From HH v2.1-23
0th

Percentile

##### Draw a "ladder of powers" plot, plotting each of several powers of y against the same powers of x.

Draw a "ladder of powers" plot, plotting each of several powers of y against the same powers of x. The powers are

result <- data.frame(-1/x, -1/sqrt(x), log(x), sqrt(x), x, x^2)

names(result) <- c(-1, -.5, 0, .5, 1, 2)

Keywords
manip, hplot, dplot
##### Usage
ladder(formula.in, data=sys.parent(),
panel.in=panel.cartesian,
xlab=deparse(formula.in[[3]]),
ylab=deparse(formula.in[[2]]),
scales=list(alternating=if.R(s=TRUE, r=FALSE),
labels=FALSE, ticks=FALSE, cex=.6),
par.strip.text=list(cex=.6),
cex=.5, pch=16, between=list(x=.3, y=.3),
dsx=xlab,
dsy=ylab,
strip.number=1,
strip.names,
strip.style=1,
strip,
oma=c(0,0,0,0),  ## S-Plus
axis3.line=.61,
layout=c(length(tmp$x.power), length(tmp$y.power)),
axis.key.padding = 10, ## R right axis
key.axis.padding = 10, ## R top axis
dsx=deparse(substitute(x)),
dsy=deparse(substitute(y)),
which.panel,
var.name,
factor.levels,
shingle.intervals,
strip.names=c(TRUE,TRUE),
style=1,
...)
##### Arguments
formula.in
A formula with exactly one variable on each side.
data
data.frame
main.in
main title for xyplot
panel.in
panel.cartesian has many arguments in addition to the arguments in panel.xyplot. Any replacement panel function must have those argument names, even if it doesn't do anything with them.
xlab, ylab
Trellis arguments, default to right- and left-sides of the formula.in.
strip
Strip function. Our default is strip.ladder (see below). The other viable argument value is FALSE.
cex, pch, between, scales, layout
arguments for xyplot.
dsx, dsy
Names to be used as level names in ladder.function for the generated factor distinguishing the powers. They default to xlab, ylab. For long variable names, an abbreviated name here will decrease clutter in the ladder of pow
function to use to create data.frame of powers of input variable.
strip.number
Number of strip labels in each panel of the display. 0: no strip labels; 1: one strip label of the form y^p ~ x^q; 2: two strip labels of the form ylab: y^p and xlab: x^q, where p and q
strip.style
style argument to strip.
oma
argument to par in S-Plus.
...
other arguments to xyplot.
axis3.line
extra space to make the top axis align with the top of the top row of panels. Trial and error to choose a good value.
Extra space on right of set of panels in R.
Extra space on top of set of panels in R.
x, y
variables.
which.given, which.panel, var.name, factor.levels, shingle.intervals, par.strip.text
See strip.default in R or strip.default in S-Plus.
strip.names, style
We always print the strip.names in style=1. Multicolored styles are too busy.
##### Details

The ladder function uses panel.cartesian which is defined differently in R (using grid graphics) and S-Plus (using traditional graphics). Therefore the fine control over appearance uses different arguments or different values for the same arguments.

##### Value

• ladder returns a "trellis" object.

The functions ladder.fstar and ladder.f take an input vector x of non-negative values and construct a data.frame by taking the input to the powers c(-1, -.5, 0, .5, 1, 2), one column per power. ladder.f uses the simple powers and ladder.fstar uses the scaled Box--Cox transformation. llr{ ladder.fstar ladder.fstar notation (x^p - 1)/p (x^p - 1)/p p (1/x - 1)/(-1) (1/x - 1)/(-1) -1.0 (1/sqrt(x)-1)/(-.5) (1/sqrt(x)-1)/(-.5) -0.5 log(x) log(x) 0.0 ((sqrt(x)-1)/.5) ((sqrt(x)-1)/.5) 0.5 x-1 x-1 1.0 (x^2 - 1)/2 (x^2 - 1)/2 2.0 }

ladder3 takes two vectors as arguments. It returns a data.frame with five columns:

X, Y: data to be plotted. The column X contains the data from the input x taken to all the powers and aligned with the similarly expanded column Y.

x, y: symbolic labeling of the power corresponding to X,Y.

group: result from pasting the labels in x, y with * between them.

##### References

Heiberger, Richard M. and Holland, Burt (2004b). Statistical Analysis and Data Display: An Intermediate Course with Examples in S-Plus, R, and SAS. Springer Texts in Statistics. Springer. ISBN 0-387-40270-5.

Hoaglin, D.~C., Mosteller, F., and Tukey, J.~W., editors (1983). Understanding Robust and Exploratory Data Analysis. Wiley.

Box, G. E.~P. and Cox, D.~R. (1964). An analysis of transformations. J. Royal Statist Soc B, 26:211--252.

panel.cartesian

##### Examples
## some country names have embedded blanks
tv <- if.R(r=
widths=c(22,6,7,7,4,2),
strip.white=TRUE,
na.strings="*",
row.names=1)
,s=
sep=c(1,23,29,36,43,47),
na.strings="*")
)
names(tv) <- c("life.exp","ppl.per.tv","ppl.per.phys",
"fem.life.exp","male.life.exp")

## Default: single strip label per panel
main="Ladder of Powers for Life Expectancy and People per Physician",
dsx="ppp", dsy="le")

## double strip label
if.R(r=
main="Ladder of Powers for Life Expectancy and People per Physician",
strip.number=2,
dsx="ppp", dsy="le")
,s=
main="Ladder of Powers for Life Expectancy and People per Physician",
strip.number=2,
dsx="ppp", dsy="le",
axis3.line=1.2)
)

## turn off strip labels
if.R(r=
)