Q-Q Plot with Theoretical Distribution

Draw quantile-Quantile plots of a sample against a theoretical distribution, possibly conditioned on other variables.

Usage

qqmath(x, data, ...)

# S3 method for class 'formula'
qqmath(x,
       data,
       allow.multiple = is.null(groups) || outer,
       outer = !is.null(groups),
       distribution = qnorm,
       f.value = NULL,
       auto.key = lattice.getOption("default.args")$auto.key,
       aspect = "fill",
       panel = lattice.getOption("panel.qqmath"),
       prepanel = NULL,
       scales, strip, groups,
       xlab, xlim, ylab, ylim,
       drop.unused.levels = lattice.getOption("drop.unused.levels"),
       ...,
       lattice.options = NULL,
       default.scales = list(),
       default.prepanel = lattice.getOption("prepanel.default.qqmath"),
       subscripts,
       subset)

# S3 method for class 'data.frame'
qqmath(x, data = NULL, formula = data, ...)

# S3 method for class 'numeric'
qqmath(x, data = NULL, ylab, ...)

Arguments

x

The object on which method dispatch is carried out.

For the "formula" method, x should be a formula of the form ~ x | g1 * g2 * ..., where x should be a numeric variable. For the "numeric" method, x should be a numeric vector.

data

For the formula method, an optional data source (usually a data frame) in which variables are to be evaluated (see xyplot for details). data should not be specified for the other methods, and is ignored with a warning if it is.

formula

The formula to be used for the "data.frame" methods. See documentation for argument x for details.

distribution

A quantile function that takes a vector of probabilities as argument and produces the corresponding quantiles from a theoretical distribution. Possible values are qnorm, qunif, etc. Distributions with other required arguments need to be provided as user-defined functions (see example with qt).

f.value

An optional numeric vector of probabilities, quantiles corresponding to which should be plotted. This can also be a function of a single integer (representing sample size) that returns such a numeric vector. A typical value for this argument is the function ppoints, which is also the S-PLUS default. If specified, the probabilities generated by this function is used for the plotted quantiles, through the quantile function for the sample, and the function specified as the distribution argument for the theoretical distribution.

f.value defaults to NULL, which has the effect of using ppoints for the quantiles of the theoretical distribution, but the exact data values for the sample. This is similar to what happens for qqnorm, but different from the S-PLUS default of f.value=ppoints.

For large x, this argument can be used to restrict the number of points plotted. See also the tails.n argument in panel.qqmath.

panel

A function, called once for each panel, that uses the packet (subset of panel variables) corresponding to the panel to create a display. The default panel function panel.qqmath is documented separately, and has arguments that can be used to customize its output in various ways. Such arguments can usually be directly supplied to the high-level function.

allow.multiple, outer

See xyplot.

auto.key

See xyplot.

aspect

See xyplot.

prepanel

See xyplot.

scales

See xyplot.

strip

See xyplot.

groups

See xyplot.

xlab, ylab

See xyplot.

xlim, ylim

See xyplot.

drop.unused.levels

See xyplot.

lattice.options

See xyplot.

default.scales

See xyplot.

subscripts

See xyplot.

subset

See xyplot.

default.prepanel

Fallback prepanel function. See xyplot.

...

Further arguments. See corresponding entry in xyplot for non-trivial details.

Value

An object of class "trellis". The update method can be used to update components of the object and the print method (usually called by default) will plot it on an appropriate plotting device.

Details

qqmath produces Q-Q plots of the given sample against a theoretical distribution. The default behaviour of qqmath is different from the corresponding S-PLUS function, but is similar to qqnorm. See the entry for f.value for specifics.

The implementation details are also different from S-PLUS. In particular, all the important calculations are done by the panel (and prepanel function) and not qqmath itself. In fact, both the arguments distribution and f.value are passed unchanged to the panel and prepanel function. This allows, among other things, display of grouped Q-Q plots, which are often useful. See the help page for panel.qqmath for further details.

This and all other high level Trellis functions have several arguments in common. These are extensively documented only in the help page for xyplot, which should be consulted to learn more detailed usage.

Author

Deepayan Sarkar Deepayan.Sarkar@R-project.org

See also

xyplot, panel.qqmath, panel.qqmathline, prepanel.qqmathline, Lattice, quantile

Examples

qqmath(~ rnorm(100), distribution = function(p) qt(p, df = 10))

qqmath(~ height | voice.part, aspect = "xy", data = singer,
       prepanel = prepanel.qqmathline,
       panel = function(x, ...) {
          panel.qqmathline(x, ...)
          panel.qqmath(x, ...)
       })

vp.comb <-
    factor(sapply(strsplit(as.character(singer$voice.part), split = " "),
                  "[", 1),
           levels = c("Bass", "Tenor", "Alto", "Soprano"))
vp.group <-
    factor(sapply(strsplit(as.character(singer$voice.part), split = " "),
                  "[", 2))
qqmath(~ height | vp.comb, data = singer,
       groups = vp.group, auto.key = list(space = "right"),
       aspect = "xy",
       prepanel = prepanel.qqmathline,
       panel = function(x, ...) {
          panel.qqmathline(x, ...)
          panel.qqmath(x, ...)
       })