DepthProc (version 1.0.7)

ddPlot: Depth versus depth plot

Description

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

Usage

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

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_x

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

name_y

name for data set y.

title

title of the plot.

...

Parameters passed to depth function

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

require(sn)
require(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)