Bivariate (Two-Dimensional) Confidence Region and Frequency Distribution

Description

This package provides generic functions to analyze the distribution of two continuous variables.

Details

Bivariate calculations:

Examples:

Author(s)

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

References

Bivand, R.S., Pebesma, E., and Gomez-Rubio, V. (2013). Applied Spatial Data Analysis with R. Second edition. New York: Springer.

Venables, W.N. and Ripley, B.D. (2002). Modern Applied Statistics with S. Fourth edition. New York: Springer.

Wand, M.P. and Jones, M.C. (1995). Kernel Smoothing. London: Chapman and Hall.

See Also

Combines existing tools from the KernSmooth, MASS, and sp packages.

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

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:

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)

Bivariate (Two-Dimensional) Frequency Distribution

Description

Calculate a frequency distribution for two continuous variables.

Usage

freq2d(x, ...)

## S3 method for class 'formula'
freq2d(formula, data, subset, ...)

## Default S3 method:
freq2d(x, y, n=20, pad=0, layout=1, print=TRUE, dnn=NULL, ...)

Arguments

Details

The exact number of bins is determined by the pretty function, based on the value of n.

Padding the margins with zeros can be helpful for subsequent analysis, such as smoothing.

The print logical flag only has an effect when layout=1.

Value

The layout argument specifies one of the following formats for the binned frequency output:

1. table that is easy to read, aligned like a scatterplot.

2. list with three elements (x, y, table) that can be passed to various plotting functions.

3. data.frame with three columns (x, y, frequency) that can be analyzed further.

Author(s)

Arni Magnusson.

See Also

cut, table, and print.table are the basic underlying functions.

hist2d in the gplots package is a related function with graphical capabilities.

conf2d calculates a bivariate empirical confidence region, a smooth polygon.

r2d2-package gives an overview of the package.

Examples

freq2d(Ushape)
freq2d(quakes$long, quakes$lat, dnn="")
freq2d(lat~long, quakes, n=c(10,20), pad=1)

# Supress display
freq2d(saithe)
range(freq2d(saithe, print=FALSE))

# Layout, plot
freq2d(saithe, layout=2)
freq2d(saithe, layout=3)
contour(freq2d(saithe, layout=2))
lattice::contourplot(Freq~Bio+HR, freq2d(saithe,layout=3))

MCMC Results from Saithe Assessment

Description

Markov chain Monte Carlo results from the analysis of the saithe (Pollachius virens) fishery in Icelandic waters.

Usage

saithe

Format

Data frame containing 1000 rows and 2 columns:

References

Magnusson, A. (2013). Icelandic saithe. In: Report of the North Western Working Group (NWWG). ICES CM 2013/ACOM:07, pp. 231–252. doi:10.17895/ices.pub.5284.

Magnusson, A., Punt, A.E., and Hilborn, R. (2013). Measuring uncertainty in fisheries stock assessment: the delta method, bootstrap, and MCMC. Fish and Fisheries 14, 325–342. doi:10.1111/j.1467-2979.2012.00473.x.

Examples

conf2d(saithe, level=0.9)
freq2d(saithe)

U-Shaped Cloud

Description

Bivariate scatter shaped like an open circle, for testing spatial algorithms.

Usage

Ushape

Format

Matrix containing 1000 rows and 2 columns:

Examples

freq2d(Ushape)
conf2d(Ushape)