conf2d: Bivariate (Two-Dimensional) Confidence Region

In r2d2: Bivariate (Two-Dimensional) Confidence Region and Frequency Distribution

Bivariate (Two-Dimensional) Confidence Region

Description

Calculate an empirical confidence region for two variables, and optionally overlay the smooth polygon on a scatterplot.

Usage

conf2d(x, ...)

## S3 method for class 'formula'
conf2d(formula, data, subset, ...)

## Default S3 method:
conf2d(x, y, level=0.95, n=200, method="wand", shape=1, smooth=50,
       plot=TRUE, add=FALSE, xlab=NULL, ylab=NULL, col.points="gray",
       col="black", lwd=2, ...)

conf2d_int(x, y, surf, level, n)  # internal function

Arguments

x	a vector of x values, or a data frame whose first two columns contain the x and y values.
y	a vector of y values.
formula	a formula, such as y~x.
data	a data.frame, matrix, or list from which the variables in formula should be taken.
subset	an optional vector specifying a subset of observations to be used.
level	the proportion of points that should be inside the region.
n	the number of regions to evaluate, before choosing the region that matches level best.
method	kernel smoothing function to use: "wand" or "mass".
shape	a bandwidth scaling factor, affecting the polygon shape.
smooth	the number of bins (scalar or vector of length 2), affecting the polygon smoothness.
plot	whether to plot a scatterplot and overlay the region as a polygon.
add	whether to add a polygon to an existing plot.
xlab	a label for the x axis.
ylab	a label for the y axis.
col.points	color of points.
col	color of polygon.
lwd	line width of polygon.
...	further arguments passed to plot and polygon.
surf	a list whose first three elements are x coordinates, y coordinates, and a surface matrix.

Details

This function constructs a large number (n) of smooth polygons, and then chooses the polygon that comes closest to containing a given proportion (level) of the total points.

The default method="wand" calls the bkde2D kernel smoother from the KernSmooth package, while method="mass" calls kde2d from the MASS package.

The conf2d function calls bkde2D or kde2d to compute a smooth surface from x and y. If users already have a smoothed surface to work from, the internal conf2d_int can be used directly to find the empirical confidence region that matches level best.

Value

List containing five elements:

x	x coordinates defining the region.
y	y coordinates defining the region.
inside	logical vector indicating which of the original data coordinates are inside the region.
area	area inside the region.
prop	actual proportion of points inside the region.

Note

The area of a bivariate region is analogous to the range of a univariate interval. This allows a quantitative comparison of different confidence regions.

Ellipses are a more restrictive approach to calculate an empirical bivariate confidence region. Smooth polygons make fewer assumptions about how x and y covary.

The conf2d and freq2d functions are closely related. The advantage of conf2d is that it returns a region as a smooth polygon. The advantage of freq2d is that it returns a set that is guaranteed to contain the correct proportion of points, even for spatially complex datasets.

Author(s)

Arni Magnusson and Julian Burgos, based on an earlier function by Gregory R. Warnes.

See Also

quantile is the corresponding univariate equivalent.

The distfree.cr package uses a different smoothing algorithm to calculate bivariate empirical confidence regions.

ci2d in the gplots package is a predecessor of conf2d.

freq2d calculates a discrete frequency distribution for two continuous variables.

r2d2-package gives an overview of the package.

Examples

conf2d(Ushape)$prop
conf2d(saithe, pch=16, cex=1.2, col.points=rgb(0,0,0,0.1), lwd=3)

# First surface, then region
plot(saithe, col="gray")
surf <- MASS::kde2d(saithe$Bio, saithe$HR, h=0.25, n=100)
region <- conf2d_int(saithe$Bio, saithe$HR, surf, level=0.95, n=200)
polygon(region, lwd=2)

r2d2 documentation built on May 11, 2022, 5:18 p.m.