stat_qq_band: Quantile-quantile confidence bands

In qqplotr: Quantile-Quantile Plot Extensions for 'ggplot2'

Quantile-quantile confidence bands

Description

Draws quantile-quantile confidence bands, with an additional detrend option.

Usage

geom_qq_band(
  mapping = NULL,
  data = NULL,
  stat = "qq_band",
  position = "identity",
  na.rm = TRUE,
  show.legend = NA,
  inherit.aes = TRUE,
  distribution = "norm",
  dparams = list(),
  detrend = FALSE,
  identity = FALSE,
  qtype = 7,
  qprobs = c(0.25, 0.75),
  bandType = "pointwise",
  B = 1000,
  conf = 0.95,
  mu = NULL,
  sigma = NULL,
  ...
)

stat_qq_band(
  mapping = NULL,
  data = NULL,
  geom = "qq_band",
  position = "identity",
  na.rm = TRUE,
  show.legend = NA,
  inherit.aes = TRUE,
  distribution = "norm",
  dparams = list(),
  detrend = FALSE,
  identity = FALSE,
  qtype = 7,
  qprobs = c(0.25, 0.75),
  bandType = "pointwise",
  B = 1000,
  conf = 0.95,
  mu = NULL,
  sigma = NULL,
  ...
)

Arguments

mapping	Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.
data	The data to be displayed in this layer. There are three options: If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot(). A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created. A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).
stat	statistic to use to calculate confidence bands. Should be 'qq_band'.
position	A position adjustment to use on the data for this layer. This can be used in various ways, including to prevent overplotting and improving the display. The position argument accepts the following: The result of calling a position function, such as position_jitter(). This method allows for passing extra arguments to the position. A string naming the position adjustment. To give the position as a string, strip the function name of the position_ prefix. For example, to use position_jitter(), give the position as "jitter". For more information and other ways to specify the position, see the layer position documentation.
na.rm	If FALSE, the default, missing values are removed with a warning. If TRUE, missing values are silently removed.
show.legend	logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display. To include legend keys for all levels, even when no data exists, use TRUE. If NA, all levels are shown in legend, but unobserved levels are omitted.
inherit.aes	If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification
distribution	Character. Theoretical probability distribution function to use. Do not provide the full distribution function name (e.g., "dnorm"). Instead, just provide its shortened name (e.g., "norm"). If you wish to provide a custom distribution, you may do so by first creating the density, quantile, and random functions following the standard nomenclature from the stats package (i.e., for "custom", create the dcustom, pcustom, qcustom, and rcustom functions).
dparams	List of additional parameters passed on to the previously chosen distribution function. If an empty list is provided (default) then the distributional parameters are estimated via MLE. MLE for custom distributions is currently not supported, so you must provide the appropriate dparams in that case.
detrend	Logical. Should the plot objects be detrended? If TRUE, the objects will be detrended according to the reference Q-Q line. This procedure was described by Thode (2002), and may help reducing visual bias caused by the orthogonal distances from Q-Q points to the reference line.
identity	Logical. Should an identity line be used as the reference line used to construct the confidence bands? If TRUE, the identity line is used. If FALSE (default), the commonly-used Q-Q line that intercepts two data quantiles specified in qprobs is used. Please notice that the chosen reference line will also be used for the detrending procedure, if detrend = TRUE.
qtype	Integer between 1 and 9. Type of the quantile algorithm to be used by the quantile function to construct the Q-Q line.
qprobs	Numeric vector of length two. Represents the quantiles used by the quantile function to construct the Q-Q line.
bandType	Character. Either "pointwise", "boot", "ks" or "ts", or "ell". "pointwise" constructs pointwise confidence bands based on Normal confidence intervals. "boot" creates pointwise confidence bands based on a parametric bootstrap; parameters are estimated with MLEs. "ks" constructs simultaneous confidence bands based on the Kolmogorov-Smirnov test. "ts" constructs tail-sensitive confidence bands, as described by Aldor-Noiman et al. (2013) (also, see 'Note' for limitations). Finally, "ell" constructs simultaenous bands using the equal local levels test describe by Weine et al. (2021).
B	Integer. If bandType = "boot", then B is the number of bootstrap replicates. If bandType = "ts", then B is the number of simulated samples.
conf	Numerical. Confidence level of the bands.
mu	Numerical. Only used if bandType = "ts". Center distributional parameter used to construct the simulated tail-sensitive confidence bands. If either mu or sigma are NULL, then those parameters are estimated using Qn and s_Qn, respectively.
sigma	Numerical. Only used if bandType = "ts". Scale distributional parameter used to construct the simulated tail-sensitive confidence bands. If either mu or sigma are NULL, then those parameters are estimated using robust estimates from the stats package.
...	Other arguments passed on to layer()'s params argument. These arguments broadly fall into one of 4 categories below. Notably, further arguments to the position argument, or aesthetics that are required can not be passed through .... Unknown arguments that are not part of the 4 categories below are ignored. Static aesthetics that are not mapped to a scale, but are at a fixed value and apply to the layer as a whole. For example, colour = "red" or linewidth = 3. The geom's documentation has an Aesthetics section that lists the available options. The 'required' aesthetics cannot be passed on to the params. Please note that while passing unmapped aesthetics as vectors is technically possible, the order and required length is not guaranteed to be parallel to the input data. When constructing a layer using a ⁠stat_*()⁠ function, the ... argument can be used to pass on parameters to the geom part of the layer. An example of this is stat_density(geom = "area", outline.type = "both"). The geom's documentation lists which parameters it can accept. Inversely, when constructing a layer using a ⁠geom_*()⁠ function, the ... argument can be used to pass on parameters to the stat part of the layer. An example of this is geom_area(stat = "density", adjust = 0.5). The stat's documentation lists which parameters it can accept. The key_glyph argument of layer() may also be passed on through .... This can be one of the functions described as key glyphs, to change the display of the layer in the legend.
geom	The geometric object to use to display the data for this layer. When using a ⁠stat_*()⁠ function to construct a layer, the geom argument can be used to override the default coupling between stats and geoms. The geom argument accepts the following: A Geom ggproto subclass, for example GeomPoint. A string naming the geom. To give the geom as a string, strip the function name of the geom_ prefix. For example, to use geom_point(), give the geom as "point". For more information and other ways to specify the geom, see the layer geom documentation.

Note

• Tail-sensitive confidence bands are only implemented for Normal Q-Q plots. As a future update, we intend to generalize to other distributions.

• Bootstrap bands are constructed based on a MLE parametric bootstrap. Hence, it is not possible to construct such bands if the sample and theoretical distributions present mismatching supports.

References

• Thode, H. (2002), Testing for Normality. CRC Press, 1st Ed.

• \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00031305.2013.847865")}

• Weine, E. et al. (2021). Application of Equal Local Levels to Improve Q-Q Plot Testing Bands with R Package qqconf.

Examples

# generate random Normal data
set.seed(0)
smp <- data.frame(norm = rnorm(100))

# Normal Q-Q plot of Normal data
gg <- ggplot(data = smp, mapping = aes(sample = norm)) +
 stat_qq_band() +
 stat_qq_line() +
 stat_qq_point()
gg + labs(x = "Theoretical Quantiles", y = "Sample Quantiles")

# Normal Q-Q plot of Normal data with equal local levels (ell) bands
bt <- "ell"
gg <- ggplot(data = smp, mapping = aes(sample = norm)) +
 stat_qq_band(bandType = bt) +
 stat_qq_line() +
 stat_qq_point() +
 labs(x = "Theoretical Quantiles", y = "Sample Quantiles")
gg

# Exponential Q-Q plot of mean ozone levels (airquality dataset)
di <- "exp"
dp <- list(rate = 1)
gg <- ggplot(data = airquality, mapping = aes(sample = Ozone)) +
 stat_qq_band(distribution = di, dparams = dp) +
 stat_qq_line(distribution = di, dparams = dp) +
 stat_qq_point(distribution = di, dparams = dp) +
 labs(x = "Theoretical Quantiles", y = "Sample Quantiles")
gg

# Detrended Exponential Q-Q plot of mean ozone levels
di <- "exp"
dp <- list(rate = 1)
de <- TRUE
gg <- ggplot(data = airquality, mapping = aes(sample = Ozone)) +
 stat_qq_band(distribution = di, detrend = de) +
 stat_qq_line(distribution = di, detrend = de) +
 stat_qq_point(distribution = di, detrend = de) +
 labs(x = "Theoretical Quantiles", y = "Sample Quantiles")
gg

## Not run: 
# Normal Q-Q plot of Normal data with bootstrap confidence bands
bt <- "boot"
gg <- ggplot(data = smp, mapping = aes(sample = norm)) +
 stat_qq_band(bandType = bt) +
 stat_qq_line() +
 stat_qq_point() +
 labs(x = "Theoretical Quantiles", y = "Sample Quantiles")
gg

# Normal Q-Q plot of Normal data with tail-sensitive confidence bands
bt <- "ts"
gg <- ggplot(data = smp, mapping = aes(sample = norm)) +
 stat_qq_band(bandType = bt) +
 stat_qq_line() +
 stat_qq_point() +
 labs(x = "Theoretical Quantiles", y = "Sample Quantiles")
gg

## End(Not run)

qqplotr documentation built on Sept. 9, 2025, 5:58 p.m.