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block_E_ii.html
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block_E_ii.html
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<!doctype html>
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<div class="reveal">
<div class="slides">
<section id="section" class="level1">
<h1></h1>
<section id="geographic-data-science" class="level2">
<h2>Geographic Data Science</h2>
<CENTER>
Types of <span class="math inline"><em>W</em></span>
</CENTER>
<CENTER>
<a href="http://darribas.org">Dani Arribas-Bel</a>
</CENTER>
</section>
</section>
<section id="section-1" class="level1">
<h1></h1>
<section id="what-is-a-neighbor" class="level2">
<h2><em>What is a neighbor?</em></h2>
<p>A neighbor is “somebody” who is:</p>
<ul>
<li>Next door <span class="fragment"> <span class="math inline">→</span> <strong>Contiguity</strong>-based <span class="math inline"><em>W</em></span>s</li>
<li>Close <span class="fragment"> <span class="math inline">→</span> <strong>Distance</strong>-based <span class="math inline"><em>W</em></span>s</li>
<li>In the same “place” as us <span class="fragment"> <span class="math inline">→</span> <strong>Block</strong> weights</li>
<li>…</li>
</ul>
<p><span class="fragment"> See <a href="http://www.amazon.com/Modern-Spatial-Econometrics-Practice-GeoDaSpace/dp/0986342106/ref=sr_1_1?ie=UTF8&qid=1421531753&sr=8-1&keywords=anselin+spatial+econometrics">Anselin & Rey (2014)</a> for an in-detail discussion and more types of <span class="math inline"><em>W</em></span>. </span></p>
</section>
<section id="contiguity-based-weights" class="level2">
<h2>Contiguity-based weights</h2>
<p><strong>Sharing boundaries</strong> to any extent</p>
<ul>
<li>Rook</li>
<li>Queen</li>
<li>…</li>
</ul>
</section>
<section id="section-2" class="level2" data-background="../figs/l05_queen.png">
<h2 data-background="../figs/l05_queen.png"></h2>
</section>
<section id="distance-based-weights" class="level2">
<h2>Distance-based weights</h2>
<p>Weight is (inversely) proportional to distance between observations</p>
<ul>
<li>Inverse distance (threshold)</li>
<li>KNN (fixed number of neighbors)</li>
<li>…</li>
</ul>
</section>
<section id="section-3" class="level2" data-background="..//figs/l05_dist.png">
<h2 data-background="..//figs/l05_dist.png"></h2>
</section>
<section id="section-4" class="level2">
<h2></h2>
<center>
<img src="../figs/l05_queen.png" alt=""
style="width:400px;height:400px;"/> <img src="../figs/l05_dist.png" alt=""
style="width:400px;height:400px;"/>
</center>
</section>
<section id="block-weights" class="level2">
<h2>Block weights</h2>
<p>Weights are assigned based on discretionary rules loosely related to geography</p>
<p>For example:</p>
<ul>
<li>LSOAs into MSOAs</li>
<li>Post-codes within city boundaries</li>
<li>Counties within states</li>
<li>…</li>
</ul>
</section>
<section id="section-5" class="level2" data-background="../figs/l05_block.png">
<h2 data-background="../figs/l05_block.png"></h2>
</section>
<section id="how-much-of-a-neighbor" class="level2">
<h2><em>How much of a neighbor?</em></h2>
<p>No neighbors receive zero weight: <span class="math inline"><em>w</em><sub><em>i</em><em>j</em></sub> = 0</span></p>
<p>Neighbors, it depends, <span class="math inline"><em>w</em><sub><em>i</em><em>j</em></sub></span> can be:</p>
<ul>
<li><p>One <span class="math inline"><em>w</em><sub><em>i</em><em>j</em></sub> = 1</span> <span class="math inline">→</span> <span class="hlg">Binary</span></p></li>
<li><p>Some proportion (<span class="math inline">0 < <em>w</em><sub><em>i</em><em>j</em></sub> < 1</span>, <span class="hlg">continuous</span>) which can be a function of:</p>
<ul>
<li>Distance</li>
<li>Strength of interaction (e.g. commuting flows, trade, etc.)</li>
<li>…</li>
</ul></li>
</ul>
</section>
<section id="choice-of-w" class="level2">
<h2>Choice of <span class="math inline"><em>W</em></span></h2>
<p>Should be based on and reflect the <strong>underlying channels of interaction</strong> for the question at hand.</p>
<p>Examples:</p>
<ul>
<li>Processes propagated by inmediate contact (e.g. disease contagion) <span class="math inline">→</span> Contiguity weights</li>
<li>Accessibility <span class="math inline">→</span> Distance weights</li>
<li>Effects of county differences in laws <span class="math inline">→</span> Block weights</li>
</ul>
</section>
<section id="standardization" class="level2">
<h2>Standardization</h2>
<p>In some applications (e.g. spatial autocorrelation) it is common to <em>standardize</em> <span class="math inline"><em>W</em></span></p>
<p>The most widely used standardization is <strong>row-based</strong>: divide every element by the sum of the row:</p>
<p>
<script type="math/tex; mode=display">
\bar{w_{ij}} = \dfrac{w_{ij}}{w_{i\cdotp}}
</script>
</p>
<p>where <span class="math inline"><em>w</em><sub><em>i</em>·</sub></span> is the sum of a row.</p>
</section>
</section>
<section id="section-6" 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>
</section>
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