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<html><head><title>R: Simple Correspondence Analysis</title>
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<table width="100%" summary="page for corresp {MASS}"><tr><td>corresp {MASS}</td><td align="right">R Documentation</td></tr></table>
<h2>Simple Correspondence Analysis</h2>
<h3>Description</h3>
<p>
Find the principal canonical correlation and corresponding row- and
column-scores from a correspondence analysis of a two-way contingency
table.
</p>
<h3>Usage</h3>
<pre>
corresp(x, ...)
## S3 method for class 'matrix':
corresp(x, nf = 1, ...)
## S3 method for class 'factor':
corresp(x, y, ...)
## S3 method for class 'data.frame':
corresp(x, ...)
## S3 method for class 'xtabs':
corresp(x, ...)
## S3 method for class 'formula':
corresp(formula, data, ...)
</pre>
<h3>Arguments</h3>
<table summary="R argblock">
<tr valign="top"><td><code>x, formula</code></td>
<td>
The function is generic, accepting various forms of the principal
argument for specifying a two-way frequency table. Currently accepted
forms are matrices, data frames (coerced to frequency tables), objects
of class <code>"<a href="../../stats/html/xtabs.html">xtabs</a>"</code> and formulae of the form <code>~ F1 + F2</code>,
where <code>F1</code> and <code>F2</code> are factors.
</td></tr>
<tr valign="top"><td><code>nf</code></td>
<td>
The number of factors to be computed. Note that although 1 is the most
usual, one school of thought takes the first two singular vectors for
a sort of biplot.
</td></tr>
<tr valign="top"><td><code>y</code></td>
<td>
a second factor for a cross-classification</td></tr>
<tr valign="top"><td><code>data</code></td>
<td>
a data frame against which to preferentially resolve
variables in the formula.</td></tr>
<tr valign="top"><td><code>...</code></td>
<td>
If the principal argument is a formula, a data frame may be specified
as well from which variables in the formula are preferentially
satisfied.
</td></tr>
</table>
<h3>Details</h3>
<p>
See Venables & Ripley (2002). The <code>plot</code> method produces a graphical
representation of the table if <code>nf=1</code>, with the <EM>areas</EM> of circles
representing the numbers of points. If <code>nf</code> is two or more the
<code>biplot</code> method is called, which plots the second and third columns of
the matrices <code>A = Dr^(-1/2) U L</code> and <code>B = Dc^(-1/2) V L</code> where the
singular value decomposition is <code>U L V</code>. Thus the x-axis is the
canonical correlation times the row and column scores. Although this
is called a biplot, it does <EM>not</EM> have any useful inner product
relationship between the row and column scores. Think of this as an
equally-scaled plot with two unrelated sets of labels. The origin is
marked on the plot with a cross. (For other versions of this plot see
the book.)
</p>
<h3>Value</h3>
<p>
An list object of class <code>"correspondence"</code> for which
<code>print</code>, <code>plot</code> and <code>biplot</code> methods are supplied.
The main components are the canonical correlation(s) and the row
and column scores.</p>
<h3>References</h3>
<p>
Venables, W. N. and Ripley, B. D. (2002)
<EM>Modern Applied Statistics with S.</EM> Fourth edition. Springer.
</p>
<p>
Gower, J. C. and Hand, D. J. (1996)
<EM>Biplots.</EM> Chapman & Hall.
</p>
<h3>See Also</h3>
<p>
<code><a href="../../base/html/svd.html">svd</a></code>, <code><a href="../../stats/html/princomp.html">princomp</a></code>
</p>
<h3>Examples</h3>
<pre>
(ct <- corresp(~ Age + Eth, data = quine))
## Not run: plot(ct)
corresp(caith)
biplot(corresp(caith, nf = 2))
</pre>
<hr><div align="center">[Package <em>MASS</em> version 7.2-44 <a href="00Index.html">Index]</a></div>
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