, oma=rep(0,4), gap=0, xaxt="n", yaxt="n")
We now effect a display of all pairs using zenplot
.
## Plotting character and size are chosen to match that ## of the pairs plot. ## zenpath ensures that all pairs of variates appear ## in the zenplot. ## The last argument, n2dcol, is chosen so that the zenplot ## has the same number of plots across the page as does the ## pairs plot. zenplot(attenu[, zenpath(ncol(attenu))], n2dcol=4)
Each display shows scatterplot of all choose(5,2) =
r choose(ncol(attenu),
2)
pairs of variates for this data. Each display occupies the same total area.
With pairs
each plot is displayed twice and arranged in a symmetric matrix
layout with the variate labels appearing along the diagonal. This makes for
easy look-up but uses a lot of space.
With zenplot
, each plot appears only once with its coordinate defining
variates appearing as labels on horizontal (top or bottom) and vertical (left or
right) axis positions. The layout follows the order of the variates in which
the variates appear in the call to zenplot
beginning in the top left corner of
the display and then zig-zagging from top left to bottom right; when the
rightmost boundary or the display is reached, the direction is reversed
horizontally and the zigzag moves from top right to bottom left. The following
display illustrates the pattern (had by simply calling zenplot
):
## Call zenplot exactly as before, except that each scatterplot is replaced ## by an arrow that shows the direction of the layout. zenplot(attenu[, zenpath(ncol(attenu))], plot2d="arrow", n2dcol=4)
The zig zag pattern of plots appears as follows.
zenplot
display) has horizontal variate event
and vertical variate mag
.mag
but now with
horizontal variate station
. Note that the variate station
has some
missing values and this is recorded on its label as station (some NA)
.station
but now
with vertical variate event
. Since this is the first repeat appearance of
event
it appears with a suffix as event.1
.event
and new horizontal
variate dist
.dist
and as vertical
variate the first repeat of the variate mag
.mag
and new horizontal
variate accel
.Like the pairs
plot, the zenplot
lays its plots out on a two dimensional
grid -- the argument n2dcol=4
specifies the number of columns for the 2d
plots (e.g. scatterplots). As shown, this can lead to a lot of unused space in
the display.
The zenplot
layout can be made more compact by different choices of the
argument n2dcol
(odd values provide a more compact layout). For example,
## The default n2dcol is used zenplot(attenu[, zenpath(ncol(attenu))], n2dcol=5)
By default, zenplot
tries to determine a value for n2dcol
that minimizes the
space unused by its zigzag layout.
## The default n2dcol is used zenplot(attenu[, zenpath(ncol(attenu))])
with layout directions as
## The directions zenplot(attenu[, zenpath(ncol(attenu))], plot2d="arrow")
As the direction arrows show, the default layout is to zigzag horizontally first as much as possible.
This is clearly a much more compact display. Again, axes are shared wherever a label appears between plots.
Unless explicitly specified, the value of n2dcol
is determined by the
aregument scaling
which can either be a numerical value specifying the ratio
of the height to the width of the zenplot
layout or be a string describing a
page whose ratio of height to width will be used. The possible strings are
letter'' (the default),
square'', A4'',
golden'' (for the golden ratio),
or ``legal''.
The display arrangement of a scatterplot matrix facilitates the lookup of the scatterplot for any particular pair of variates by simply identifying the corresponding row and columns.
The scatterplot matrix also simplifies the visual comparison of the one variate to each of several others by scanning along any single row (or column). Note however that this single row scan does come at the price of doubling the number of scatterplots in the display.
These two visual search facilities are diminished by the layout of a zenplot
.
Although the same information is available in a zenplot
the layout does not
lend itself to easy lookup from variates to plots. If the zenplot
layout is
used in an interactive graphical system, other means of interaction could be
implemented to have, for example, all plots containing a particular variate (or
pair of variates) distinguish themselves visually by having their background
colour change temporarily.
On the other hand, the reverse lookup from plot to variates is simpler in a
zenplot
than in a scatterplot matrix, particularly for large numbers of
variates.
Both layouts allow a visual search for patterns in the point configurations. Having many plots be presented at once enables a quick visual search over a large space for the existence of interesting point configurations (e.g. correlations, outliers, grouping in data, lines, etc.).
When the number of plots is very large, an efficient compact layout can
dramatically increase the size of the visual search space. This is where
zenplot
's zigzag layout outperforms the scatterplot matrix.
This could be illustrated this on the following example.
In the zenplots
package the data set de_elect
contains the district results
of two German federal elections (2002 and 2005) as well as a number of
socio-economic variates as well.
## Access the German election data from zenplots package data(de_elect)
There are r nrow(de_elect)
districts and r ncol(de_elect)
variates yielding
a possible choose(68,2) =
r choose(68,2)
different scatterplots.
This many scatterplots will overwhelm a pairs
plot. In its most compact form,
the pairs plot for the first 34 variates already occupies a fair bit of space:
## pairs(de_elect[,1:34], oma=rep(0,4), gap=0, pch=".", xaxt="n", yaxt="n")
(N.B. We do not execute any of these large plots simply to keep the storage needs of this vignette to a minimum. We do encourage the reader to execute the code however on their own.)
If you execute the above code you will see interesting point configurations including: some very strong positive correlations, some positive and negative correlations, non-linear relations, the existence of some outlying points, clustering, striation, etc.
Because this scatterplot matrix is for only half of the variates it shows
choose(34,2) =
r choose(ncol(de_elect)/2,2)
different scatterplots, each one
twice. For a display of r 2* choose(ncol(de_elect)/2,2)
plots, only about one
quarter of all r choose(ncol(de_elect),2)
pairwise variate scatterplots
available in the data set appear in this display.
A second scatterplot matrix on the remaining 34 variates would also show only a quarter of the plots. The remaining half, $34 \times 34 = 1156$ plots, are missing from both plots.
In contrast, the zenplot
shows all r choose(ncol(de_elect),2)
plots at once.
In fact, because an Eulerian sequence requires a graph to be even (i.e. each
node has an even number of edges), whenever the number of variates, $p$, is even
zenpath(...)
will repeat exactly $p/2$ pairs somewhere in the sequence it
returns.
To produce the zenplot
of all pairs of variates on the German election data we
call zenplot(de_elect[,zenpath(68)], pch=".")
. (Again, we don't produce it
here so as to minimize the storage footprint of this vignette.)
## Try invoking the plot with the following ## zenplot(de_elect[,zenpath(68)], pch=".", n2dcol="square",col=adjustcolor("black",0.5))
In approximately the same visual space as the scatterplot matrix (showing only
r choose(ncol(de_elect)/2,2)
unique plots), the zenplot
has efficiently and
compactly laid out all r choose(ncol(de_elect),2)
different plots plus r
ncol(de_elect)
duplicate plots. This efficient layout means that zenplot
can
facilitate visual search for interesting point configurations over much larger
collections of variate pairs -- in the case of the German election data, this
all possible pairs of variates are presented simultaneously.
In contrast, all pairs loses most of the detail
## pairs(de_elect, oma=rep(0,4), gap=0, pch=".", xaxt="n", yaxt="n",col=adjustcolor("black",0.5))
Zenplots also accomodate a list of data sets whose pairwise contents are to be displayed. The need for this can arise quite naturally in many applications.
The German election data, for instance, contains socio-economic data whose variates naturally group together. For example, we might gather variates related to education into one group and those related to employment into another.
Education <- c("School.finishers", "School.wo.2nd", "School.2nd", "School.Real", "School.UED") Employment <- c("Employed", "FFF", "Industry", "CTT", "OS" )
We could plot all pairs for these two groups in a single zenplot
.
EducationData <- de_elect[, Education] EmploymentData <- de_elect[, Employment] ## Plot all pairs within each group zenplot(list(Educ= EducationData[, zenpath(ncol(EducationData))], Empl= EmploymentData[, zenpath(ncol(EmploymentData))]))
All pairs of education variates are plotted first in zigzag order followed by a blank plot then continuing in the same zigzag pattern by plots all pairs of employment variates.
In addition to the Education
and Employment
groups above, a number of
different groupings of variates having a shared context. For example, these
might include the following:
## Grouping variates in the German election data Regions <- c("District", "State", "Density") PopDist <- c("Men", "Citizens", "Pop.18.25", "Pop.25.35", "Pop.35.60", "Pop.g.60") PopChange <- c("Births", "Deaths", "Move.in", "Move.out", "Increase") Agriculture <- c("Farms", "Agriculture") Mining <- c("Mining", "Mining.employees") Apt <- c("Apt.new", "Apt") Motorized <- c("Motorized") Education <- c("School.finishers", "School.wo.2nd", "School.2nd", "School.Real", "School.UED") Unemployment <- c("Unemployment.03", "Unemployment.04") Employment <- c("Employed", "FFF", "Industry", "CTT", "OS" ) Voting.05 <- c("Voters.05", "Votes.05", "Invalid.05", "Valid.05") Voting.02 <- c("Voters.02", "Votes.02", "Invalid.02", "Valid.02") Voting <- c(Voting.02, Voting.05) VotesByParty.02 <- c("Votes.SPD.02", "Votes.CDU.CSU.02", "Votes.Gruene.02", "Votes.FDP.02", "Votes.Linke.02") VotesByParty.05 <- c("Votes.SPD.05", "Votes.CDU.CSU.05", "Votes.Gruene.05", "Votes.FDP.05", "Votes.Linke.05") VotesByParty <- c(VotesByParty.02, VotesByParty.05) PercentByParty.02 <- c("SPD.02", "CDU.CSU.02", "Gruene.02", "FDP.02", "Linke.02", "Others.02") PercentByParty.05 <- c("SPD.05", "CDU.CSU.05", "Gruene.05", "FDP.05", "Linke.05", "Others.05") PercentByParty <- c(PercentByParty.02, PercentByParty.05)
The groups can now be used to explore internal group relations for many different groups in the same plot. Here the following helper function comes in handy.
groups <- list(Regions=Regions, Pop=PopDist, Change = PopChange, Agric=Agriculture, Mining=Mining, Apt=Apt, Cars=Motorized, Educ=Education, Unemployed=Unemployment, Employed=Employment#, # Vote02=Voting.02, Vote05=Voting.05, # Party02=VotesByParty.02, Party05=VotesByParty.05, # Perc02=PercentByParty.02, Perc05=PercentByParty.05 ) group_paths <- lapply(groups, FUN= function(g) g[zenpath(length(g), method = "front.loaded")] ) x <- groupData(de_elect, indices=group_paths) zenplot(x, pch = ".", cex=0.7, col = "grey10")
All pairs within each group are presented following the zigzag pattern; each
group is separated by an empty plot. The zenplot
provides a quick overview of
the pairwise relationships between variates within all groups.
The plot can be improved some by using shorter names for the variates. With a little work we can replace these within each group of x
.
# ## Grouping variates in the German election data RegionsShort <- c("ED", "State", "density") PopDistShort <- c("men", "citizen", "18-25", "25-35", "35-60", "> 60") PopChangeShort <- c("births", "deaths", "in", "out", "up") AgricultureShort <- c("farms", "hectares") MiningShort <- c("firms", "employees") AptShort <- c("new", "all") TransportationShort <- c("cars") EducationShort <- c("finishers", "no.2nd", "2nd", "Real", "UED") UnemploymentShort<- c("03", "04") EmploymentShort <- c("employed", "FFF", "Industry", "CTT", "OS" ) Voting.05Short <- c("eligible", "votes", "invalid", "valid") Voting.02Short <- c("eligible", "votes", "invalid", "valid") VotesByParty.02Short <- c("SPD", "CDU.CSU", "Gruene", "FDP", "Linke") VotesByParty.05Short <- c("SPD", "CDU.CSU", "Gruene", "FDP", "Linke") PercentByParty.02Short <- c("SPD", "CDU.CSU", "Gruene", "FDP", "Linke", "rest") PercentByParty.05Short <- c("SPD", "CDU.CSU", "Gruene", "FDP", "Linke", "rest") shortNames <- list(RegionsShort, PopDistShort, PopChangeShort, AgricultureShort, MiningShort, AptShort, TransportationShort, EducationShort, UnemploymentShort, EmploymentShort, Voting.05Short, Voting.02Short, VotesByParty.02Short, VotesByParty.05Short, PercentByParty.02Short, PercentByParty.05Short) # Now replace the names in x by these. nGroups <- length(x) for (i in 1:nGroups) { longNames <- colnames(x[[i]]) newNames <- shortNames[[i]] oldNames <- groups[[i]] #print(longNames) #print(newNames) for (j in 1:length(longNames)) { for (k in 1:length(newNames)) { if (grepl(oldNames[k], longNames[j])) { longNames[longNames == longNames[j]] <- newNames[k] } } } colnames(x[[i]]) <- longNames } zenplot(x, pch = ".", cex=0.75)
It can also be of interest to compare variates between groups. For example, to compare the various levels of education with the employment categories.
crossedGroups <- c(Employment, Education) crossedPaths <- zenpath(c(length(Employment), length(Education)), method="eulerian.cross") zenplot(de_elect[,crossedGroups][crossedPaths])
A zenplot
can be thought of as taking a data set whose variates are to be
plotted in the order given. A sequence of one dimensional plots, as determined
by the argument plot1d
, are constructed in the order of the variates. Between
each pair of these 1d
plots, a two dimensional plot is constructed from the
variates of the 1d
plots. One variate provides the vertical y
values and
the other the horizontal x
values. If the orientation of the preceding
one-dimensional plot is horizontal, then that variate gives the x
values; if
it's vertical then the vertical y
coordinates.
1d
and 2d
plotsThe actual displays depend on the arguments plot1d
and plot2d
. There are
numerous built-in choices provided.
For plot1d
any of the following strings may be selected to produce a one-dimensional plot:
"label"
, "rug"
, "points"
, "jitter"
, "density"
, "boxplot"
, "hist"
, "arrow"
, "rect"
, "lines"
. The first in the list is
the default.
For plot2d
any of the following strings can be given:
"points"
, "density"
, "axes"
, "label"
, "arrow"
, "rect"
.
Again, the first of these is the default value.
turns
For example, we could produce a boxplot
for the measured variates of the
earthquake data as follows:
earthquakes <- attenu[, c(1,2,4,5)] # ignore the station id zenplot(earthquakes, plot1d="boxplot", plot2d=NULL, width1d=5, width2d=1, turns=c("r","r","r","r","r","r","r"))
There are a few things to note here. First that every variate in the data set
has a boxplot of its values presented and that the extent of boxplot display is
that variate's range. Second, the argument specification plot2d=NULL
causes
a null plot to be produced for each of the variate pairs. Third, the arguments
width1d
and width2d
determine the relative widths of the two displays.
Finally, the argument turns
determines the layout of the plots by specifying
where the next display (1d
or 2d
) is to appear in relation to the current
one. Here every display appears to the right of the existing display.
An alternative layout of the same boxplots can be had by adjusting the turns
.
zenplot(earthquakes, plot1d="boxplot", plot2d=NULL, width1d=1, width2d=1, # now widths must be the same turns=c("r","d","d","l","l","u","u"))
To better see how the turns work, arrows could be used instead to show the directions of the turns.
zenplot(earthquakes, plot1d= "arrow", plot2d="arrow", width1d=1, width2d=2, turns=c("r","d","d","l","l","u","u"))
Adding a rectangle to outline the drawing space will make the layout a little clearer and illustrate the arguments that are passed on to the pne and two dimensional plot functions.
zenplot(earthquakes, plot1d = function(zargs, ...) { rect_1d_graphics(zargs, ...) arrow_1d_graphics(zargs, col="firebrick", lwd=3, add=TRUE, ...) }, plot2d = function(zargs, ...) { rect_2d_graphics(zargs, ...) arrow_2d_graphics(zargs, col="steelblue", lwd=3, lty=2, add=TRUE, ...) }, width1d = 1, width2d = 2, turns=c("r","d","d","l","l","u","u"))
The red arrows are the turns for the 1d
plots, the blue dashed arrows
for the 2d
plots. The turns are interlaced and begin at the topmost red arrow
for the 1d
plot. It points right, matching the first turn "r"
in the list
of turns
. The remaining arrows follow each other in clockwise order. As can
be seen, there is an arrow for each plot: red for the 1d
plots, black for the
2d
plots.
The above example also introduces some other important features of zenplot
.
The value "arrow"
of plot2d
argument caused an arrow to be drawn wherever a
2d
plot was to appear in the direction of the turn associated with that plot.
As the value of plot1d
here suggests, the argument could also have been a
function.
In fact, when given a string value for plot2d
, zenplot
calls a function
whose name is constructed with this string. In the case of plot2d = "arrow"
,
zenplot
calls the function arrow_2d_graphics
to produce a 2d
plot whenever
one is required. The naming convention constructs the function name from the
string supplied, here "arrow", the dimensionality of the plot (here 2d
) and
the R
graphics package that is being used (here the base graphics
package).
The function of that name is called on arguments appropriate to draw the plot.
The same construction is also used when a string is given as the value of the
plot1d
argument. For example plot1d = "arrow"
causes the function named
arrow_1d_graphics
to be called to draw the 1d
plots.
Should, for example, the user wish to extend the base functionality of zenplot
to include say "myplot"
, they need only write functions myplot_1d_graphics
and/or myplot_2d_graphics
to allow the value "myplot"
to be used for
plot1d
and/or plot2d
in the base graphics
package in R
. Note that two
other R
plotting packages besides the base graphics
are supported by
zenplot
, namely either the highly customizable grid
package or the highly
interactive loon
package. The default package is graphics
but either of the
other two may be specified via the pkg
argument to zenplot
as in pkg =
"grid"
or pkg = "loon"
.
When zenplot
is called with plot1d="arrow"
, say, then one of the functions
arrow_1d_graphics
, arrow_1d_grid
, or arrow_1d_loon
will be called upon
depending on the value of the argument pkg
. This means that a true extension
of zenplot
to include, say, plot1d = "myplot"
would require writing three
functions, namely myplot_1d_graphics
, myplot_1d_grid
, and myplot_1d_loon
,
to complete the functionality.
More often, as shown in the boxplot example, it will be a one-off functionality
that might be required for either plot2d
or plot1d
.
In this case, any function passed as the argument value will be used by
zenplot
to construct the corresponding plots. In the boxplot example, the
default functions boxplot_1d_graphics
and arrow_1d_graphics
were both called
so that one could be plotted on top of the other in each 1d
plot of the
zenplot
.
zenplot
can be used to layout graphics produced by any of the three pkg
(i.e. graphics
, grid
, or loon
) provided all graphics used are from the
same package.
For example, suppose we were interested in the marginal distributions of the earthquake data. We might craft the following plot to investigate all marginal distributions and to compare each marginal to every other (i.e. all pairs).
library(qqtest) zenplot(earthquakes[,zenpath(ncol(earthquakes))], width1d = 1, width2d = 2, n2dcol=5, plot1d = function(zargs, ...) { r <- extract_1d(zargs) # extract arguments for 1d col <- adjustcolor(if (r$horizontal) "firebrick" else "steelblue", alpha.f = 0.7) hist_1d_graphics(zargs, col=col, ...) }, plot2d=function(zargs, ...) { r <- extract_2d(zargs) # extract arguments for 2d x <- as.matrix(r$x) xlim <- r$xlim y <- as.matrix(r$y) ylim <- r$ylim qqtest(y, dataTest=x, xlim=xlim, ylim=ylim, cex=0.3, col="black", pch=19, legend=FALSE, main="", axes=FALSE, ...) })
Here we are using the function qqtest
from the package of that name and whose
display capability is built using only the base graphics
package. For 2d
data qqtest
compares the two empirical distributions by drawing an empirical
quantile-quantile plot which should be near a straight line if the marginal
distributions are of the same shape. The empirical quantile-quantile plot is
supplemented by simulated values of empirical quantiles from the empirical
distribution of the horizontal variate. The results of 1,000 draws from this
distribution are shown in shades of grey on the qqplot. The 1d
plots are
shown as histograms coloured "grey"
when that histogram was used to generate
the simulated values and in "steelblue"
when the histogram was not.
As can be seen from the qqplots, since numerous points are outside the gray envelopes of each plot, no two marginal distributions would appear to be alike.
plot1d
functionsEvery plot1d
function must take arbitrarily many arguments, accepting at least
the following set:
x
, a vector of values for a single variatehorizontal
, which is TRUE
if the 1d
plot is to be horizontal,plotAsp
, the aspect ratio of the plot (i.e. the smaller/larger side ration in [0,1])turn
, the single character turn out from the current plotplotID
, a list containing information on the identification of the plot
.If the plot1d
function is from the package grid
, then it should also expect
to receive a vp
or viewport argument; if it is from the package loon
, it
might also receive a parent
argument. These arguments should be familiar to
users of either package.
For a plot1d
function, the plotID
consists of
group
, the number of the group in which this 1d
plot is placed,number.within.group
, the within group index of this variate,index
, the index of the variate among all variates in the data set(s)label
, the variate label, andplotNo
, the number of the 1d
plot being displayed (i.e its position in
order among only those which are 1d
).All other functions in the ellipsis, ...
, are passed on to the drawing functions.
plot2d
functionsEvery plot2d
function must take arbitrarily many arguments, accepting at least
the following set:
x
, a vector of values for the horizontal variatey
, a vector of values for the vertical variateturn
, the single character turn out from the current plotplotID
, a list containing information on the identification of the plot
.If the plot2d
function is from the package grid
, then it should also expect
to receive a vp
or viewport argument; if it is from the package loon
, it
might also receive a parent
argument. These arguments should be familiar to
users of either package.
For a plot2d
function, the plotID
consists of
group
, the number of the group in which this 2d
plot is placed,number.within.group
, the within group index for these variates (same index),index
, the indices of the variates among all variates in the data set(s)label
, the labels of the variates, andplotNo
, the number of the 2d
the plot being displayed (i.e its position
in order among only those which are 2d
).All other functions in the ellipsis, ...
, are passed on to the drawing
functions.
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