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block_E_iii.html
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block_E_iii.html
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<!doctype html>
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<section id="section" class="level1">
<h1></h1>
<section id="geographic-data-science" class="level2">
<h2>Geographic Data Science</h2>
<CENTER>
The spatial lag
</CENTER>
<CENTER>
<a href="http://darribas.org">Dani Arribas-Bel</a>
</CENTER>
</section>
</section>
<section id="section-1" class="level1">
<h1></h1>
<section id="the-spatial-lag" class="level2">
<h2>The spatial lag</h2>
<p>Product of a spatial weights matrix <span class="math inline"><em>W</em></span> and a given variably <span class="math inline"><em>Y</em></span></p>
<p class="fragment">
<span class="math display"><em>Y</em><sub><em>s</em><em>l</em></sub> = <em>W</em><em>Y</em></span> <span class="math display"><em>y</em><sub><em>s</em><em>l</em> − <em>i</em></sub> = ∑<sub><em>j</em></sub><em>w</em><sub><em>i</em><em>j</em></sub><em>y</em><sub><em>j</em></sub></span>
</p>
</section>
<section id="section-2" class="level2">
<h2></h2>
<ul>
<li>Measure that captures the behaviour of a variable in the neighborhood of a given observation <span class="math inline"><em>i</em></span>.</li>
<li>If <span class="math inline"><em>W</em></span> is <strong>standardized</strong>, the spatial lag is the <em>average value of the variable in the neighborhood</em></li>
</ul>
</section>
<section id="section-3" class="level2">
<h2></h2>
<ul>
<li><p>Common way to introduce space formally in a statistical framework</p></li>
<li><p>Heavily used in both ESDA and spatial regression to delineate neighborhoods. Examples:</p>
<ul>
<li>Moran’s I</li>
<li>LISAs</li>
<li>Spatial models (lag, error…)</li>
</ul></li>
</ul>
</section>
</section>
<section id="section-4" class="level1">
<h1></h1>
<p><a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">A course on Geographic Data Science</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="http://darribas.org" property="cc:attributionName" rel="cc:attributionURL">Dani Arribas-Bel</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a>.</p>
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