These functions produce axes for the original scale of
transformed variables. Typically these would appear as additional
axes to the right or
at the top of the plot, but if the plot is produced with
`axes=FALSE`

, then these functions could be used for axes below or to
the left of the plot as well.

```
basicPowerAxis(power, base=exp(1),
side=c("right", "above", "left", "below"),
at, start=0, lead.digits=1, n.ticks, grid=FALSE, grid.col=gray(0.50),
grid.lty=2,
axis.title="Untransformed Data", cex=1, las=par("las"))
```bcPowerAxis(power, side=c("right", "above", "left", "below"),
at, start=0, lead.digits=1, n.ticks, grid=FALSE, grid.col=gray(0.50),
grid.lty=2,
axis.title="Untransformed Data", cex=1, las=par("las"))
bcnPowerAxis(power, shift, side=c("right", "above", "left", "below"),
at, start=0, lead.digits=1, n.ticks, grid=FALSE, grid.col=gray(0.50),
grid.lty=2,
axis.title="Untransformed Data", cex=1, las=par("las"))
yjPowerAxis(power, side=c("right", "above", "left", "below"),
at, lead.digits=1, n.ticks, grid=FALSE, grid.col=gray(0.50),
grid.lty=2,
axis.title="Untransformed Data", cex=1, las=par("las"))

probabilityAxis(scale=c("logit", "probit"),
side=c("right", "above", "left", "below"),
at, lead.digits=1, grid=FALSE, grid.lty=2, grid.col=gray(0.50),
axis.title = "Probability", interval = 0.1, cex = 1, las=par("las"))

power

power for Box-Cox, Box-Cox with negatives, Yeo-Johnson, or simple power transformation.

shift

the shift (gamma) parameter for the Box-Cox with negatives family.

scale

transformation used for probabilities, `"logit"`

(the default) or `"probit"`

.

side

side at which the axis is to be drawn; numeric
codes are also permitted: `side = 1`

for the bottom of the plot,
`side=2`

for the left side,
`side = 3`

for the top, `side = 4`

for the right side.

at

numeric vector giving location of tick marks on original scale; if missing, the function will try to pick nice locations for the ticks.

start

if a *start* was added to a variable (e.g., to make all
data values positive), it can now be subtracted from the tick labels.

lead.digits

number of leading digits for determining `nice' numbers
for tick labels (default is `1`

.

n.ticks

number of tick marks; if missing, same as corresponding transformed axis.

grid

if `TRUE`

grid lines for the axis will be drawn.

grid.col

color of grid lines.

grid.lty

line type for grid lines.

axis.title

title for axis.

cex

relative character expansion for axis label.

las

if `0`

, ticks labels are drawn parallel to the
axis; set to `1`

for horizontal labels (see `par`

).

base

base of log transformation for `power.axis`

when `power = 0`

.

interval

desired interval between tick marks on the probability scale.

These functions are used for their side effects: to draw axes.

The transformations corresponding to the three functions are as follows:

`basicPowerAxis`

:Simple power transformation, \(x^{\prime }=x^{p}\) for \(p\neq 0\) and \(x^{\prime }=\log x\) for \(p=0\).

`bcPowerAxis`

:Box-Cox power transformation, \(x^{\prime }=(x^{\lambda }-1)/\lambda\) for \(\lambda \neq 0\) and \(x^{\prime }=\log x\) for \(\lambda =0\).

`bcnPowerAxis`

:Box-Cox with negatives power transformation, the Box-Cox power transformation of \(z = .5 * (y + (y^2 + \gamma^2)^{1/2})\), where \(\gamma\) is strictly positive if \(y\) includes negative values and non-negative otherwise. The value of \(z\) is always positive.

`yjPowerAxis`

:Yeo-Johnson power transformation, for non-negative \(x\), the Box-Cox transformation of \(x + 1\); for negative \(x\), the Box-Cox transformation of \(|x| + 1\) with power \(2 - p\).

`probabilityAxis`

:logit or probit transformation, logit \(=\log [p/(1-p)]\), or probit \(=\Phi^{-1}(p)\), where \(\Phi^{-1}\) is the standard-normal quantile function.

These functions will try to place tick marks at reasonable locations, but
producing a good-looking graph sometimes requires some fiddling with the
`at`

argument.

Fox, J. and Weisberg, S. (2019)
*An R Companion to Applied Regression*, Third Edition, Sage.

# NOT RUN { UN <- na.omit(UN) par(mar=c(5, 4, 4, 4) + 0.1) # leave space on right with(UN, plot(log(ppgdp, 10), log(infantMortality, 10))) basicPowerAxis(0, base=10, side="above", at=c(50, 200, 500, 2000, 5000, 20000), grid=TRUE, axis.title="GDP per capita") basicPowerAxis(0, base=10, side="right", at=c(5, 10, 20, 50, 100), grid=TRUE, axis.title="infant mortality rate per 1000") with(UN, plot(bcPower(ppgdp, 0), bcPower(infantMortality, 0))) bcPowerAxis(0, side="above", grid=TRUE, axis.title="GDP per capita") bcPowerAxis(0, side="right", grid=TRUE, axis.title="infant mortality rate per 1000") with(UN, qqPlot(logit(infantMortality/1000))) probabilityAxis() with(UN, qqPlot(qnorm(infantMortality/1000))) probabilityAxis(at=c(.005, .01, .02, .04, .08, .16), scale="probit") qqPlot(bcnPower(Ornstein$interlocks, lambda=1/3, gamma=0.1)) bcnPowerAxis(1/3, 0.1, at=c(o=0, 5, 10, 20, 40, 80)) # }