Quantile-comparison plots

Usage

qqfun(
  x,
  distribution = "norm",
  ylab = deparse(substitute(x)),
  xlab = paste(distribution, "quantiles"),
  main = NULL,
  las = par("las"),
  envelope = 0.95,
  labels = FALSE,
  col = palette()[4],
  lcol = palette()[2],
  xlim = NULL,
  ylim = NULL,
  lwd = 1,
  pch = 1,
  bg = palette()[4],
  cex = 0.4,
  line = c("quartiles", "robust", "none"),
  ...
)

Arguments

x: vector of numeric values.
distribution: root name of comparison distribution – e.g., norm for the normal distribution; t for the t-distribution.
ylab: label for vertical (empirical quantiles) axis.
xlab: label for horizontal (comparison quantiles) axis.
main: label for plot.
las: if 0, ticks labels are drawn parallel to the axis; set to 1 for horizontal labels (see graphics::par).
envelope: confidence level for point-wise confidence envelope, or FALSE for no envelope.
labels: vector of point labels for interactive point identification, or FALSE for no labels.
col: color for points; the default is the fourth entry in the current color palette (see grDevices::palette and graphics::par).
lcol: color for lines; the default is the second entry as above.
xlim: the x limits (x1, x2) of the plot. Note that x1 > x2 is allowed and leads to a reversed axis.
ylim: the y limits of the plot.
lwd: line width; default is 1 (see graphics::par). Confidence envelopes are drawn at half this line width.
pch: plotting character for points; default is 1 (a circle, see graphics::par).
bg: background color of points.
cex: factor for expanding the size of plotted symbols; the default is .4.
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.
...: arguments such as df to be passed to the appropriate quantile function.

Value

These functions are used only for their side effect (to make a graph).

Details

Plots empirical quantiles of a variable against theoretical quantiles of a comparison distribution.

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. Studentized residuals are plotted against the appropriate t-distribution.

This is adapted from car::qq.plot with different values for points and lines, more options, more transparent code and examples in the current setting. Another similar but sophisticated function is lattice::qqmath.

References

Davison AC (2003). Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge University Press (2003-08-04). doi:10.1017/CBO9780511815850 . Leemis LM, McQueston JT (2008). “Univariate Distribution Relationships.” The American Statistician, 62(1), 45-53. doi:10.1198/000313008X270448 .

Author

John Fox, Jing Hua Zhao

Examples

if (FALSE) { # \dontrun{
p <- runif(100)
alpha <- 1/log(10)

qqfun(p,distribution="unif")
qqfun(-log10(p),distribution="exp",rate=alpha,pch=21)

library(car)
qq.plot(p,dist="unif")
qq.plot(-log10(p),dist="exp",rate=alpha)

library(lattice)
qqmath(~ -log10(p), distribution=function(p) qexp(p,rate=alpha))
} # }