Theoretical QQ plot — eda_theo • tukeyedar

eda_theo generates a theoretical QQ plot for many common distributions including the Normal, uniform and gamma distributions.

Usage

eda_theo(
  x,
  p = 1L,
  tukey = FALSE,
  base = exp(1),
  q.type = 5,
  dist = "norm",
  dist.l = list(),
  resid = FALSE,
  stat = mean,
  plot = TRUE,
  show.par = TRUE,
  grey = 0.6,
  pch = 21,
  p.col = "grey50",
  p.fill = "grey80",
  size = 1,
  alpha = 0.8,
  med = TRUE,
  q = FALSE,
  iqr = TRUE,
  grid = FALSE,
  tails = FALSE,
  inner = 0.75,
  tail.pch = 21,
  tail.p.col = "grey70",
  tail.p.fill = NULL,
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  t.size = 1.2,
  ...
)

Arguments

x: Vector of continuous values.
p: Power transformation to apply to x.
tukey: Boolean determining if a Tukey transformation should be adopted (FALSE adopts a Box-Cox transformation).
base: Base used with the log() function if p = 0.
q.type: An integer between 4 and 9 selecting one of the nine quantile algorithms. (See the eda_fval function).
dist: Choice of theoretical distribution.
dist.l: List of parameters passed to the distribution quantile function.
resid: Boolean determining if residuals should be plotted. Residuals are computed using the stat parameter.
stat: Statistic to use if residuals are to be computed. Currently mean (default) or median.
plot: Boolean determining if plot should be generated.
show.par: Boolean determining if parameters such as power transformation or formula should be displayed.
grey: Grey level to apply to plot elements (0 to 1 with 1 = black).
pch: Point symbol type.
p.col: Color for point symbol.
p.fill: Point fill color passed to bg (Only used for pch ranging from 21-25).
size: Point size (0-1)
alpha: Point transparency (0 = transparent, 1 = opaque). Only applicable if rgb() is not used to define point colors.
med: Boolean determining if median lines should be drawn.
q: Boolean determining if inner data region should be shaded.
iqr: Boolean determining if an IQR line should be fitted to the points.
grid: Boolean determining if a grid should be added.
tails: Boolean determining if points outside of the inner region should be symbolized differently. Tail-end points are symbolized via the tail.pch, tail.p.col and tail.p.fill arguments.
inner: Fraction of the data considered as "mid values". Defaults to 75\ which of the tail-end points are to be symbolized differently, tails.
tail.pch: Tail-end point symbol type (See tails).
tail.p.col: Tail-end color for point symbol (See tails).
tail.p.fill: Tail-end point fill color passed to bg (Only used for tail.pch ranging from 21-25).
xlab: X label for output plot.
ylab: Y label for output plot.
title: Title to add to plot.
t.size: Title size.
...: Not used

Value

A dataframe with the input vector elements and matching theoretical quantiles. Any transformation applied to x is reflected in the output.

Details

The function generates a theoretical QQ plot. Currently, only the Normal QQ plot (dist="norm"), exponential QQ plot (dist="exp"), uniform QQ plot (dist="unif"), gamma QQ plot (dist="gamma"), chi-squared QQ plot (dist="chisq"), and the Weibull QQ plot (dist="weibull") are supported. By default, the Normal QQ plot maps the unit Normal quantiles to the x-axis (i.e. centered on a mean of 0 and standard deviation of 1 unit).

Note that arguments can be passed to the respective quantile functions via the d.list argument. Some quantile functions require at least one argument. For example, the qgamma function requires that the shape parameter be specified and the qchisq function requires that the degrees of freedom, df, be specified. See examples.

References

John M. Chambers, William S. Cleveland, Beat Kleiner, Paul A. Tukey. Graphical Methods for Data Analysis (1983)
Quantile-Quantile plot article

Examples


 singer <- lattice::singer
 bass2 <- subset(singer, voice.part == "Bass 2", select = height, drop = TRUE )

 # Generate a normal QQ plot
 eda_theo(bass2)


 # Generate a chi-squared QQ plot. The distribution requires that the degrees
 # of freedom be specified. The inner 70% shaded region is added.
 set.seed(270); x <- rchisq(100, df =3)
 eda_theo(x, dist = "chisq", dist.l = list(df = 3), q = TRUE)


 # Generate a gamma QQ plot. Note that gamma requires at the very least the
 # shape parameter. The chi-squared distribution is a special case of the
 # gamma distribution where shape = df/2 and rate = 1/2.
 eda_theo(x, dist = "gamma", dist.l = list(shape = 3/2, rate = 1/2), q = TRUE)


 # Generate a uniform QQ plot
 eda_theo(bass2, dist = "unif")


 # The uniform QQ plot can double as a quantile plot
 eda_theo(bass2, dist = "unif", q = FALSE, med = FALSE,
          iqr = FALSE, grid = TRUE, xlab = "f-value")