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2 changes: 2 additions & 0 deletions _quarto.yml
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reference-location: margin
mermaid:
theme: neutral
pdf:
documentclass: scrreprt

editor: visual

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</section></section><section id="assessment" class="level2" data-number="1.5"><h2 data-number="1.5" class="anchored" data-anchor-id="assessment">
<span class="header-section-number">1.5</span> Assessment</h2>
<p>The final module mark is composed of the <em>two computational essays</em>. Together they are designed to cover the materials introduced in the entirety of content covered during the semester. A computational essay is an essay whose narrative is supported by code and computational results that are included in the essay itself. Each teaching week, you will be required to address a set of questions relating to the module content covered in that week, and to use the material that you will produce for this purpose to build your computational essay.</p>
<p><strong>Assignment 1 (50%)</strong> refer to the set of questions at the end of <a href="04-points.html" class="quarto-xref"><span>Chapter 4</span></a>, <a href="05-flows.html" class="quarto-xref"><span>Chapter 5</span></a> and <a href="06-spatial-econometrics.html" class="quarto-xref"><span>Chapter 6</span></a>. You are required to use your responses to build your computational essay. Each chapter provides more specific guidance of the tasks and discussion that you are required to consider in your assignment.</p>
<p><strong>Assignment 2 (50%)</strong> refer to the set of questions at the end of <a href="07-multilevel-01.html" class="quarto-xref"><span>Chapter 7</span></a>, <a href="08-multilevel-02.html" class="quarto-xref"><span>Chapter 8</span></a>, <a href="09-gwr.html" class="quarto-xref"><span>Chapter 9</span></a> and <a href="10-st_analysis.html" class="quarto-xref"><span>Chapter 10</span></a>. You are required to use your responses to build your computational essay. Each chapter provides more specific guidance of the tasks and discussion that you are required to consider in your assignment.</p>
<p><strong>Assignment 1 (50%)</strong> refer to the set of questions at the end of <a href="#sec-chp4" class="quarto-xref"><span class="quarto-unresolved-ref">sec-chp4</span></a>, <a href="#sec-chp5" class="quarto-xref"><span class="quarto-unresolved-ref">sec-chp5</span></a> and <a href="#sec-chp6" class="quarto-xref"><span class="quarto-unresolved-ref">sec-chp6</span></a>. You are required to use your responses to build your computational essay. Each chapter provides more specific guidance of the tasks and discussion that you are required to consider in your assignment.</p>
<p><strong>Assignment 2 (50%)</strong> refer to the set of questions at the end of <a href="#sec-chp7" class="quarto-xref"><span class="quarto-unresolved-ref">sec-chp7</span></a>, <a href="#sec-chp8" class="quarto-xref"><span class="quarto-unresolved-ref">sec-chp8</span></a>, <a href="#sec-chp9" class="quarto-xref"><span class="quarto-unresolved-ref">sec-chp9</span></a> and <a href="#sec-chp10" class="quarto-xref"><span class="quarto-unresolved-ref">sec-chp10</span></a>. You are required to use your responses to build your computational essay. Each chapter provides more specific guidance of the tasks and discussion that you are required to consider in your assignment.</p>
<section id="format-requirements" class="level3" data-number="1.5.1"><h3 data-number="1.5.1" class="anchored" data-anchor-id="format-requirements">
<span class="header-section-number">1.5.1</span> Format Requirements</h3>
<p>Both assignments will have the same requirements:</p>
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</header><p>This chapter is based on the following references, which are great follow-up’s on the topic:</p>
<ul>
<li>
<span class="citation" data-cites="lovelace2019">Lovelace, Nowosad, and Muenchow (<a href="references.html#ref-lovelace2019" role="doc-biblioref">2019</a>)</span> offer a great introduction.</li>
<li>Chapter 6 of <span class="citation" data-cites="comber2015">Brunsdon and Comber (<a href="references.html#ref-comber2015" role="doc-biblioref">2015</a>)</span>, in particular subsections 6.3 and 6.7.</li>
<span class="citation" data-cites="lovelace2019">Lovelace, Nowosad, and Muenchow (<a href="#ref-lovelace2019" role="doc-biblioref">2019</a>)</span> offer a great introduction.</li>
<li>Chapter 6 of <span class="citation" data-cites="comber2015">Brunsdon and Comber (<a href="#ref-comber2015" role="doc-biblioref">2015</a>)</span>, in particular subsections 6.3 and 6.7.</li>
<li>
<span class="citation" data-cites="bivand2013">Bivand, Pebesma, and Gómez-Rubio (<a href="references.html#ref-bivand2013" role="doc-biblioref">2013</a>)</span> provides an in-depth treatment of spatial data in R.</li>
<span class="citation" data-cites="bivand2013">Bivand, Pebesma, and Gómez-Rubio (<a href="#ref-bivand2013" role="doc-biblioref">2013</a>)</span> provides an in-depth treatment of spatial data in R.</li>
</ul>
<section id="dependencies" class="level2" data-number="4.1"><h2 data-number="4.1" class="anchored" data-anchor-id="dependencies">
<span class="header-section-number">4.1</span> Dependencies</h2>
<p>We will rely on the following libraries in this section, all of them included in <a href="01-overview.html#sec-dependencies" class="quarto-xref"><span>Section 1.4.1</span></a>:</p>
<p>We will rely on the following libraries in this section, all of them included in <a href="#sec-dependencies" class="quarto-xref"><span class="quarto-unresolved-ref">sec-dependencies</span></a>:</p>
<div class="cell">
<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r code-with-copy"><code class="sourceCode R"><span><span class="co"># data manipulation, transformation and visualisation</span></span>
<span><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://tidyverse.tidyverse.org">tidyverse</a></span><span class="op">)</span></span>
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<span class="header-section-number">4.5</span> Spatial Interpolation</h2>
<p>The previous section demonstrates how to visualize the distribution of a set of spatial objects represented as points. In particular, given a bunch of house locations, it shows how one can effectively visualize their distribution over space and get a sense of the density of occurrences. Such visualization, because it is based on KDE, is based on a smooth continuum, rather than on a discrete approach (as a choropleth would do, for example).</p>
<p>Many times however, we are not particularly interested in learning about the density of occurrences, but about the distribution of a given value attached to each location. Think for example of weather stations and temperature: the location of the stations is no secret and rarely changes, so it is not of particular interest to visualize the density of stations; what we are usually interested instead is to know how temperature is distributed over space, given we only measure it in a few places. One could argue the example we have been working with so far, house prices in AirBnb, fits into this category as well: although where a house is advertised may be of relevance, more often we are interested in finding out what the “surface of price” looks like. Rather than <em>where are most houses being advertised?</em> we usually want to know <em>where the most expensive or most affordable</em> houses are located.</p>
<p>In cases where we are interested in creating a surface of a given value, rather than a simple density surface of occurrences, KDE cannot help us. In these cases, what we are interested in is <em>spatial interpolation</em>, a family of techniques that aim at exactly that: creating continuous surfaces for a particular phenomenon (e.g.&nbsp;temperature, house prices) given only a finite sample of observations. Spatial interpolation is a large field of research that is still being actively developed and that can involve a substantial amount of mathematical complexity in order to obtain the most accurate estimates possible<a href="#fn1" class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a>. In this chapter, we will introduce the simplest possible way of interpolating values, hoping this will give you a general understanding of the methodology and, if you are interested, you can check out further literature. For example, <span class="citation" data-cites="banerjee2014hierarchical">Banerjee, Carlin, and Gelfand (<a href="references.html#ref-banerjee2014hierarchical" role="doc-biblioref">2014</a>)</span> or <span class="citation" data-cites="cressie2015statistics">Cressie (<a href="references.html#ref-cressie2015statistics" role="doc-biblioref">2015</a>)</span> are hard but good overviews.</p>
<p>In cases where we are interested in creating a surface of a given value, rather than a simple density surface of occurrences, KDE cannot help us. In these cases, what we are interested in is <em>spatial interpolation</em>, a family of techniques that aim at exactly that: creating continuous surfaces for a particular phenomenon (e.g.&nbsp;temperature, house prices) given only a finite sample of observations. Spatial interpolation is a large field of research that is still being actively developed and that can involve a substantial amount of mathematical complexity in order to obtain the most accurate estimates possible<a href="#fn1" class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a>. In this chapter, we will introduce the simplest possible way of interpolating values, hoping this will give you a general understanding of the methodology and, if you are interested, you can check out further literature. For example, <span class="citation" data-cites="banerjee2014hierarchical">Banerjee, Carlin, and Gelfand (<a href="#ref-banerjee2014hierarchical" role="doc-biblioref">2014</a>)</span> or <span class="citation" data-cites="cressie2015statistics">Cressie (<a href="#ref-cressie2015statistics" role="doc-biblioref">2015</a>)</span> are hard but good overviews.</p>
<div class="no-row-height column-margin column-container"><p><sup>1</sup>&nbsp;There is also an important economic incentive to do this: some of the most popular applications are in the oil and gas or mining industries. In fact, the very creator of this technique, <a href="https://en.wikipedia.org/wiki/Danie_G._Krige">Danie G. Krige</a>, was a mining engineer. His name is usually used to nickname spatial interpolation as <em>kriging</em>.</p></div><section id="inverse-distance-weight-idw-interpolation" class="level3 page-columns page-full" data-number="4.5.1"><h3 data-number="4.5.1" class="anchored" data-anchor-id="inverse-distance-weight-idw-interpolation">
<span class="header-section-number">4.5.1</span> Inverse Distance Weight (IDW) interpolation</h3>
<p>The technique we will cover here is called <em>Inverse Distance Weighting</em>, or IDW for convenience. <span class="citation" data-cites="comber2015">Brunsdon and Comber (<a href="references.html#ref-comber2015" role="doc-biblioref">2015</a>)</span> offer a good description:</p>
<p>The technique we will cover here is called <em>Inverse Distance Weighting</em>, or IDW for convenience. <span class="citation" data-cites="comber2015">Brunsdon and Comber (<a href="#ref-comber2015" role="doc-biblioref">2015</a>)</span> offer a good description:</p>
<blockquote class="blockquote">
<p>In the <em>inverse distance weighting</em> (IDW) approach to interpolation, to estimate the value of <span class="math inline">\(z\)</span> at location <span class="math inline">\(x\)</span> a weighted mean of nearby observations is taken […]. To accommodate the idea that observations of <span class="math inline">\(z\)</span> at points closer to <span class="math inline">\(x\)</span> should be given more importance in the interpolation, greater weight is given to these points […]</p>
<p>— Page 204</p>
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<div id="refs" class="references csl-bib-body hanging-indent" data-entry-spacing="0" role="list" style="display: none">
<div id="refs" class="references csl-bib-body hanging-indent" data-entry-spacing="0" role="list">
<div id="ref-banerjee2014hierarchical" class="csl-entry" role="listitem">
Banerjee, Sudipto, Bradley P Carlin, and Alan E Gelfand. 2014. <em>Hierarchical Modeling and Analysis for Spatial Data</em>. Crc Press.
</div>
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