Axes for Transformed Variables

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.

Usage

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"))

Arguments

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.

Details

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.

Value

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

Author

John Fox jfox@mcmaster.ca

References

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

Examples

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)))
#> [1] 155  75
probabilityAxis()


with(UN, qqPlot(qnorm(infantMortality/1000)))
#> [1]  1 33
probabilityAxis(at=c(.005, .01, .02, .04, .08, .16), scale="probit")


qqPlot(bcnPower(Ornstein$interlocks, lambda=1/3, gamma=0.1))
#> [1] 2 3
bcnPowerAxis(1/3, 0.1, at=c(o=0, 5, 10, 20, 40, 80))