DepthProc (version 2.1.6)

ddPlot: Depth versus depth plot

Description

Produces a DD plot which allows to compare two multivariate datasets or to compare a subject dataset with theoretical distribution.

Usage

ddPlot(
  x,
  y,
  scale = FALSE,
  location = FALSE,
  name = "X",
  name_y = "Y",
  title = "Depth vs. depth plot",
  depth_params = list()
)

Arguments

x

The first or only data sample for ddPlot.

y

The second data sample. x and y must be of the same space.

scale

logical. determines whether the dispersion is to be aligned.

location

determines whether the location is to be aligned to 0 vector with depth median.

name

name for data set x. It will be passed to drawing function.

name_y

as above for y

title

title of the plot.

depth_params

list of parameters for function depth (method, threads, ndir, la, lb, pdim, mean, cov, exact).

Author

Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.

Details

For two probability distributions \( F \) and \( G \), both in \( {{{R}} ^ {d}} \), we can define depth vs. depth plot being very useful generalization of the one dimensional quantile-quantile plot: $$ DD(F, G) = \left\{\left( D({z}, F), D({z}, G) \right), {z} \in {{{R}} ^ {d}} \right\} $$ Its sample counterpart calculated for two samples \( {{{X}} ^ {n}} = \{{{X}_{1}}, ..., {{X}_{n}}\} \) from \( F \), and \( {{Y} ^ {m}} = \{{{Y}_{1}}, ..., {{Y}_{m}}\} \) from \( G \) is defined as $$ DD({{F}_{n}}, {{G}_{m}}) = \left\{\left( D({z}, {{F}_{n}}), D({z}, {{G}_{m}}) \right), {z} \in \{{{{X}} ^ {n}} \cup {{{Y}} ^ {m}}\} \right\} $$

References

Liu, R.Y., Parelius, J.M. and Singh, K. (1999), Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion), Ann. Statist., 27, 822--831.

Liu, R.Y., Singh K. (1993), A Quality Index Based on Data Depth and Multivariate Rank Test, Journal of the American Statistical Association vol. 88.

Examples

library(sn)
library(mvtnorm)

# EXAMPLE 1: Location difference
standard <- mvrnorm(1000, c(0, 0), diag(2))
shift <- mvrnorm(1000, c(0.5, 0), diag(2))
ddPlot(x = standard, y = shift, title = "Difference in position")
ddPlot(x = standard, y = shift, location = TRUE, title = "Location aligned")

# EXAMPLE 2: Scale difference
standard <- mvrnorm(1000, c(0, 0), diag(2))
scale <- mvrnorm(1000, c(0, 0), 4 * diag(2))
ddPlot(x = standard, y = scale)
ddPlot(x = standard, y = scale, scale = TRUE)