qqPlot: Quantile-Comparison Plot in car: Companion to Applied Regression (2024)

qqPlot

R Documentation

Quantile-Comparison Plot

Description

Plots empirical quantiles of a variable, or of studentized residuals froma linear model, against theoretical quantiles of a comparison distribution. Includesoptions 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 thenormal 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 bygroups – for example `c(1, 3)` for 1 row and 3 columns; if omitted, thenumber of rows and columns will be selected automatically; the specified numberof rows and columns must be sufficient to accomodate the number of groups; ignoredif there is no grouping factor.
`formula`	one-sided formula specifying a single variable to be plotted or a two-sided formula ofthe form `variable ~ factor`, where a QQ plot will be drawn for `variable` within eachlevel 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 commony-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 theaxis; set to `1` for horizontal labels (see `par`).
`col`	color for points; the default is the first entryin the current car palette (see `carPalette`and `par`).
`col.lines`	color for lines; the default is the second entryin 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 extremeverical values — studentized residuals for the `"lm"` method. Points labels are by defaulttaken 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 thegraph

Details

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

Any distribution for which quantile anddensity 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 statisticsof 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-wiseconfidence 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:

Value

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

Author(s)

John Fox jfox@mcmaster.ca

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.

Examples

x<-rchisq(100, df=2)qqPlot(x)qqPlot(x, dist="chisq", df=2, envelope=list(style="lines"))qqPlot(~ income, data=Prestige, subset = type == "prof")qqPlot(income ~ type, data=Prestige, layout=c(1, 3))qqPlot(lm(prestige ~ income + education + type, data=Duncan),envelope=.99)