EVOLUTION-MANAGER

Edit File: USCounties.html

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<table width="100%" summary="page for USCounties {Matrix}"><tr><td>USCounties {Matrix}</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>USCounties Contiguity Matrix</h2>

<h3>Description</h3>

<p>This matrix represents the contiguities of 3111 US counties using the
Queen criterion of at least a single shared boundary point. The
representation is as a row standardised spatial weights matrix
transformed to a symmetric matrix (see Ord (1975), p. 125).
</p>

<h3>Usage</h3>

<pre>data(USCounties)</pre>

<h3>Format</h3>

<p>A <i>3111 ^2</i> symmetric sparse matrix of class
<code><a href="dsCMatrix-class.html">dsCMatrix</a></code> with 9101 non-zero entries.
</p>

<h3>Details</h3>

<p>The data were read into <span style="font-family: Courier New, Courier; color: #666666;"><b>R</b></span> using <code><a href="../../spdep/html/read.gal.html">read.gal</a></code>, and
row-standardised and transformed to symmetry using
<code><a href="../../spdep/html/nb2listw.html">nb2listw</a></code> and <code><a href="../../spdep/html/similar.listw.html">similar.listw</a></code>.
This spatial weights object was converted to class
<code><a href="dsCMatrix-class.html">dsCMatrix</a></code> using
<code><a href="../../spdep/html/as_dsTMatrix_listw.html">as_dsTMatrix_listw</a></code> and coercion.
</p>

<h3>Source</h3>

<p>The data were retrieved from <code>http://sal.uiuc.edu/weights/zips/usc.zip</code>,
files &ldquo;usc.txt&rdquo; and &ldquo;usc\_q.GAL&rdquo;, with permission for use
and distribution from Luc Anselin.
</p>

<h3>References</h3>

<p>Ord, J. K. (1975)
Estimation methods for models of spatial interaction;
<em>Journal of the American Statistical Association</em> <b>70</b>, 120&ndash;126.
</p>

<h3>Examples</h3>

<pre>
data(USCounties)
(n &lt;- ncol(USCounties))
IM &lt;- .symDiagonal(n)
nn &lt;- 50
set.seed(1)
rho &lt;- runif(nn, 0, 1)
system.time(MJ &lt;- sapply(rho, function(x)
	determinant(IM - x * USCounties, logarithm = TRUE)$modulus))

## can be done faster, by update()ing the Cholesky factor:
nWC &lt;- -USCounties
C1 &lt;- Cholesky(nWC, Imult = 2)
system.time(MJ1 &lt;- n * log(rho) +
            sapply(rho, function(x)
                   2 * c(determinant(update(C1, nWC, 1/x))$modulus)))
all.equal(MJ, MJ1)

C2 &lt;- Cholesky(nWC, super = TRUE, Imult = 2)
system.time(MJ2 &lt;- n * log(rho) +
            sapply(rho, function(x)
                   2 * c(determinant(update(C2, nWC, 1/x))$modulus)))
all.equal(MJ, MJ2)  
system.time(MJ3 &lt;- n * log(rho) + Matrix:::ldetL2up(C1, nWC, 1/rho))
stopifnot(all.equal(MJ, MJ3))
system.time(MJ4 &lt;- n * log(rho) + Matrix:::ldetL2up(C2, nWC, 1/rho))
stopifnot(all.equal(MJ, MJ4))
</pre>

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