Title: | Bivariate (Two-Dimensional) Confidence Region and Frequency Distribution |
---|---|
Description: | Generic functions to analyze the distribution of two continuous variables: 'conf2d' to calculate a smooth empirical confidence region, and 'freq2d' to calculate a frequency distribution. |
Authors: | Arni Magnusson [aut, cre], Julian Burgos [aut], Gregory R. Warnes [ctb] |
Maintainer: | Arni Magnusson <[email protected]> |
License: | GPL-3 |
Version: | 1.0.2 |
Built: | 2024-10-22 02:21:24 UTC |
Source: | https://github.com/arni-magnusson/r2d2 |
This package provides generic functions to analyze the distribution of two continuous variables.
Bivariate calculations:
conf2d |
empirical confidence region, a smooth polygon |
freq2d |
frequency distribution, a table |
Examples:
saithe |
MCMC results in two columns |
Ushape |
U-shaped cloud in two columns |
Arni Magnusson and Julian Burgos, based on earlier functions by Gregory R. Warnes.
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.
Combines existing tools from the KernSmooth, MASS, and sp packages.
Calculate an empirical confidence region for two variables, and optionally overlay the smooth polygon on a scatterplot.
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
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
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 |
data |
a |
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 |
method |
kernel smoothing function to use: |
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 |
surf |
a list whose first three elements are x coordinates, y coordinates, and a surface matrix. |
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.
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. |
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.
Arni Magnusson and Julian Burgos, based on an earlier function by Gregory R. Warnes.
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.
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$HR, surf, level=0.95, n=200) polygon(region, lwd=2)
conf2d(Ushape)$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)
Calculate a frequency distribution for two continuous variables.
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, ...)
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, ...)
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 |
data |
a |
subset |
an optional vector specifying a subset of observations to be used. |
n |
the desired number of bins for the output, a scalar or a vector of length 2. |
pad |
number of rows and columns to add to each margin, containing only zeros. |
layout |
one of three layouts for the output: |
print |
whether to display the resulting table on the screen using dots for zeros. |
dnn |
the names to be given to the dimensions in the result. |
... |
named arguments to be passed to the default method. |
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
.
The layout
argument specifies one of the following formats for
the binned frequency output:
table
that is easy to read, aligned like a
scatterplot.
list
with three elements (x, y, table) that can be
passed to various plotting functions.
data.frame
with three columns (x, y, frequency) that
can be analyzed further.
Arni Magnusson.
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.
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))
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))
Markov chain Monte Carlo results from the analysis of the saithe (Pollachius virens) fishery in Icelandic waters.
saithe
saithe
Data frame containing 1000 rows and 2 columns:
Bio
|
population biomass in 2013, relative to the expected long-term biomass under optimal harvest rate. |
HR
|
harvest rate in 2013, relative to the optimal harvest rate. |
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.
conf2d(saithe, level=0.9) freq2d(saithe)
conf2d(saithe, level=0.9) freq2d(saithe)
Bivariate scatter shaped like an open circle, for testing spatial algorithms.
Ushape
Ushape
Matrix containing 1000 rows and 2 columns:
x
|
x coordinates. |
y
|
y coordinates. |
freq2d(Ushape) conf2d(Ushape)
freq2d(Ushape) conf2d(Ushape)