Quantile-Comparison Plot

Plots empirical quantiles of a variable, or of studentized residuals from a linear model, against theoretical quantiles of a comparison distribution. Includes options not available in the qqnorm function.

Usage

qqPlot(x, ...)

qqp(...)

# Default S3 method
qqPlot(x, distribution="norm", groups, layout,
    ylim=range(x, na.rm=TRUE), ylab=deparse(substitute(x)),
    xlab=paste(distribution, "quantiles"), glab=deparse(substitute(groups)),
    main=NULL, las=par("las"),
    envelope=TRUE, col=carPalette()[1], col.lines=carPalette()[2],
    lwd=2, pch=1, cex=par("cex"),
    line=c("quartiles", "robust", "none"), id=TRUE, grid=TRUE, ...)

# S3 method for class 'formula'
qqPlot(formula, data, subset, id=TRUE, ylab, glab, ...)

# S3 method for class 'lm'
qqPlot(x, xlab=paste(distribution, "Quantiles"),
    ylab=paste("Studentized Residuals(",
                deparse(substitute(x)), ")", sep=""),
    main=NULL, distribution=c("t", "norm"),
    line=c("robust", "quartiles", "none"), las=par("las"),
    simulate=TRUE, envelope=TRUE,  reps=100,
    col=carPalette()[1], col.lines=carPalette()[2], lwd=2, pch=1, cex=par("cex"),
    id=TRUE, grid=TRUE, ...)

Arguments

x: vector of numeric values or lm object.
distribution: root name of comparison distribution – e.g., "norm" for the normal distribution; t for the t-distribution.
groups: an optional factor; if specified, a QQ plot will be drawn for x within each level of groups.
layout: a 2-vector with the number of rows and columns for plotting by groups – for example c(1, 3) for 1 row and 3 columns; if omitted, the number of rows and columns will be selected automatically; the specified number of rows and columns must be sufficient to accomodate the number of groups; ignored if there is no grouping factor.
formula: one-sided formula specifying a single variable to be plotted or a two-sided formula of the form variable ~ factor, where a QQ plot will be drawn for variable within each level of factor.
data: optional data frame within which to evaluage the formula.
subset: optional subset expression to select cases to plot.
ylim: limits for vertical axis; defaults to the range of x. If plotting by groups, a common y-axis is used for all groups.
ylab: label for vertical (empirical quantiles) axis.
xlab: label for horizontal (comparison quantiles) axis.
glab: label for the grouping variable.
main: label for plot.
envelope: TRUE (the default), FALSE, a confidence level such as 0.95, or a list specifying how to plot a point-wise confidence envelope (see Details).
las: if 0, ticks labels are drawn parallel to the axis; set to 1 for horizontal labels (see par).
col: color for points; the default is the first entry in the current car palette (see carPalette and par).
col.lines: color for lines; the default is the second entry in the current car palette.
pch: plotting character for points; default is 1 (a circle, see par).
cex: factor for expanding the size of plotted symbols; the default is 1.
id: controls point identification; if FALSE, no points are identified; can be a list of named arguments to the showLabels function; TRUE is equivalent to list(method="y", n=2, cex=1, col=carPalette()[1], location="lr"), which identifies the 2 points with the 2 points with the most extreme verical values — studentized residuals for the "lm" method. Points labels are by default taken from the names of the variable being plotted is any, else case indices are used. Unlike most graphical functions in car, the default is id=TRUE to include point identification.
lwd: line width; default is 2 (see par).
line: "quartiles" to pass a line through the quartile-pairs, or "robust" for a robust-regression line; the latter uses the rlm function in the MASS package. Specifying line = "none" suppresses the line.
simulate: if TRUE calculate confidence envelope by parametric bootstrap; for lm object only. The method is due to Atkinson (1985).
reps: integer; number of bootstrap replications for confidence envelope.
...: arguments such as df to be passed to the appropriate quantile function.
grid: If TRUE, the default, a light-gray background grid is put on the graph

Details

Draws theoretical quantile-comparison plots for variables and for studentized residuals from a linear model. A comparison line is drawn on the plot either through the quartiles of the two distributions, or by robust regression.

Any distribution for which quantile and density functions exist in R (with prefixes q and d, respectively) may be used. When plotting a vector, the confidence envelope is based on the SEs of the order statistics of an independent random sample from the comparison distribution (see Fox, 2016). Studentized residuals from linear models are plotted against the appropriate t-distribution with a point-wise confidence envelope computed by default by a parametric bootstrap, as described by Atkinson (1985). The function qqp is an abbreviation for qqPlot.

The envelope argument can take a list with the following named elements; if an element is missing, then the default value is used:

level: confidence level (default 0.95).
style: one of "filled" (the default), "lines", or "none".
col: color (default is the value of col.lines).
alpha: transparency/opacity of a filled confidence envelope, a number between 0 and 1 (default 0.15).
border: controls whether a border is drawn around a filled confidence envelope (default TRUE).

Value

These functions return the labels of identified points, unless a grouping factor is employed, in which case NULL is returned invisibly.

References

Fox, J. (2016) Applied Regression Analysis and Generalized Linear Models, Third Edition. Sage.

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

Atkinson, A. C. (1985) Plots, Transformations, and Regression. Oxford.

Author

John Fox jfox@mcmaster.ca

Examples

x<-rchisq(100, df=2)
qqPlot(x)

#> [1] 67 41
qqPlot(x, dist="chisq", df=2, envelope=list(style="lines"))

#> [1] 67 41

qqPlot(~ income, data=Prestige, subset = type == "prof")

#> general.managers       physicians 
#>                2               24 
qqPlot(income ~ type, data=Prestige, layout=c(1, 3))


qqPlot(lm(prestige ~ income + education + type, data=Duncan),
  envelope=.99)

#>  minister machinist 
#>         6        28