Create a Bagplot (Bivariate Boxplot)

Draws a bagplot (bivariate boxplot) based on halfspace (Tukey) depth. The bag contains the innermost 50\ hull of all non-outlying points, and points outside the fence (the bag inflated by factor, not drawn) are flagged as outliers.

Usage

plotBag(x, ...)

# S3 method for class 'formula'
plotBag(
  formula,
  data,
  subset,
  na.action = na.omit,
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  ...
)

# Default S3 method
plotBag(
  x,
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  xlim = NULL,
  ylim = NULL,
  factor = 3,
  eps = 0.00000001,
  dither = FALSE,
  points = TRUE,
  bag = TRUE,
  loop = TRUE,
  fence = FALSE,
  out = TRUE,
  median = TRUE,
  grid = FALSE,
  box = TRUE,
  stamp = .useTheme,
  ...
)

Arguments

x: a numeric matrix or data frame with exactly two columns, or a formula of the form y ~ x (see the formula method). Incomplete rows are removed.
...: additional graphical parameters passed to par().
formula: a formula of the form y ~ x, where both variables are numeric. x is drawn on the horizontal, y on the vertical axis.
data: an optional data frame containing the variables in formula.
subset: an optional expression indicating which observations to use, evaluated in data (subset = Weight > 2500), as in plot.formula().
na.action: a function specifying how missing values are handled. Defaults to stats::na.omit(), as the depth computation requires complete pairs.
main: main title. NULL (default) draws none, unless the theme sets autoTitle = TRUE (see theme); the title is then derived from the input: the formula, or the name of x. "", NA or FALSE always suppress it and compact the top margin; any other string is used as given.
xlab, ylab: axis labels. NULL (default) uses the variable names of the formula, resp. the column names of x (empty if it has none).
xlim, ylim: numeric vectors of length 2 specifying axis limits. NULL (default) uses the range of the data, extended to the fence if it is drawn.
factor: inflation factor for the fence (default: 3).
eps: numeric tolerance used in depth computation and geometry, relative to the standardized coordinates.
dither: logical, whether to add small noise (order eps) to the data. Default FALSE: ties are handled exactly, and dithering would only break duplicates apart and so lower their depth.
points, bag, loop, fence, out, median, grid, box: object-oriented control of plot elements (see Details).
stamp: controls the corner stamp. .useTheme (default) resolves to getTheme()$stamp. TRUE/FALSE/NULL, a string, or a named list for stamp().

Value

Invisibly returns a list of class "bagplot" with components:

center - Tukey median.
depth - depth of the innermost region bounding the bag.
bag - bag polygon (matrix).
fence - fence polygon (matrix, not drawn by default).
loop - loop polygon (matrix).
outliers - outlier points (matrix).
depths - halfspace depth of all observations.

Details

All graphical elements are controlled via an object-oriented interface: each element can be specified as TRUE, FALSE, or a list(...) of graphical parameters. Internally, this is handled via bedrock::callIf().

The construction follows Rousseeuw, Ruts and Tukey (1999):

The halfspace (Tukey) depth of every observation is computed using a direct port of the original Fortran routine TUKDEPTH (Rousseeuw & Ruts, 1996).
The Tukey median is approximated by the mean of all observations with maximal depth.
The bag is obtained by radial interpolation between the convex hulls of two adjacent depth regions, calibrated such that it contains $\lfloor n/2 \rfloor$ observations (up to ties on the polygon boundary).
The fence is the bag inflated by factor relative to the Tukey median. Following the original proposal it is used for classification only and not drawn by default.
Observations outside the fence are flagged as outliers.
The loop is the convex hull of all non-outlying observations, so it always lies within the data range.

Two approximations remain relative to the strict theory: the Tukey median is not computed via HALFMED, and the bag interpolates hulls of sample depth regions rather than exact isodepth contours. Borderline outlier classifications may therefore differ slightly from other implementations (e.g. aplpack).

The depth computation handles exact ties and collinear configurations (e.g. discrete data) exactly; no dithering is needed. All computations run on standardized coordinates, so the result does not depend on the units of measurement.

Note

The halfspace depth is computed by a C++ port of the Fortran routine TUKDEPTH (Algorithm AS 307, Rousseeuw & Ruts 1996), taken from src/depth.f of the archived package 'depth' by M. Genest, J.-C. Massé and J.-F. Plante.

Element Control

Each of the following arguments accepts:

TRUE - draw element with defaults
FALSE - suppress element
list(...) - customize graphical parameters

Supported elements (in drawing order):

grid - background grid
fence - classification boundary (default FALSE)
loop - convex hull of the non-outlying points
bag - central 50\
points - raw data points
out - outliers
median - Tukey median
box - plot frame

References

Rousseeuw, P. J., Ruts, I., & Tukey, J. W. (1999). The bagplot: A bivariate boxplot. The American Statistician, 53(4), 382–387. doi:10.1080/00031305.1999.10474494

Rousseeuw, P. J., & Ruts, I. (1996). Algorithm AS 307: Bivariate location depth. Journal of the Royal Statistical Society, Series C (Applied Statistics), 45(4), 516–526. doi:10.2307/2986073

Examples

set.seed(1)
x <- cbind(rnorm(200), rnorm(200))

# data of Rousseeuw et al. (1999): car weight vs engine displacement
cardata <- data.frame(
  Weight = c(2560, 2345, 1845, 2260, 2440,
           2285, 2275, 2350, 2295, 1900, 2390, 2075, 2330, 3320, 2885,
           3310, 2695, 2170, 2710, 2775, 2840, 2485, 2670, 2640, 2655,
           3065, 2750, 2920, 2780, 2745, 3110, 2920, 2645, 2575, 2935,
           2920, 2985, 3265, 2880, 2975, 3450, 3145, 3190, 3610, 2885,
           3480, 3200, 2765, 3220, 3480, 3325, 3855, 3850, 3195, 3735,
           3665, 3735, 3415, 3185, 3690),
  Disp = c(97, 114, 81, 91, 113, 97, 97,
         98, 109, 73, 97, 89, 109, 305, 153, 302, 133, 97, 125, 146,
         107, 109, 121, 151, 133, 181, 141, 132, 133, 122, 181, 146,
         151, 116, 135, 122, 141, 163, 151, 153, 202, 180, 182, 232,
         143, 180, 180, 151, 189, 180, 231, 305, 302, 151, 202, 182,
         181, 143, 146, 146)
)

plotBag(x)


# Custom styling
plotBag(x,
  bag = list(col = adjustcolor("green", 0.3), border = "darkgreen"),
  loop = list(border = "black", lty = 3),
  out = list(col = "red", pch = 17),
  grid = TRUE
)


# Minimal plot
plotBag(x, points = FALSE, median = FALSE)


# formula interface
plotBag(Disp ~ Weight, data = cardata)


# subset, evaluated in data
plotBag(Disp ~ Weight, data = cardata, subset = Weight > 2500)


# example of Rousseeuw et al. (1999): car weight vs engine displacement;
# the axis labels default to the column names
plotBag(cardata)