Plot Results of Box-Cox Transformations

Plot the results of calling the function boxcox, which returns an object of class "boxcox". Three different kinds of plots are available.

The function plot.boxcox is automatically called by plot when given an object of class "boxcox". The names of other functions associated with Box-Cox transformations are listed under Data Transformations.

# S3 method for class 'boxcox'
plot(x, plot.type = "Objective vs. lambda", same.window = TRUE, 
    ask = same.window & plot.type != "Ojective vs. lambda", 
    plot.pos.con = 0.375, estimate.params = FALSE, 
    equal.axes = qq.line.type == "0-1" || estimate.params, add.line = TRUE, 
    qq.line.type = "least squares", duplicate.points.method = "standard", 
    points.col = 1, line.col = 1, line.lwd = par("cex"), line.lty = 1, 
    digits = .Options$digits, cex.main = 1.4 * par("cex"), cex.sub = par("cex"), 
    main = NULL, sub = NULL, xlab = NULL, ylab = NULL, xlim = NULL, 
    ylim = NULL, ...)

Arguments

x: an object of class "boxcox". See boxcox.object for details.
plot.type: character string indicating what kind of plot to create. Only one particular plot type will be created, unless plot.type="All", in which case all plots will be created sequentially. The possible values of plot.type are:
"Objective vs. lambda" (the default),
"Q-Q Plots",
"Tukey M-D Q-Q Plots", and
"All".
same.window: logical scalar indicating whether to produce all plots in the same graphics window (same.window=TRUE; the default), or to create a new graphics window for each separate plot (same.window=FALSE). The argument is relevant only when plot.type produces more than one plot (i.e., when plot.type is not equal to "Objective vs. lambda").
ask: logical scalar supplied to the function devAskNewPage, indicating whether to prompt the user before creating a new plot within a single graphics window. This argument is ignored when plot.type="Objective vs. lambda" (since only one plot is produced) or when same.window=FALSE, otherwise the default value is ask=TRUE.
points.col: numeric scalar determining the color of the points in the plot. The default value is points.col=1. See the entry for col in the R help file for par for more information.

The following arguments can be supplied when plot.type="Q-Q Plots",
plot.type="Tukey M-D Q-Q Plots", or plot.type="All" (supplied to qqPlot):

plot.pos.con: numeric scalar between 0 and 1 containing the value of the plotting position constant used to construct the Q-Q plots and/or Tukey Mean-Difference Q-Q plots. The default value is plot.pos.con=0.375. See the help files for qqPlot for more information and the motivation for this choice.
estimate.params: logical scalar indicating whether to compute quantiles based on estimating the distribution parameters (estimate.params=TRUE) or using the distribution parameters for a standard normal distribution (i.e, mean=0, sd=1). The default value is estimate.params=FALSE because a standard normal Q-Q plot will yield roughly a straight line if the observations are from any normal distribution. If you specify plot.type="Tukey M-D Q-Q Plots", then you need to set estiamte.params=TRUE unless you want to assume the transformed data come from a standard normal distribution.
equal.axes: logical scalar indicating whether to use the same range on the \(x\)- and \(y\)-axes when plot.type="Q-Q Plots". The default value is TRUE if
qq.line.type="0-1" or estimate.params=TRUE, otherwise it is FALSE.
add.line: logical scalar indicating whether to add a line to the plot. If add.line=TRUE and plot.type="Q-Q Plots", a line determined by the value of qq.line.type is added to the plot. If add.line=TRUE and plot.type="Tukey M-D Q-Q Plots", a horizontal line at \(y=0\) is added to the plot. The default value is add.line=TRUE.
qq.line.type: character string determining what kind of line to add to the plot when
plot.type="Q-Q Plots". Possible values are:
"least squares" (a least squares line; the default),
"0-1" (a line with intercept 0 and slope 1), and
"robust" (a line is fit through the first and third quartiles of the \(x\) and \(y\) data).
This argument is ignored if add.line=FALSE.
duplicate.points.method: a character string denoting how to plot points with duplicate \((x,y)\) values. Possible values are "standard" (a single plotting symbol is plotted; the default), "jitter" (a separate plotting symbol is plotted for each duplicate point, where the plotting symbols cluster around the true value of \(x\) and \(y\)), and "number" (a single number is plotted at \((x,y)\) that represents how many duplicate points are at that \((x,y)\) coordinate).
line.col: numeric scalar determining the color of the line in the plot. The default value is line.col=1. See the entry for col in the R help file for par for more information. This argument is ignored if add.line=FALSE.
line.lwd: numeric scalar determining the width of the line in the plot. The default value is line.lwd=par("cex"). See the entry for lwd in the R help file for par for more information. This argument is ignored if add.line=FALSE.
line.lty: numeric scalar determining the line type (style) of the line in the plot. The default value is line.lty=1. See the entry for lty in the R help file for par for more information. This argument is ignored if add.line=FALSE.
digits: scalar indicating how many significant digits to print for the distribution parameters and the value of the objective in the sub-title. The default value is the current setting of options("digits").

Graphics parameters:

cex.main, cex.sub, main, sub, xlab, ylab, xlim, ylim, ...: graphics parameters; see par for more information. The default value of cex.main is cex.main=1.4 * par("cex"). The default value of cex.sub is
cex.sub=par("cex").

Details

The function plot.boxcox is a method for the generic function plot for the class "boxcox" (see boxcox.object). It can be invoked by calling plot and giving it an object of class "boxcox" as the first argument, or by calling plot.boxcox directly, regardless of the class of the object given as the first argument to plot.boxcox.

Plots associated with Box-Cox transformations are produced on the current graphics device. These can be one or all of the following:

Objective vs. \(\lambda\).
Observed Quantiles vs. Normal Quantiles (Q-Q Plot) for the transformed observations for each of the values of \(\lambda\).
Tukey Mean-Difference Q-Q Plots for the transformed observations for each of the values of \(\lambda\).

See the help files for boxcox and qqPlot for more information.

Value

plot.boxcox invisibly returns the first argument, x.

References

Chambers, J. M. and Hastie, T. J. (1992). Statistical Models in S. Wadsworth & Brooks/Cole.

Author

Steven P. Millard (EnvStats@ProbStatInfo.com)

Examples

  # Generate 30 observations from a lognormal distribution with 
  # mean=10 and cv=2, call the function boxcox, and then plot 
  # the results.  
  # (Note: the call to set.seed simply allows you to reproduce this example.)

  set.seed(250) 
  x <- rlnormAlt(30, mean = 10, cv = 2) 

  # Plot the results based on the PPCC objective
  #---------------------------------------------
  boxcox.list <- boxcox(x)
  dev.new()
  plot(boxcox.list)

  # Look at Q-Q Plots for the candidate values of lambda
  #-----------------------------------------------------
  plot(boxcox.list, plot.type = "Q-Q Plots", same.window = FALSE) 


  # Look at Tukey Mean-Difference Q-Q Plots 
  # for the candidate values of lambda
  #----------------------------------------
  plot(boxcox.list, plot.type = "Tukey M-D Q-Q Plots", same.window = FALSE) 

  #==========

  # Clean up
  #---------
  rm(x, boxcox.list)
  graphics.off()