Plot Results of Goodness-of-Fit Test

Description

Plot the results of calling the function gofTest, which returns an object of class "gof" when testing the goodness-of-fit of a set of data to a distribution (i.e., when supplied with the y argument but not the x argument). Five different kinds of plots are available.

The function plot.gof is automatically called by plot when given an object of class "gof". The names of other functions associated with goodness-of-fit test are listed under Goodness-of-Fit Tests.

Usage

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## S3 method for class 'gof'
plot(x, plot.type = "Summary", 
  captions = list(PDFs = NULL, CDFs = NULL, QQ = NULL, MDQQ = NULL, Results = NULL), 
  x.labels = list(PDFs = NULL, CDFs = NULL, QQ = NULL, MDQQ = NULL), 
  y.labels = list(PDFs = NULL, CDFs = NULL, QQ = NULL, MDQQ = NULL), 
  same.window = FALSE, ask = same.window & plot.type == "All", hist.col = "cyan", 
  fitted.pdf.col = "black", fitted.pdf.lwd = 3 * par("cex"), fitted.pdf.lty = 1, 
  plot.pos.con = switch(dist.abb, norm = , lnorm = , lnormAlt = , lnorm3 = 0.375, 
    evd = 0.44, 0.4), ecdf.col = "cyan", fitted.cdf.col = "black", 
  ecdf.lwd = 3 * par("cex"), fitted.cdf.lwd = 3 * par("cex"), ecdf.lty = 1, 
  fitted.cdf.lty = 2, add.line = TRUE, 
  digits = ifelse(plot.type == "Summary", 2, .Options$digits), 
  test.result.font = 1, 
  test.result.cex = ifelse(plot.type == "Summary", 0.9, 1) * par("cex"), 
  test.result.mar = c(0, 0, 3, 0) + 0.1, 
  cex.main = ifelse(plot.type == "Summary", 1.2, 1.5) * par("cex"), 
  cex.axis = ifelse(plot.type == "Summary", 0.9, 1) * par("cex"), 
  cex.lab = ifelse(plot.type == "Summary", 0.9, 1) * par("cex"), 
  main = NULL, xlab = NULL, ylab = NULL, xlim = NULL, ylim = NULL, 
  add.om.title = TRUE, 
  oma = if (plot.type == "Summary" & add.om.title) c(0, 0, 2.5, 0) else c(0, 0, 0, 0), 
  om.title = NULL, om.font = 2, om.cex.main = 1.75 * par("cex"), om.line = 0.5, ...)

Arguments

x

an object of class "gof". See gof.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: "Summary" (the default), "PDFs: Observed and Fitted", "CDFs: Observed and Fitted", "Q-Q Plot", "Tukey M-D Q-Q Plot", "Test Results", and "All". See the DETAILS section for more information.

captions

a list with 1 to 5 components with the names "PDFs", "CDFs", "QQ", "MDQQ", and/or "Results". Each component either has the value NULL or else it is a character string containing the title for that particular kind of plot. When the component has the value NULL (the default), a default title is used. This argument is useful when you are creating more than one kind of plot with a single call to plot.gof (i.e., when plot.type="Summary" or plot.type="All") and you want to specify titles different from the default ones. If you are creating only one kind of plot, then you can just use the main argument to specify a title different from the default one.

x.labels

a list of 1 to 4 components with the names "PDFs", "CDFs", "QQ", and/or "MDQQ". Each component either has the value NULL or else it is a character string containing the label for the x-axis for that particular kind of plot. When the component has the value NULL (the default), a default x-axis label is used. This argument is useful when you are creating more than one kind of plot with a single call to plot.gof (i.e., when plot.type="Summary" or plot.type="All") and you want to specify x-axis labels different from the default ones. If you are creating only one plot, then you can just use the xlab argument to specify an x-axis label different from the default one.

y.labels

a list of 1 to 4 components with the names "PDFs", "CDFs", "QQ", and/or "MDQQ". Each component either has the value NULL or else it is a character string containing the label for the y-axis for that particular kind of plot. When the component has the value NULL (the default), a default y-axis label is used. This argument is useful when you are creating more than one kind of plot with a single call to plot.gof (i.e., when plot.type="Summary" or plot.type="All") and you want to specify y-axis labels different from the default ones. If you are creating only one plot, then you can just use the ylab argument to specify a y-axis label different from the default one.

same.window

logical scalar indicating whether to produce all plots in the same graphics window (same.window=TRUE), or to create a new graphics window for each separate plot (same.window=FALSE; the default). The argument is relevant only when plot.type="All".

ask

logical scalar supplied to the function devAskNewPage, indicating whether to prompt the user before creating a new plot within a single graphics window. The default value is FALSE unless same.window=TRUE and plot.type == "All".

digits

scalar indicating how many significant digits to print for the distribution parameters. If plot.type == "Summary", the default value is digits=2, otherwise it is .Options$digits (i.e., the current setting of options("digits")). This argument is ignored when plot.type="PDFs: Observed and Fitted".

Arguments associated with plot.type="PDFs: Observed and Fitted":

hist.col

a character string or numeric scalar determining the color of the histogram used to display the distribution of the observed values. The default value is hist.col="cyan". See the entry for col in the R help file for par for more information.

fitted.pdf.col

a character string or numeric scalar determining the color of the fitted PDF (which is displayed as a line for continuous distributions and a histogram for discrete distributions). The default value is fitted.pdf.col="black". See the entry for col in the R help file for par for more information.

fitted.pdf.lwd

numeric scalar determining the width of the line used to display the fitted PDF. The default value is fitted.pdf.lwd=3*par("cex"). See the entry for lwd in the R help file for par for more information.

fitted.pdf.lty

numeric scalar determining the line type used to display the fitted PDF. The default value is fitted.pdf.lty=1. See the entry for lty in the R help file for par for more information.

Arguments associated with plot.type="CDFs: Observed and Fitted":

plot.pos.con

numeric scalar between 0 and 1 containing the value of the plotting position constant used to construct the observed (empirical) CDF. The default value of plot.pos.con depends on the value of gof.obj$distribution (i.e., the distribution assumed for the goodness-of-fit test). For the normal, lognormal, and three-parameter lognormal distributions, the default value is
plot.pos.con=0.375. For the Type I extreme value (Gumbel) distribution, the default value is plot.pos.con=0.44. For all other distributions, the default value is plot.pos.con=0.4. See the help files for ecdfPlot and qqPlot for more information and the motivation for these choices of values.

NOTE: This argument is also used to determine the value of the plotting position constant for the Q-Q plot (plot.type="Q-Q Plot"), or the Tukey Mean-Difference Q-Q plot (plot.type="Tukey M-D Q-Q Plot").

ecdf.col

a character string or numeric scalar determining the color of the line used to display the empirical CDF. The default value is ecdf.col="cyan". See the entry for col in the R help file for par for more information.

fitted.cdf.col

a character string or numeric scalar determining the color of the line used to display the fitted CDF. The default value is fitted.cdf.col="black". See the entry for col in the R help file for par for more information.

ecdf.lwd

numeric scalar determining the width of the line used to display the empirical CDF. The default value is ecdf.lwd=3*par("cex"). See the entry for lwd in the R help file for par for more information.

fitted.cdf.lwd

numeric scalar determining the width of the line used to display the fitted CDF. The default value is fitted.cdf.lwd=3*par("cex"). See the entry for lwd in the R help file for par for more information.

ecdf.lty

numeric scalar determining the line type used to display the empirical CDF. The default value is ecdf.lty=1. See the entry for lty in the R help file for par for more information.

fitted.cdf.lty

numeric scalar determining the line type used to display the fitted CDF. The default value is fitted.cdf.lty=2. See the entry for lty in the R help file for par for more information.

Arguments associated with plot.type="Q-Q Plot" or
plot.type="Tukey M-D Q-Q Plot":

As explained above, plot.pos.con is used for these plot types. Also:

add.line

logical scalar indicating whether to add a line to the plot. If add.line=TRUE and plot.type="Q-Q Plot", a 0-1 line is added to the plot. If add.line=TRUE and plot.type="Tukey M-D Q-Q Plot", a horizontal line at y=0 is added to the plot. The default value is add.line=TRUE.

Arguments associated with plot.type="Test Results"

test.result.font

numeric scalar indicating which font to use to print out the test results. The default value is test.result.font=1. See the description of the font argument in the help file for par for more information. You may get better results if you use a font number that corresponds to a fixed font (e.g., courier).

test.result.cex

numeric scalar indicating the value of cex to use to print out the test results. The default value is 0.9*par("cex") when plot.type="Summary", otherwise it is par("cex"). See the description of the cex argument in the help file for par for more information.

test.result.mar

numeric vector indicating the value of mar to use to print out the test results. The default value is test.result.mar=c(0, 0, 3, 0)+0.1. See the description of the mar argument in the help file for par for more information.

Arguments associated with plot.type="Summary"

add.om.title

logical scalar indicating whether to add a title in the outer margin when
plot.type="Summary". The default value is add.om.title=TRUE.

om.title

character string containing the outer margin title. The default value is
om.title=NULL, which will result in a default title.

om.font

numeric scalar indicating the font to use for the outer margin. The default value is om.font=2.

om.cex.main

numeric scalar indicating the value of cex for the outer margin title. The default value is 1.75 * par("cex").

om.line

numeric scalar indicating the line to place the outer margin title on. The default value is om.line=0.5.

Graphics parameters:

cex.main, cex.axis, cex.lab, main, xlab, ylab, xlim, ylim, oma, ...

additional graphics parameters. See the help file for par.

Details

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

Plots associated with the goodness-of-fit test are produced on the current graphics device. These can be one or all of the following:

  • Observed distribution overlaid with fitted distribution
    (plot.type="PDFs: Observed and Fitted"). See the help files for hist and pdfPlot.

  • Observed empirical distribution overlaid with fitted cumulative distribution
    (plot.type="CDFs: Observed and Fitted"). See the help file for cdfCompare.

  • Observed quantiles vs. fitted quantiles (Q-Q Plot) (plot.type="Q-Q Plot"). See the help file for qqPlot.

  • Tukey mean-difference Q-Q plot (plot.type="Tukey M-D Q-Q Plot"). See the help file for qqPlot.

  • Results of the goodness-of-fit test (plot.type="Test Results"). See the help file for print.gof.

See the help file for gofTest for more information.

Value

plot.gof invisibly returns the first argument, x.

Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

References

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

See Also

gofTest, gof.object, print.gof, Goodness-of-Fit Tests, plot.

Examples

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  # Create an object of class "gof" then plot the results.
  # (Note: the call to set.seed simply allows you to reproduce 
  # this example.)

  set.seed(250) 
  dat <- rnorm(20, mean = 3, sd = 2) 
  gof.obj <- gofTest(dat) 

  # Summary plot (the default)
  #---------------------------
  dev.new()
  plot(gof.obj)


  # Make your own titles for the summary plot
  #------------------------------------------
  dev.new()
  plot(gof.obj, captions = list(PDFs = "Compare PDFs", 
    CDFs = "Compare CDFs", QQ = "Q-Q Plot", Results = "Results"),
    om.title = "Summary")


  # Just the Q-Q Plot
  #------------------
  dev.new()
  plot(gof.obj, plot.type="Q-Q")


  # Make your own title for the Q-Q Plot
  #-------------------------------------
  dev.new()
  plot(gof.obj, plot.type="Q-Q", main = "Q-Q Plot")

  #==========

  # Clean up
  #---------
  rm(dat, gof.obj)
  graphics.off()

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