代码拉取完成，页面将自动刷新
<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=edge" />
<title>Chapter 10 Activity 4: Point Pattern Analysis I | An Introduction to Spatial Data Analysis and Statistics: A Course in R</title>
<meta name="description" content="This book was created as a resource for teaching applied spatial statistics at McMaster University by Antonio Paez, with support from Anastassios Dardas, Rajveer Ubhi, Megan Coad, and Alexis Polidoro. The book is published with support of an Open Educational Resources grant from MacPherson Institute, McMaster University." />
<meta name="generator" content="bookdown 0.24 and GitBook 2.6.7" />
<meta property="og:title" content="Chapter 10 Activity 4: Point Pattern Analysis I | An Introduction to Spatial Data Analysis and Statistics: A Course in R" />
<meta property="og:type" content="book" />
<meta property="og:image" content="/images/cover.jpg" />
<meta property="og:description" content="This book was created as a resource for teaching applied spatial statistics at McMaster University by Antonio Paez, with support from Anastassios Dardas, Rajveer Ubhi, Megan Coad, and Alexis Polidoro. The book is published with support of an Open Educational Resources grant from MacPherson Institute, McMaster University." />
<meta name="github-repo" content="paezha/spatial-analysis-R" />
<meta name="twitter:card" content="summary" />
<meta name="twitter:title" content="Chapter 10 Activity 4: Point Pattern Analysis I | An Introduction to Spatial Data Analysis and Statistics: A Course in R" />
<meta name="twitter:description" content="This book was created as a resource for teaching applied spatial statistics at McMaster University by Antonio Paez, with support from Anastassios Dardas, Rajveer Ubhi, Megan Coad, and Alexis Polidoro. The book is published with support of an Open Educational Resources grant from MacPherson Institute, McMaster University." />
<meta name="twitter:image" content="/images/cover.jpg" />
<meta name="author" content="Antonio Paez" />
<meta name="date" content="2021-12-14" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="apple-mobile-web-app-capable" content="yes" />
<meta name="apple-mobile-web-app-status-bar-style" content="black" />
<link rel="prev" href="point-pattern-analysis-i.html"/>
<link rel="next" href="point-pattern-analysis-ii.html"/>
<script src="libs/header-attrs-2.11/header-attrs.js"></script>
<script src="libs/jquery-3.6.0/jquery-3.6.0.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/fuse.js@6.4.6/dist/fuse.min.js"></script>
<link href="libs/gitbook-2.6.7/css/style.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-table.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-bookdown.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-highlight.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-search.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-fontsettings.css" rel="stylesheet" />
<link href="libs/gitbook-2.6.7/css/plugin-clipboard.css" rel="stylesheet" />
<link href="libs/anchor-sections-1.0.1/anchor-sections.css" rel="stylesheet" />
<script src="libs/anchor-sections-1.0.1/anchor-sections.js"></script>
<script src="libs/htmlwidgets-1.5.4/htmlwidgets.js"></script>
<link href="libs/leaflet-1.3.1/leaflet.css" rel="stylesheet" />
<script src="libs/leaflet-1.3.1/leaflet.js"></script>
<link href="libs/leafletfix-1.0.0/leafletfix.css" rel="stylesheet" />
<script src="libs/proj4-2.6.2/proj4.min.js"></script>
<script src="libs/Proj4Leaflet-1.0.1/proj4leaflet.js"></script>
<link href="libs/rstudio_leaflet-1.3.1/rstudio_leaflet.css" rel="stylesheet" />
<script src="libs/leaflet-binding-2.0.4.1/leaflet.js"></script>
<link href="libs/leaflet-markercluster-1.0.5/MarkerCluster.css" rel="stylesheet" />
<link href="libs/leaflet-markercluster-1.0.5/MarkerCluster.Default.css" rel="stylesheet" />
<script src="libs/leaflet-markercluster-1.0.5/leaflet.markercluster.js"></script>
<script src="libs/leaflet-markercluster-1.0.5/leaflet.markercluster.freezable.js"></script>
<script src="libs/leaflet-markercluster-1.0.5/leaflet.markercluster.layersupport.js"></script>
<script src="libs/lfx-heat-0.1.0/lfx-heat-prod.js"></script>
<script src="libs/lfx-heat-0.1.0/lfx-heat-bindings.js"></script>
<script src="libs/plotly-binding-4.10.0/plotly.js"></script>
<script src="libs/typedarray-0.1/typedarray.min.js"></script>
<link href="libs/crosstalk-1.2.0/css/crosstalk.min.css" rel="stylesheet" />
<script src="libs/crosstalk-1.2.0/js/crosstalk.min.js"></script>
<link href="libs/plotly-htmlwidgets-css-2.5.1/plotly-htmlwidgets.css" rel="stylesheet" />
<script src="libs/plotly-main-2.5.1/plotly-latest.min.js"></script>
<link href="libs/colourpicker-1.1/colourpicker.min.css" rel="stylesheet" />
<script src="libs/colourpicker-1.1/colourpicker.min.js"></script>
<meta name="viewport" content="width=device-width, initial-scale=1" />
<link href="libs/bootstrap-grid-3.4.1/bootstrap-grid.min.css" rel="stylesheet" />
<script src="libs/kePrint-0.0.1/kePrint.js"></script>
<link href="libs/lightable-0.0.1/lightable.css" rel="stylesheet" />
<style type="text/css">
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span.al { color: #ff0000; font-weight: bold; } /* Alert */
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
code span.at { color: #7d9029; } /* Attribute */
code span.bn { color: #40a070; } /* BaseN */
code span.bu { } /* BuiltIn */
code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */
code span.ch { color: #4070a0; } /* Char */
code span.cn { color: #880000; } /* Constant */
code span.co { color: #60a0b0; font-style: italic; } /* Comment */
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */
code span.do { color: #ba2121; font-style: italic; } /* Documentation */
code span.dt { color: #902000; } /* DataType */
code span.dv { color: #40a070; } /* DecVal */
code span.er { color: #ff0000; font-weight: bold; } /* Error */
code span.ex { } /* Extension */
code span.fl { color: #40a070; } /* Float */
code span.fu { color: #06287e; } /* Function */
code span.im { } /* Import */
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
code span.kw { color: #007020; font-weight: bold; } /* Keyword */
code span.op { color: #666666; } /* Operator */
code span.ot { color: #007020; } /* Other */
code span.pp { color: #bc7a00; } /* Preprocessor */
code span.sc { color: #4070a0; } /* SpecialChar */
code span.ss { color: #bb6688; } /* SpecialString */
code span.st { color: #4070a0; } /* String */
code span.va { color: #19177c; } /* Variable */
code span.vs { color: #4070a0; } /* VerbatimString */
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
</style>
<style type="text/css">
/* Used with Pandoc 2.11+ new --citeproc when CSL is used */
div.csl-bib-body { }
div.csl-entry {
clear: both;
}
.hanging div.csl-entry {
margin-left:2em;
text-indent:-2em;
}
div.csl-left-margin {
min-width:2em;
float:left;
}
div.csl-right-inline {
margin-left:2em;
padding-left:1em;
}
div.csl-indent {
margin-left: 2em;
}
</style>
<link rel="stylesheet" href="style.css" type="text/css" />
</head>
<body>
<div class="book without-animation with-summary font-size-2 font-family-1" data-basepath=".">
<div class="book-summary">
<nav role="navigation">
<ul class="summary">
<li><a href="./">Spatial Analysis in R</a></li>
<li class="divider"></li>
<li><a href="index.html#section"></a></li>
<li class="chapter" data-level="" data-path="front-matter.html"><a href="front-matter.html"><i class="fa fa-check"></i>Front Matter</a>
<ul>
<li class="chapter" data-level="" data-path="front-matter.html"><a href="front-matter.html#what-is-this-book-and-who-is-it-for"><i class="fa fa-check"></i>What is this book and who is it for?</a></li>
<li class="chapter" data-level="" data-path="front-matter.html"><a href="front-matter.html#allied-resources"><i class="fa fa-check"></i>Allied resources</a></li>
<li class="chapter" data-level="" data-path="front-matter.html"><a href="front-matter.html#contributing"><i class="fa fa-check"></i>Contributing</a>
<ul>
<li class="chapter" data-level="0.0.1" data-path="front-matter.html"><a href="front-matter.html#license"><i class="fa fa-check"></i><b>0.0.1</b> License</a></li>
</ul></li>
<li class="chapter" data-level="" data-path="front-matter.html"><a href="front-matter.html#how-to-support-this-project"><i class="fa fa-check"></i>How to support this project</a></li>
</ul></li>
<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html"><i class="fa fa-check"></i>Preface</a>
<ul>
<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#spatial-analysis-and-spatial-statistics"><i class="fa fa-check"></i>Spatial Analysis and Spatial Statistics</a></li>
<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#why-this-text"><i class="fa fa-check"></i>Why this Text?</a></li>
<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#plan"><i class="fa fa-check"></i>Plan</a></li>
<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#audience"><i class="fa fa-check"></i>Audience</a></li>
<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#requisites"><i class="fa fa-check"></i>Requisites</a></li>
<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#words-of-appreciation"><i class="fa fa-check"></i>Words of Appreciation</a></li>
<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html#versioning"><i class="fa fa-check"></i>Versioning</a></li>
</ul></li>
<li class="part"><span><b>I Part I: Getting to Know the Technology</b></span></li>
<li class="chapter" data-level="1" data-path="preliminaries-installing-r-and-rstudio.html"><a href="preliminaries-installing-r-and-rstudio.html"><i class="fa fa-check"></i><b>1</b> Preliminaries: Installing <code>R</code> and RStudio</a>
<ul>
<li class="chapter" data-level="1.1" data-path="preliminaries-installing-r-and-rstudio.html"><a href="preliminaries-installing-r-and-rstudio.html#introduction"><i class="fa fa-check"></i><b>1.1</b> Introduction</a></li>
<li class="chapter" data-level="1.2" data-path="preliminaries-installing-r-and-rstudio.html"><a href="preliminaries-installing-r-and-rstudio.html#learning-objectives"><i class="fa fa-check"></i><b>1.2</b> Learning Objectives</a></li>
<li class="chapter" data-level="1.3" data-path="preliminaries-installing-r-and-rstudio.html"><a href="preliminaries-installing-r-and-rstudio.html#r-the-open-statistical-computing-project"><i class="fa fa-check"></i><b>1.3</b> <code>R</code>: The Open Statistical Computing Project</a>
<ul>
<li class="chapter" data-level="1.3.1" data-path="preliminaries-installing-r-and-rstudio.html"><a href="preliminaries-installing-r-and-rstudio.html#what-is-r"><i class="fa fa-check"></i><b>1.3.1</b> What is <code>R</code>?</a></li>
<li class="chapter" data-level="1.3.2" data-path="preliminaries-installing-r-and-rstudio.html"><a href="preliminaries-installing-r-and-rstudio.html#the-rstudio-ide"><i class="fa fa-check"></i><b>1.3.2</b> The RStudio IDE</a></li>
</ul></li>
<li class="chapter" data-level="1.4" data-path="preliminaries-installing-r-and-rstudio.html"><a href="preliminaries-installing-r-and-rstudio.html#packages-in-r"><i class="fa fa-check"></i><b>1.4</b> Packages in R</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="basic-operations-and-data-structures-in-r.html"><a href="basic-operations-and-data-structures-in-r.html"><i class="fa fa-check"></i><b>2</b> Basic Operations and Data Structures in <code>R</code></a>
<ul>
<li class="chapter" data-level="2.1" data-path="basic-operations-and-data-structures-in-r.html"><a href="basic-operations-and-data-structures-in-r.html#learning-objectives-1"><i class="fa fa-check"></i><b>2.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="2.2" data-path="basic-operations-and-data-structures-in-r.html"><a href="basic-operations-and-data-structures-in-r.html#rstudio-ide"><i class="fa fa-check"></i><b>2.2</b> RStudio IDE</a></li>
<li class="chapter" data-level="2.3" data-path="basic-operations-and-data-structures-in-r.html"><a href="basic-operations-and-data-structures-in-r.html#some-basic-operations"><i class="fa fa-check"></i><b>2.3</b> Some Basic Operations</a></li>
<li class="chapter" data-level="2.4" data-path="basic-operations-and-data-structures-in-r.html"><a href="basic-operations-and-data-structures-in-r.html#data-classes-in-r"><i class="fa fa-check"></i><b>2.4</b> Data Classes in R</a></li>
<li class="chapter" data-level="2.5" data-path="basic-operations-and-data-structures-in-r.html"><a href="basic-operations-and-data-structures-in-r.html#data-types-in-r"><i class="fa fa-check"></i><b>2.5</b> Data Types in R</a></li>
<li class="chapter" data-level="2.6" data-path="basic-operations-and-data-structures-in-r.html"><a href="basic-operations-and-data-structures-in-r.html#indexing-and-data-transformations"><i class="fa fa-check"></i><b>2.6</b> Indexing and Data Transformations</a></li>
<li class="chapter" data-level="2.7" data-path="basic-operations-and-data-structures-in-r.html"><a href="basic-operations-and-data-structures-in-r.html#visualization"><i class="fa fa-check"></i><b>2.7</b> Visualization</a></li>
<li class="chapter" data-level="2.8" data-path="basic-operations-and-data-structures-in-r.html"><a href="basic-operations-and-data-structures-in-r.html#creating-a-simple-map"><i class="fa fa-check"></i><b>2.8</b> Creating a Simple Map</a></li>
<li class="chapter" data-level="2.9" data-path="basic-operations-and-data-structures-in-r.html"><a href="basic-operations-and-data-structures-in-r.html#references"><i class="fa fa-check"></i><b>2.9</b> References</a></li>
</ul></li>
<li class="part"><span><b>II Part II: Statistics and Maps</b></span></li>
<li class="chapter" data-level="3" data-path="introduction-to-mapping-in-r.html"><a href="introduction-to-mapping-in-r.html"><i class="fa fa-check"></i><b>3</b> Introduction to Mapping in <code>R</code></a>
<ul>
<li class="chapter" data-level="3.1" data-path="introduction-to-mapping-in-r.html"><a href="introduction-to-mapping-in-r.html#learning-objectives-2"><i class="fa fa-check"></i><b>3.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="3.2" data-path="introduction-to-mapping-in-r.html"><a href="introduction-to-mapping-in-r.html#suggested-readings"><i class="fa fa-check"></i><b>3.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="3.3" data-path="introduction-to-mapping-in-r.html"><a href="introduction-to-mapping-in-r.html#preliminaries"><i class="fa fa-check"></i><b>3.3</b> Preliminaries</a></li>
<li class="chapter" data-level="3.4" data-path="introduction-to-mapping-in-r.html"><a href="introduction-to-mapping-in-r.html#packages"><i class="fa fa-check"></i><b>3.4</b> Packages</a></li>
<li class="chapter" data-level="3.5" data-path="introduction-to-mapping-in-r.html"><a href="introduction-to-mapping-in-r.html#exploring-dataframes-and-a-simple-proportional-symbols-map"><i class="fa fa-check"></i><b>3.5</b> Exploring Dataframes and a Simple Proportional Symbols Map</a></li>
<li class="chapter" data-level="3.6" data-path="introduction-to-mapping-in-r.html"><a href="introduction-to-mapping-in-r.html#improving-on-the-proportional-symbols-map"><i class="fa fa-check"></i><b>3.6</b> Improving on the Proportional Symbols Map</a></li>
<li class="chapter" data-level="3.7" data-path="introduction-to-mapping-in-r.html"><a href="introduction-to-mapping-in-r.html#some-simple-spatial-analysis"><i class="fa fa-check"></i><b>3.7</b> Some Simple Spatial Analysis</a></li>
<li class="chapter" data-level="3.8" data-path="introduction-to-mapping-in-r.html"><a href="introduction-to-mapping-in-r.html#other-resources"><i class="fa fa-check"></i><b>3.8</b> Other Resources</a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="activity-1-statistical-maps-i.html"><a href="activity-1-statistical-maps-i.html"><i class="fa fa-check"></i><b>4</b> Activity 1: Statistical Maps I</a>
<ul>
<li class="chapter" data-level="4.1" data-path="activity-1-statistical-maps-i.html"><a href="activity-1-statistical-maps-i.html#housekeeping-questions"><i class="fa fa-check"></i><b>4.1</b> Housekeeping Questions</a></li>
<li class="chapter" data-level="4.2" data-path="activity-1-statistical-maps-i.html"><a href="activity-1-statistical-maps-i.html#learning-objectives-3"><i class="fa fa-check"></i><b>4.2</b> Learning Objectives</a></li>
<li class="chapter" data-level="4.3" data-path="activity-1-statistical-maps-i.html"><a href="activity-1-statistical-maps-i.html#preliminaries-1"><i class="fa fa-check"></i><b>4.3</b> Preliminaries</a></li>
<li class="chapter" data-level="4.4" data-path="activity-1-statistical-maps-i.html"><a href="activity-1-statistical-maps-i.html#creating-a-simple-thematic-map"><i class="fa fa-check"></i><b>4.4</b> Creating a simple thematic map</a></li>
<li class="chapter" data-level="4.5" data-path="activity-1-statistical-maps-i.html"><a href="activity-1-statistical-maps-i.html#activity"><i class="fa fa-check"></i><b>4.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="5" data-path="mapping-in-r-continued.html"><a href="mapping-in-r-continued.html"><i class="fa fa-check"></i><b>5</b> Mapping in R: Continued</a>
<ul>
<li class="chapter" data-level="5.1" data-path="mapping-in-r-continued.html"><a href="mapping-in-r-continued.html#learning-objectives-4"><i class="fa fa-check"></i><b>5.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="5.2" data-path="mapping-in-r-continued.html"><a href="mapping-in-r-continued.html#suggested-readings-1"><i class="fa fa-check"></i><b>5.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="5.3" data-path="mapping-in-r-continued.html"><a href="mapping-in-r-continued.html#preliminaries-2"><i class="fa fa-check"></i><b>5.3</b> Preliminaries</a></li>
<li class="chapter" data-level="5.4" data-path="mapping-in-r-continued.html"><a href="mapping-in-r-continued.html#summarizing-a-dataframe"><i class="fa fa-check"></i><b>5.4</b> Summarizing a Dataframe</a></li>
<li class="chapter" data-level="5.5" data-path="mapping-in-r-continued.html"><a href="mapping-in-r-continued.html#factors"><i class="fa fa-check"></i><b>5.5</b> Factors</a></li>
<li class="chapter" data-level="5.6" data-path="mapping-in-r-continued.html"><a href="mapping-in-r-continued.html#subsetting-data"><i class="fa fa-check"></i><b>5.6</b> Subsetting Data</a></li>
<li class="chapter" data-level="5.7" data-path="mapping-in-r-continued.html"><a href="mapping-in-r-continued.html#pipe-operator"><i class="fa fa-check"></i><b>5.7</b> Pipe Operator</a></li>
<li class="chapter" data-level="5.8" data-path="mapping-in-r-continued.html"><a href="mapping-in-r-continued.html#more-on-visualization"><i class="fa fa-check"></i><b>5.8</b> More on Visualization</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="activity-2-statistical-maps-ii.html"><a href="activity-2-statistical-maps-ii.html"><i class="fa fa-check"></i><b>6</b> Activity 2: Statistical Maps II</a>
<ul>
<li class="chapter" data-level="6.1" data-path="activity-2-statistical-maps-ii.html"><a href="activity-2-statistical-maps-ii.html#housekeeping-questions-1"><i class="fa fa-check"></i><b>6.1</b> Housekeeping Questions</a></li>
<li class="chapter" data-level="6.2" data-path="activity-2-statistical-maps-ii.html"><a href="activity-2-statistical-maps-ii.html#learning-objectives-5"><i class="fa fa-check"></i><b>6.2</b> Learning objectives</a></li>
<li class="chapter" data-level="6.3" data-path="activity-2-statistical-maps-ii.html"><a href="activity-2-statistical-maps-ii.html#suggested-reading"><i class="fa fa-check"></i><b>6.3</b> Suggested reading</a></li>
<li class="chapter" data-level="6.4" data-path="activity-2-statistical-maps-ii.html"><a href="activity-2-statistical-maps-ii.html#preliminaries-3"><i class="fa fa-check"></i><b>6.4</b> Preliminaries</a></li>
<li class="chapter" data-level="6.5" data-path="activity-2-statistical-maps-ii.html"><a href="activity-2-statistical-maps-ii.html#activity-1"><i class="fa fa-check"></i><b>6.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="7" data-path="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html"><a href="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html"><i class="fa fa-check"></i><b>7</b> Maps as Processes: Null Landscapes, Spatial Processes, and Statistical Maps</a>
<ul>
<li class="chapter" data-level="7.1" data-path="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html"><a href="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html#learning-objectives-6"><i class="fa fa-check"></i><b>7.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="7.2" data-path="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html"><a href="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html#suggested-readings-2"><i class="fa fa-check"></i><b>7.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="7.3" data-path="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html"><a href="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html#preliminaries-4"><i class="fa fa-check"></i><b>7.3</b> Preliminaries</a></li>
<li class="chapter" data-level="7.4" data-path="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html"><a href="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html#random-numbers"><i class="fa fa-check"></i><b>7.4</b> Random Numbers</a></li>
<li class="chapter" data-level="7.5" data-path="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html"><a href="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html#null-landscapes"><i class="fa fa-check"></i><b>7.5</b> Null Landscapes</a></li>
<li class="chapter" data-level="7.6" data-path="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html"><a href="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html#stochastic-processes"><i class="fa fa-check"></i><b>7.6</b> Stochastic Processes</a></li>
<li class="chapter" data-level="7.7" data-path="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html"><a href="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html#simulating-spatial-processes"><i class="fa fa-check"></i><b>7.7</b> Simulating Spatial Processes</a></li>
<li class="chapter" data-level="7.8" data-path="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html"><a href="maps-as-processes-null-landscapes-spatial-processes-and-statistical-maps.html#processes-and-patterns"><i class="fa fa-check"></i><b>7.8</b> Processes and Patterns</a></li>
</ul></li>
<li class="chapter" data-level="8" data-path="activity-3-maps-as-processes.html"><a href="activity-3-maps-as-processes.html"><i class="fa fa-check"></i><b>8</b> Activity 3: Maps as Processes</a>
<ul>
<li class="chapter" data-level="8.1" data-path="activity-3-maps-as-processes.html"><a href="activity-3-maps-as-processes.html#practice-questions"><i class="fa fa-check"></i><b>8.1</b> Practice Questions</a></li>
<li class="chapter" data-level="8.2" data-path="activity-3-maps-as-processes.html"><a href="activity-3-maps-as-processes.html#learning-objectives-7"><i class="fa fa-check"></i><b>8.2</b> Learning Objectives</a></li>
<li class="chapter" data-level="8.3" data-path="activity-3-maps-as-processes.html"><a href="activity-3-maps-as-processes.html#suggested-reading-1"><i class="fa fa-check"></i><b>8.3</b> Suggested Reading</a></li>
<li class="chapter" data-level="8.4" data-path="activity-3-maps-as-processes.html"><a href="activity-3-maps-as-processes.html#preliminaries-5"><i class="fa fa-check"></i><b>8.4</b> Preliminaries</a></li>
<li class="chapter" data-level="8.5" data-path="activity-3-maps-as-processes.html"><a href="activity-3-maps-as-processes.html#activity-2"><i class="fa fa-check"></i><b>8.5</b> Activity</a></li>
</ul></li>
<li class="part"><span><b>III Part III: Analysis of Point Patterns</b></span></li>
<li class="chapter" data-level="9" data-path="point-pattern-analysis-i.html"><a href="point-pattern-analysis-i.html"><i class="fa fa-check"></i><b>9</b> Point Pattern Analysis I</a>
<ul>
<li class="chapter" data-level="9.1" data-path="point-pattern-analysis-i.html"><a href="point-pattern-analysis-i.html#learning-objectives-8"><i class="fa fa-check"></i><b>9.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="9.2" data-path="point-pattern-analysis-i.html"><a href="point-pattern-analysis-i.html#suggested-readings-3"><i class="fa fa-check"></i><b>9.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="9.3" data-path="point-pattern-analysis-i.html"><a href="point-pattern-analysis-i.html#preliminaries-6"><i class="fa fa-check"></i><b>9.3</b> Preliminaries</a></li>
<li class="chapter" data-level="9.4" data-path="point-pattern-analysis-i.html"><a href="point-pattern-analysis-i.html#point-patterns"><i class="fa fa-check"></i><b>9.4</b> Point Patterns</a></li>
<li class="chapter" data-level="9.5" data-path="point-pattern-analysis-i.html"><a href="point-pattern-analysis-i.html#processes-and-point-patterns"><i class="fa fa-check"></i><b>9.5</b> Processes and Point Patterns</a></li>
<li class="chapter" data-level="9.6" data-path="point-pattern-analysis-i.html"><a href="point-pattern-analysis-i.html#intensity-and-density"><i class="fa fa-check"></i><b>9.6</b> Intensity and Density</a></li>
<li class="chapter" data-level="9.7" data-path="point-pattern-analysis-i.html"><a href="point-pattern-analysis-i.html#quadrats-and-density-maps"><i class="fa fa-check"></i><b>9.7</b> Quadrats and Density Maps</a></li>
<li class="chapter" data-level="9.8" data-path="point-pattern-analysis-i.html"><a href="point-pattern-analysis-i.html#defining-the-region-for-analysis"><i class="fa fa-check"></i><b>9.8</b> Defining the Region for Analysis</a></li>
</ul></li>
<li class="chapter" data-level="10" data-path="activity-4-point-pattern-analysis-i.html"><a href="activity-4-point-pattern-analysis-i.html"><i class="fa fa-check"></i><b>10</b> Activity 4: Point Pattern Analysis I</a>
<ul>
<li class="chapter" data-level="10.1" data-path="activity-4-point-pattern-analysis-i.html"><a href="activity-4-point-pattern-analysis-i.html#practice-questions-1"><i class="fa fa-check"></i><b>10.1</b> Practice questions</a></li>
<li class="chapter" data-level="10.2" data-path="activity-4-point-pattern-analysis-i.html"><a href="activity-4-point-pattern-analysis-i.html#learning-objectives-9"><i class="fa fa-check"></i><b>10.2</b> Learning objectives</a></li>
<li class="chapter" data-level="10.3" data-path="activity-4-point-pattern-analysis-i.html"><a href="activity-4-point-pattern-analysis-i.html#suggested-reading-2"><i class="fa fa-check"></i><b>10.3</b> Suggested reading</a></li>
<li class="chapter" data-level="10.4" data-path="activity-4-point-pattern-analysis-i.html"><a href="activity-4-point-pattern-analysis-i.html#preliminaries-7"><i class="fa fa-check"></i><b>10.4</b> Preliminaries</a></li>
<li class="chapter" data-level="10.5" data-path="activity-4-point-pattern-analysis-i.html"><a href="activity-4-point-pattern-analysis-i.html#activity-3"><i class="fa fa-check"></i><b>10.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="11" data-path="point-pattern-analysis-ii.html"><a href="point-pattern-analysis-ii.html"><i class="fa fa-check"></i><b>11</b> Point Pattern Analysis II</a>
<ul>
<li class="chapter" data-level="11.1" data-path="point-pattern-analysis-ii.html"><a href="point-pattern-analysis-ii.html#learning-objectives-10"><i class="fa fa-check"></i><b>11.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="11.2" data-path="point-pattern-analysis-ii.html"><a href="point-pattern-analysis-ii.html#suggested-readings-4"><i class="fa fa-check"></i><b>11.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="11.3" data-path="point-pattern-analysis-ii.html"><a href="point-pattern-analysis-ii.html#preliminaries-8"><i class="fa fa-check"></i><b>11.3</b> Preliminaries</a></li>
<li class="chapter" data-level="11.4" data-path="point-pattern-analysis-ii.html"><a href="point-pattern-analysis-ii.html#a-quadrat-based-test-for-spatial-independence"><i class="fa fa-check"></i><b>11.4</b> A Quadrat-based Test for Spatial Independence</a></li>
<li class="chapter" data-level="11.5" data-path="point-pattern-analysis-ii.html"><a href="point-pattern-analysis-ii.html#limitations-of-quadrat-analysis-size-and-number-of-quadrats"><i class="fa fa-check"></i><b>11.5</b> Limitations of Quadrat Analysis: Size and Number of Quadrats</a></li>
<li class="chapter" data-level="11.6" data-path="point-pattern-analysis-ii.html"><a href="point-pattern-analysis-ii.html#limitations-of-quadrat-analysis-relative-position-of-events"><i class="fa fa-check"></i><b>11.6</b> Limitations of Quadrat Analysis: Relative Position of Events</a></li>
<li class="chapter" data-level="11.7" data-path="point-pattern-analysis-ii.html"><a href="point-pattern-analysis-ii.html#kernel-density"><i class="fa fa-check"></i><b>11.7</b> Kernel Density</a></li>
</ul></li>
<li class="chapter" data-level="12" data-path="activity-5-point-pattern-analysis-ii.html"><a href="activity-5-point-pattern-analysis-ii.html"><i class="fa fa-check"></i><b>12</b> Activity 5: Point Pattern Analysis II</a>
<ul>
<li class="chapter" data-level="12.1" data-path="activity-5-point-pattern-analysis-ii.html"><a href="activity-5-point-pattern-analysis-ii.html#practice-questions-2"><i class="fa fa-check"></i><b>12.1</b> Practice questions</a></li>
<li class="chapter" data-level="12.2" data-path="activity-5-point-pattern-analysis-ii.html"><a href="activity-5-point-pattern-analysis-ii.html#learning-objectives-11"><i class="fa fa-check"></i><b>12.2</b> Learning objectives</a></li>
<li class="chapter" data-level="12.3" data-path="activity-5-point-pattern-analysis-ii.html"><a href="activity-5-point-pattern-analysis-ii.html#suggested-reading-3"><i class="fa fa-check"></i><b>12.3</b> Suggested reading</a></li>
<li class="chapter" data-level="12.4" data-path="activity-5-point-pattern-analysis-ii.html"><a href="activity-5-point-pattern-analysis-ii.html#preliminaries-9"><i class="fa fa-check"></i><b>12.4</b> Preliminaries</a></li>
<li class="chapter" data-level="12.5" data-path="activity-5-point-pattern-analysis-ii.html"><a href="activity-5-point-pattern-analysis-ii.html#activity-4"><i class="fa fa-check"></i><b>12.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="13" data-path="point-pattern-analysis-iii.html"><a href="point-pattern-analysis-iii.html"><i class="fa fa-check"></i><b>13</b> Point Pattern Analysis III</a>
<ul>
<li class="chapter" data-level="13.1" data-path="point-pattern-analysis-iii.html"><a href="point-pattern-analysis-iii.html#learning-objectives-12"><i class="fa fa-check"></i><b>13.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="13.2" data-path="point-pattern-analysis-iii.html"><a href="point-pattern-analysis-iii.html#suggested-readings-5"><i class="fa fa-check"></i><b>13.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="13.3" data-path="point-pattern-analysis-iii.html"><a href="point-pattern-analysis-iii.html#preliminaries-10"><i class="fa fa-check"></i><b>13.3</b> Preliminaries</a></li>
<li class="chapter" data-level="13.4" data-path="point-pattern-analysis-iii.html"><a href="point-pattern-analysis-iii.html#motivation"><i class="fa fa-check"></i><b>13.4</b> Motivation</a></li>
<li class="chapter" data-level="13.5" data-path="point-pattern-analysis-iii.html"><a href="point-pattern-analysis-iii.html#nearest-neighbors"><i class="fa fa-check"></i><b>13.5</b> Nearest Neighbors</a></li>
<li class="chapter" data-level="13.6" data-path="point-pattern-analysis-iii.html"><a href="point-pattern-analysis-iii.html#g-function"><i class="fa fa-check"></i><b>13.6</b> <span class="math inline">\(G\)</span>-function</a></li>
</ul></li>
<li class="chapter" data-level="14" data-path="activity-6-point-pattern-analysis-iii.html"><a href="activity-6-point-pattern-analysis-iii.html"><i class="fa fa-check"></i><b>14</b> Activity 6: Point Pattern Analysis III</a>
<ul>
<li class="chapter" data-level="14.1" data-path="activity-6-point-pattern-analysis-iii.html"><a href="activity-6-point-pattern-analysis-iii.html#practice-questions-3"><i class="fa fa-check"></i><b>14.1</b> Practice questions</a></li>
<li class="chapter" data-level="14.2" data-path="activity-6-point-pattern-analysis-iii.html"><a href="activity-6-point-pattern-analysis-iii.html#learning-objectives-13"><i class="fa fa-check"></i><b>14.2</b> Learning objectives</a></li>
<li class="chapter" data-level="14.3" data-path="activity-6-point-pattern-analysis-iii.html"><a href="activity-6-point-pattern-analysis-iii.html#suggested-reading-4"><i class="fa fa-check"></i><b>14.3</b> Suggested reading</a></li>
<li class="chapter" data-level="14.4" data-path="activity-6-point-pattern-analysis-iii.html"><a href="activity-6-point-pattern-analysis-iii.html#preliminaries-11"><i class="fa fa-check"></i><b>14.4</b> Preliminaries</a></li>
<li class="chapter" data-level="14.5" data-path="activity-6-point-pattern-analysis-iii.html"><a href="activity-6-point-pattern-analysis-iii.html#activity-5"><i class="fa fa-check"></i><b>14.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="15" data-path="point-pattern-analysis-iv.html"><a href="point-pattern-analysis-iv.html"><i class="fa fa-check"></i><b>15</b> Point Pattern Analysis IV</a>
<ul>
<li class="chapter" data-level="15.1" data-path="point-pattern-analysis-iv.html"><a href="point-pattern-analysis-iv.html#learning-objectives-14"><i class="fa fa-check"></i><b>15.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="15.2" data-path="point-pattern-analysis-iv.html"><a href="point-pattern-analysis-iv.html#suggested-readings-6"><i class="fa fa-check"></i><b>15.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="15.3" data-path="point-pattern-analysis-iv.html"><a href="point-pattern-analysis-iv.html#preliminaries-12"><i class="fa fa-check"></i><b>15.3</b> Preliminaries</a></li>
<li class="chapter" data-level="15.4" data-path="point-pattern-analysis-iv.html"><a href="point-pattern-analysis-iv.html#motivation-1"><i class="fa fa-check"></i><b>15.4</b> Motivation</a></li>
<li class="chapter" data-level="15.5" data-path="point-pattern-analysis-iv.html"><a href="point-pattern-analysis-iv.html#f-function"><i class="fa fa-check"></i><b>15.5</b> F-function</a></li>
<li class="chapter" data-level="15.6" data-path="point-pattern-analysis-iv.html"><a href="point-pattern-analysis-iv.html#hatk-function"><i class="fa fa-check"></i><b>15.6</b> <span class="math inline">\(\hat{K}\)</span>-function</a></li>
</ul></li>
<li class="chapter" data-level="16" data-path="activity-7-point-pattern-analysis-iv.html"><a href="activity-7-point-pattern-analysis-iv.html"><i class="fa fa-check"></i><b>16</b> Activity 7: Point Pattern Analysis IV</a>
<ul>
<li class="chapter" data-level="16.1" data-path="activity-7-point-pattern-analysis-iv.html"><a href="activity-7-point-pattern-analysis-iv.html#practice-questions-4"><i class="fa fa-check"></i><b>16.1</b> Practice questions</a></li>
<li class="chapter" data-level="16.2" data-path="activity-7-point-pattern-analysis-iv.html"><a href="activity-7-point-pattern-analysis-iv.html#learning-objectives-15"><i class="fa fa-check"></i><b>16.2</b> Learning objectives</a></li>
<li class="chapter" data-level="16.3" data-path="activity-7-point-pattern-analysis-iv.html"><a href="activity-7-point-pattern-analysis-iv.html#suggested-reading-5"><i class="fa fa-check"></i><b>16.3</b> Suggested reading</a></li>
<li class="chapter" data-level="16.4" data-path="activity-7-point-pattern-analysis-iv.html"><a href="activity-7-point-pattern-analysis-iv.html#preliminaries-13"><i class="fa fa-check"></i><b>16.4</b> Preliminaries</a></li>
<li class="chapter" data-level="16.5" data-path="activity-7-point-pattern-analysis-iv.html"><a href="activity-7-point-pattern-analysis-iv.html#activity-6"><i class="fa fa-check"></i><b>16.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="17" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html"><i class="fa fa-check"></i><b>17</b> Point Pattern Analysis V</a>
<ul>
<li class="chapter" data-level="17.1" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html#learning-objectives-16"><i class="fa fa-check"></i><b>17.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="17.2" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html#suggested-readings-7"><i class="fa fa-check"></i><b>17.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="17.3" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html#preliminaries-14"><i class="fa fa-check"></i><b>17.3</b> Preliminaries</a></li>
<li class="chapter" data-level="17.4" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html#motivation-hypothesis-testing"><i class="fa fa-check"></i><b>17.4</b> Motivation: Hypothesis Testing</a></li>
<li class="chapter" data-level="17.5" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html#null-landscapes-revisited"><i class="fa fa-check"></i><b>17.5</b> Null Landscapes Revisited</a></li>
<li class="chapter" data-level="17.6" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html#simulation-envelopes"><i class="fa fa-check"></i><b>17.6</b> Simulation Envelopes</a></li>
<li class="chapter" data-level="17.7" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html#things-to-keep-in-mind"><i class="fa fa-check"></i><b>17.7</b> Things to Keep in Mind!</a>
<ul>
<li class="chapter" data-level="17.7.1" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html#definition-of-a-region"><i class="fa fa-check"></i><b>17.7.1</b> Definition of a Region</a></li>
<li class="chapter" data-level="17.7.2" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html#edge-effects"><i class="fa fa-check"></i><b>17.7.2</b> Edge Effects</a></li>
<li class="chapter" data-level="17.7.3" data-path="point-pattern-analysis-v.html"><a href="point-pattern-analysis-v.html#sampled-point-patterns"><i class="fa fa-check"></i><b>17.7.3</b> Sampled Point Patterns</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="18" data-path="activity-8-point-pattern-analysis-v.html"><a href="activity-8-point-pattern-analysis-v.html"><i class="fa fa-check"></i><b>18</b> Activity 8: Point Pattern Analysis V</a>
<ul>
<li class="chapter" data-level="18.1" data-path="activity-8-point-pattern-analysis-v.html"><a href="activity-8-point-pattern-analysis-v.html#practice-questions-5"><i class="fa fa-check"></i><b>18.1</b> Practice questions</a></li>
<li class="chapter" data-level="18.2" data-path="activity-8-point-pattern-analysis-v.html"><a href="activity-8-point-pattern-analysis-v.html#learning-objectives-17"><i class="fa fa-check"></i><b>18.2</b> Learning objectives</a></li>
<li class="chapter" data-level="18.3" data-path="activity-8-point-pattern-analysis-v.html"><a href="activity-8-point-pattern-analysis-v.html#suggested-reading-6"><i class="fa fa-check"></i><b>18.3</b> Suggested reading</a></li>
<li class="chapter" data-level="18.4" data-path="activity-8-point-pattern-analysis-v.html"><a href="activity-8-point-pattern-analysis-v.html#preliminaries-15"><i class="fa fa-check"></i><b>18.4</b> Preliminaries</a></li>
<li class="chapter" data-level="18.5" data-path="activity-8-point-pattern-analysis-v.html"><a href="activity-8-point-pattern-analysis-v.html#activity-7"><i class="fa fa-check"></i><b>18.5</b> Activity</a></li>
</ul></li>
<li class="part"><span><b>IV Part IV: Data in Areal Units</b></span></li>
<li class="chapter" data-level="19" data-path="area-data-i.html"><a href="area-data-i.html"><i class="fa fa-check"></i><b>19</b> Area Data I</a>
<ul>
<li class="chapter" data-level="19.1" data-path="area-data-i.html"><a href="area-data-i.html#learning-objectives-18"><i class="fa fa-check"></i><b>19.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="19.2" data-path="area-data-i.html"><a href="area-data-i.html#suggested-readings-8"><i class="fa fa-check"></i><b>19.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="19.3" data-path="area-data-i.html"><a href="area-data-i.html#preliminaries-16"><i class="fa fa-check"></i><b>19.3</b> Preliminaries</a></li>
<li class="chapter" data-level="19.4" data-path="area-data-i.html"><a href="area-data-i.html#area-data"><i class="fa fa-check"></i><b>19.4</b> Area Data</a></li>
<li class="chapter" data-level="19.5" data-path="area-data-i.html"><a href="area-data-i.html#processes-and-area-data"><i class="fa fa-check"></i><b>19.5</b> Processes and Area Data</a></li>
<li class="chapter" data-level="19.6" data-path="area-data-i.html"><a href="area-data-i.html#visualizing-area-data-choropleth-maps"><i class="fa fa-check"></i><b>19.6</b> Visualizing Area Data: Choropleth Maps</a></li>
<li class="chapter" data-level="19.7" data-path="area-data-i.html"><a href="area-data-i.html#visualizing-area-data-cartograms"><i class="fa fa-check"></i><b>19.7</b> Visualizing Area Data: Cartograms</a></li>
</ul></li>
<li class="chapter" data-level="20" data-path="activity-9-area-data-i.html"><a href="activity-9-area-data-i.html"><i class="fa fa-check"></i><b>20</b> Activity 9: Area Data I</a>
<ul>
<li class="chapter" data-level="20.1" data-path="activity-9-area-data-i.html"><a href="activity-9-area-data-i.html#practice-questions-6"><i class="fa fa-check"></i><b>20.1</b> Practice questions</a></li>
<li class="chapter" data-level="20.2" data-path="activity-9-area-data-i.html"><a href="activity-9-area-data-i.html#learning-objectives-19"><i class="fa fa-check"></i><b>20.2</b> Learning objectives</a></li>
<li class="chapter" data-level="20.3" data-path="activity-9-area-data-i.html"><a href="activity-9-area-data-i.html#suggested-reading-7"><i class="fa fa-check"></i><b>20.3</b> Suggested reading</a></li>
<li class="chapter" data-level="20.4" data-path="activity-9-area-data-i.html"><a href="activity-9-area-data-i.html#preliminaries-17"><i class="fa fa-check"></i><b>20.4</b> Preliminaries</a></li>
<li class="chapter" data-level="20.5" data-path="activity-9-area-data-i.html"><a href="activity-9-area-data-i.html#activity-8"><i class="fa fa-check"></i><b>20.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="21" data-path="area-data-ii.html"><a href="area-data-ii.html"><i class="fa fa-check"></i><b>21</b> Area Data II</a>
<ul>
<li class="chapter" data-level="21.1" data-path="area-data-ii.html"><a href="area-data-ii.html#learning-objectives-20"><i class="fa fa-check"></i><b>21.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="21.2" data-path="area-data-ii.html"><a href="area-data-ii.html#suggested-readings-9"><i class="fa fa-check"></i><b>21.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="21.3" data-path="area-data-ii.html"><a href="area-data-ii.html#preliminaries-18"><i class="fa fa-check"></i><b>21.3</b> Preliminaries</a></li>
<li class="chapter" data-level="21.4" data-path="area-data-ii.html"><a href="area-data-ii.html#proximity-in-area-data"><i class="fa fa-check"></i><b>21.4</b> Proximity in Area Data</a></li>
<li class="chapter" data-level="21.5" data-path="area-data-ii.html"><a href="area-data-ii.html#spatial-weights-matrices"><i class="fa fa-check"></i><b>21.5</b> Spatial Weights Matrices</a></li>
<li class="chapter" data-level="21.6" data-path="area-data-ii.html"><a href="area-data-ii.html#creating-spatial-weights-matrices-in-r"><i class="fa fa-check"></i><b>21.6</b> Creating Spatial Weights Matrices in <code>R</code></a></li>
<li class="chapter" data-level="21.7" data-path="area-data-ii.html"><a href="area-data-ii.html#spatial-moving-averages"><i class="fa fa-check"></i><b>21.7</b> Spatial Moving Averages</a></li>
<li class="chapter" data-level="21.8" data-path="area-data-ii.html"><a href="area-data-ii.html#other-criteria-for-coding-proximity"><i class="fa fa-check"></i><b>21.8</b> Other Criteria for Coding Proximity</a></li>
</ul></li>
<li class="chapter" data-level="22" data-path="activity-10-area-data-ii.html"><a href="activity-10-area-data-ii.html"><i class="fa fa-check"></i><b>22</b> Activity 10: Area Data II</a>
<ul>
<li class="chapter" data-level="22.1" data-path="activity-10-area-data-ii.html"><a href="activity-10-area-data-ii.html#practice-questions-7"><i class="fa fa-check"></i><b>22.1</b> Practice questions</a></li>
<li class="chapter" data-level="22.2" data-path="activity-10-area-data-ii.html"><a href="activity-10-area-data-ii.html#learning-objectives-21"><i class="fa fa-check"></i><b>22.2</b> Learning objectives</a></li>
<li class="chapter" data-level="22.3" data-path="activity-10-area-data-ii.html"><a href="activity-10-area-data-ii.html#suggested-reading-8"><i class="fa fa-check"></i><b>22.3</b> Suggested reading</a></li>
<li class="chapter" data-level="22.4" data-path="activity-10-area-data-ii.html"><a href="activity-10-area-data-ii.html#preliminaries-19"><i class="fa fa-check"></i><b>22.4</b> Preliminaries</a></li>
<li class="chapter" data-level="22.5" data-path="activity-10-area-data-ii.html"><a href="activity-10-area-data-ii.html#activity-9"><i class="fa fa-check"></i><b>22.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="23" data-path="area-data-iii.html"><a href="area-data-iii.html"><i class="fa fa-check"></i><b>23</b> Area Data III</a>
<ul>
<li class="chapter" data-level="23.1" data-path="area-data-iii.html"><a href="area-data-iii.html#learning-objectives-22"><i class="fa fa-check"></i><b>23.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="23.2" data-path="area-data-iii.html"><a href="area-data-iii.html#suggested-readings-10"><i class="fa fa-check"></i><b>23.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="23.3" data-path="area-data-iii.html"><a href="area-data-iii.html#preliminaries-20"><i class="fa fa-check"></i><b>23.3</b> Preliminaries</a></li>
<li class="chapter" data-level="23.4" data-path="area-data-iii.html"><a href="area-data-iii.html#spatial-moving-averages-and-simulation"><i class="fa fa-check"></i><b>23.4</b> Spatial Moving Averages and Simulation</a></li>
<li class="chapter" data-level="23.5" data-path="area-data-iii.html"><a href="area-data-iii.html#the-spatial-moving-average-as-a-smoother"><i class="fa fa-check"></i><b>23.5</b> The Spatial Moving Average as a Smoother</a></li>
<li class="chapter" data-level="23.6" data-path="area-data-iii.html"><a href="area-data-iii.html#spatial-moving-average-scatterplots"><i class="fa fa-check"></i><b>23.6</b> Spatial Moving Average Scatterplots</a></li>
<li class="chapter" data-level="23.7" data-path="area-data-iii.html"><a href="area-data-iii.html#spatial-autocorrelation-and-morans-i-coefficient"><i class="fa fa-check"></i><b>23.7</b> Spatial Autocorrelation and Moran’s <span class="math inline">\(I\)</span> coefficient</a></li>
<li class="chapter" data-level="23.8" data-path="area-data-iii.html"><a href="area-data-iii.html#morans-i-and-morans-scatterplot"><i class="fa fa-check"></i><b>23.8</b> Moran’s <span class="math inline">\(I\)</span> and Moran’s Scatterplot</a></li>
<li class="chapter" data-level="23.9" data-path="area-data-iii.html"><a href="area-data-iii.html#hypothesis-testing-for-spatial-autocorrelation"><i class="fa fa-check"></i><b>23.9</b> Hypothesis Testing for Spatial Autocorrelation</a></li>
</ul></li>
<li class="chapter" data-level="24" data-path="activity-11-area-data-iii.html"><a href="activity-11-area-data-iii.html"><i class="fa fa-check"></i><b>24</b> Activity 11: Area Data III</a>
<ul>
<li class="chapter" data-level="24.1" data-path="activity-11-area-data-iii.html"><a href="activity-11-area-data-iii.html#practice-questions-8"><i class="fa fa-check"></i><b>24.1</b> Practice questions</a></li>
<li class="chapter" data-level="24.2" data-path="activity-11-area-data-iii.html"><a href="activity-11-area-data-iii.html#learning-objectives-23"><i class="fa fa-check"></i><b>24.2</b> Learning objectives</a></li>
<li class="chapter" data-level="24.3" data-path="activity-11-area-data-iii.html"><a href="activity-11-area-data-iii.html#suggested-reading-9"><i class="fa fa-check"></i><b>24.3</b> Suggested reading</a></li>
<li class="chapter" data-level="24.4" data-path="activity-11-area-data-iii.html"><a href="activity-11-area-data-iii.html#preliminaries-21"><i class="fa fa-check"></i><b>24.4</b> Preliminaries</a></li>
<li class="chapter" data-level="24.5" data-path="activity-11-area-data-iii.html"><a href="activity-11-area-data-iii.html#activity-10"><i class="fa fa-check"></i><b>24.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="25" data-path="area-data-iv.html"><a href="area-data-iv.html"><i class="fa fa-check"></i><b>25</b> Area Data IV</a>
<ul>
<li class="chapter" data-level="25.1" data-path="area-data-iv.html"><a href="area-data-iv.html#learning-objectives-24"><i class="fa fa-check"></i><b>25.1</b> Learning objectives</a></li>
<li class="chapter" data-level="25.2" data-path="area-data-iv.html"><a href="area-data-iv.html#suggested-readings-11"><i class="fa fa-check"></i><b>25.2</b> Suggested readings</a></li>
<li class="chapter" data-level="25.3" data-path="area-data-iv.html"><a href="area-data-iv.html#preliminaries-22"><i class="fa fa-check"></i><b>25.3</b> Preliminaries</a></li>
<li class="chapter" data-level="25.4" data-path="area-data-iv.html"><a href="area-data-iv.html#decomposing-morans-i"><i class="fa fa-check"></i><b>25.4</b> Decomposing Moran’s <span class="math inline">\(I\)</span></a></li>
<li class="chapter" data-level="25.5" data-path="area-data-iv.html"><a href="area-data-iv.html#local-morans-i-and-mapping"><i class="fa fa-check"></i><b>25.5</b> Local Moran’s <span class="math inline">\(I\)</span> and Mapping</a></li>
<li class="chapter" data-level="25.6" data-path="area-data-iv.html"><a href="area-data-iv.html#a-quick-note-on-functions"><i class="fa fa-check"></i><b>25.6</b> A Quick Note on Functions</a></li>
<li class="chapter" data-level="25.7" data-path="area-data-iv.html"><a href="area-data-iv.html#a-concentration-approach-for-local-analysis-of-spatial-association"><i class="fa fa-check"></i><b>25.7</b> A Concentration approach for Local Analysis of Spatial Association</a></li>
<li class="chapter" data-level="25.8" data-path="area-data-iv.html"><a href="area-data-iv.html#a-short-note-on-hypothesis-testing"><i class="fa fa-check"></i><b>25.8</b> A Short Note on Hypothesis Testing</a></li>
<li class="chapter" data-level="25.9" data-path="area-data-iv.html"><a href="area-data-iv.html#detection-of-hot-and-cold-spots"><i class="fa fa-check"></i><b>25.9</b> Detection of Hot and Cold Spots</a></li>
<li class="chapter" data-level="25.10" data-path="area-data-iv.html"><a href="area-data-iv.html#other-resources-1"><i class="fa fa-check"></i><b>25.10</b> Other Resources</a></li>
</ul></li>
<li class="chapter" data-level="26" data-path="activity-12-area-data-iv.html"><a href="activity-12-area-data-iv.html"><i class="fa fa-check"></i><b>26</b> Activity 12: Area Data IV</a>
<ul>
<li class="chapter" data-level="26.1" data-path="activity-12-area-data-iv.html"><a href="activity-12-area-data-iv.html#practice-questions-9"><i class="fa fa-check"></i><b>26.1</b> Practice questions</a></li>
<li class="chapter" data-level="26.2" data-path="activity-12-area-data-iv.html"><a href="activity-12-area-data-iv.html#learning-objectives-25"><i class="fa fa-check"></i><b>26.2</b> Learning objectives</a></li>
<li class="chapter" data-level="26.3" data-path="activity-12-area-data-iv.html"><a href="activity-12-area-data-iv.html#suggested-reading-10"><i class="fa fa-check"></i><b>26.3</b> Suggested reading</a></li>
<li class="chapter" data-level="26.4" data-path="activity-12-area-data-iv.html"><a href="activity-12-area-data-iv.html#preliminaries-23"><i class="fa fa-check"></i><b>26.4</b> Preliminaries</a></li>
<li class="chapter" data-level="26.5" data-path="activity-12-area-data-iv.html"><a href="activity-12-area-data-iv.html#activity-11"><i class="fa fa-check"></i><b>26.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="27" data-path="area-data-v.html"><a href="area-data-v.html"><i class="fa fa-check"></i><b>27</b> Area Data V</a>
<ul>
<li class="chapter" data-level="27.1" data-path="area-data-v.html"><a href="area-data-v.html#learning-objectives-26"><i class="fa fa-check"></i><b>27.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="27.2" data-path="area-data-v.html"><a href="area-data-v.html#suggested-readings-12"><i class="fa fa-check"></i><b>27.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="27.3" data-path="area-data-v.html"><a href="area-data-v.html#preliminaries-24"><i class="fa fa-check"></i><b>27.3</b> Preliminaries</a></li>
<li class="chapter" data-level="27.4" data-path="area-data-v.html"><a href="area-data-v.html#regression-analysis-in-r"><i class="fa fa-check"></i><b>27.4</b> Regression Analysis in <code>R</code></a></li>
<li class="chapter" data-level="27.5" data-path="area-data-v.html"><a href="area-data-v.html#autocorrelation-as-a-model-diagnostic"><i class="fa fa-check"></i><b>27.5</b> Autocorrelation as a Model Diagnostic</a></li>
<li class="chapter" data-level="27.6" data-path="area-data-v.html"><a href="area-data-v.html#variable-transformations"><i class="fa fa-check"></i><b>27.6</b> Variable Transformations</a></li>
<li class="chapter" data-level="27.7" data-path="area-data-v.html"><a href="area-data-v.html#a-note-about-spatial-autocorrelation-in-regression-analysis"><i class="fa fa-check"></i><b>27.7</b> A Note about Spatial Autocorrelation in Regression Analysis</a></li>
</ul></li>
<li class="chapter" data-level="28" data-path="activity-13-area-data-v.html"><a href="activity-13-area-data-v.html"><i class="fa fa-check"></i><b>28</b> Activity 13: Area Data V</a>
<ul>
<li class="chapter" data-level="28.1" data-path="activity-13-area-data-v.html"><a href="activity-13-area-data-v.html#practice-questions-10"><i class="fa fa-check"></i><b>28.1</b> Practice questions</a></li>
<li class="chapter" data-level="28.2" data-path="activity-13-area-data-v.html"><a href="activity-13-area-data-v.html#learning-objectives-27"><i class="fa fa-check"></i><b>28.2</b> Learning objectives</a></li>
<li class="chapter" data-level="28.3" data-path="activity-13-area-data-v.html"><a href="activity-13-area-data-v.html#suggested-reading-11"><i class="fa fa-check"></i><b>28.3</b> Suggested reading</a></li>
<li class="chapter" data-level="28.4" data-path="activity-13-area-data-v.html"><a href="activity-13-area-data-v.html#preliminaries-25"><i class="fa fa-check"></i><b>28.4</b> Preliminaries</a></li>
<li class="chapter" data-level="28.5" data-path="activity-13-area-data-v.html"><a href="activity-13-area-data-v.html#activity-12"><i class="fa fa-check"></i><b>28.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="29" data-path="area-data-vi.html"><a href="area-data-vi.html"><i class="fa fa-check"></i><b>29</b> Area Data VI</a>
<ul>
<li class="chapter" data-level="29.1" data-path="area-data-vi.html"><a href="area-data-vi.html#learning-objectives-28"><i class="fa fa-check"></i><b>29.1</b> Learning Objectives</a></li>
<li class="chapter" data-level="29.2" data-path="area-data-vi.html"><a href="area-data-vi.html#suggested-readings-13"><i class="fa fa-check"></i><b>29.2</b> Suggested Readings</a></li>
<li class="chapter" data-level="29.3" data-path="area-data-vi.html"><a href="area-data-vi.html#preliminaries-26"><i class="fa fa-check"></i><b>29.3</b> Preliminaries</a></li>
<li class="chapter" data-level="29.4" data-path="area-data-vi.html"><a href="area-data-vi.html#residual-spatial-autocorrelation-revisited"><i class="fa fa-check"></i><b>29.4</b> Residual spatial autocorrelation revisited</a>
<ul>
<li class="chapter" data-level="29.4.1" data-path="area-data-vi.html"><a href="area-data-vi.html#incorrect-functional-form"><i class="fa fa-check"></i><b>29.4.1</b> Incorrect Functional Form</a></li>
<li class="chapter" data-level="29.4.2" data-path="area-data-vi.html"><a href="area-data-vi.html#omitted-variables"><i class="fa fa-check"></i><b>29.4.2</b> Omitted Variables</a></li>
</ul></li>
<li class="chapter" data-level="29.5" data-path="area-data-vi.html"><a href="area-data-vi.html#remedial-action"><i class="fa fa-check"></i><b>29.5</b> Remedial Action</a></li>
<li class="chapter" data-level="29.6" data-path="area-data-vi.html"><a href="area-data-vi.html#flexible-functional-forms-and-models-with-spatially-varying-coefficients"><i class="fa fa-check"></i><b>29.6</b> Flexible Functional Forms and Models with Spatially-varying Coefficients</a>
<ul>
<li class="chapter" data-level="29.6.1" data-path="area-data-vi.html"><a href="area-data-vi.html#trend-surface-analysis"><i class="fa fa-check"></i><b>29.6.1</b> Trend Surface Analysis</a></li>
<li class="chapter" data-level="29.6.2" data-path="area-data-vi.html"><a href="area-data-vi.html#models-with-spatially-varying-coefficients"><i class="fa fa-check"></i><b>29.6.2</b> Models with Spatially-varying Coefficients</a></li>
</ul></li>
<li class="chapter" data-level="29.7" data-path="area-data-vi.html"><a href="area-data-vi.html#spatial-error-model-sem"><i class="fa fa-check"></i><b>29.7</b> Spatial Error Model (SEM)</a></li>
</ul></li>
<li class="chapter" data-level="30" data-path="activity-14-area-data-vi.html"><a href="activity-14-area-data-vi.html"><i class="fa fa-check"></i><b>30</b> Activity 14: Area Data VI</a>
<ul>
<li class="chapter" data-level="30.1" data-path="activity-14-area-data-vi.html"><a href="activity-14-area-data-vi.html#practice-questions-11"><i class="fa fa-check"></i><b>30.1</b> Practice questions</a></li>
<li class="chapter" data-level="30.2" data-path="activity-14-area-data-vi.html"><a href="activity-14-area-data-vi.html#learning-objectives-29"><i class="fa fa-check"></i><b>30.2</b> Learning objectives</a></li>
<li class="chapter" data-level="30.3" data-path="activity-14-area-data-vi.html"><a href="activity-14-area-data-vi.html#suggested-reading-12"><i class="fa fa-check"></i><b>30.3</b> Suggested reading</a></li>
<li class="chapter" data-level="30.4" data-path="activity-14-area-data-vi.html"><a href="activity-14-area-data-vi.html#preliminaries-27"><i class="fa fa-check"></i><b>30.4</b> Preliminaries</a>
<ul>
<li class="chapter" data-level="30.4.1" data-path="activity-14-area-data-vi.html"><a href="activity-14-area-data-vi.html#new-york-leukemia-data"><i class="fa fa-check"></i><b>30.4.1</b> New York leukemia data</a></li>
<li class="chapter" data-level="30.4.2" data-path="activity-14-area-data-vi.html"><a href="activity-14-area-data-vi.html#pennsylvania-lung-cancer"><i class="fa fa-check"></i><b>30.4.2</b> Pennsylvania lung cancer</a></li>
</ul></li>
<li class="chapter" data-level="30.5" data-path="activity-14-area-data-vi.html"><a href="activity-14-area-data-vi.html#activity-13"><i class="fa fa-check"></i><b>30.5</b> Activity</a></li>
</ul></li>
<li class="part"><span><b>V Part V: Analysis and Prediction of Fields</b></span></li>
<li class="chapter" data-level="31" data-path="spatially-continuous-data-i.html"><a href="spatially-continuous-data-i.html"><i class="fa fa-check"></i><b>31</b> Spatially Continuous Data I</a>
<ul>
<li class="chapter" data-level="31.1" data-path="spatially-continuous-data-i.html"><a href="spatially-continuous-data-i.html#learning-objectives-30"><i class="fa fa-check"></i><b>31.1</b> Learning objectives</a></li>
<li class="chapter" data-level="31.2" data-path="spatially-continuous-data-i.html"><a href="spatially-continuous-data-i.html#suggested-readings-14"><i class="fa fa-check"></i><b>31.2</b> Suggested readings</a></li>
<li class="chapter" data-level="31.3" data-path="spatially-continuous-data-i.html"><a href="spatially-continuous-data-i.html#preliminaries-28"><i class="fa fa-check"></i><b>31.3</b> Preliminaries</a></li>
<li class="chapter" data-level="31.4" data-path="spatially-continuous-data-i.html"><a href="spatially-continuous-data-i.html#spatially-continuous-field-data"><i class="fa fa-check"></i><b>31.4</b> Spatially continuous (field) data</a></li>
<li class="chapter" data-level="31.5" data-path="spatially-continuous-data-i.html"><a href="spatially-continuous-data-i.html#exploratory-visualization"><i class="fa fa-check"></i><b>31.5</b> Exploratory visualization</a></li>
<li class="chapter" data-level="31.6" data-path="spatially-continuous-data-i.html"><a href="spatially-continuous-data-i.html#tile-based-methods"><i class="fa fa-check"></i><b>31.6</b> Tile-based methods</a></li>
<li class="chapter" data-level="31.7" data-path="spatially-continuous-data-i.html"><a href="spatially-continuous-data-i.html#inverse-distance-weighting-idw"><i class="fa fa-check"></i><b>31.7</b> Inverse distance weighting (IDW)</a></li>
<li class="chapter" data-level="31.8" data-path="spatially-continuous-data-i.html"><a href="spatially-continuous-data-i.html#k-point-means"><i class="fa fa-check"></i><b>31.8</b> <span class="math inline">\(k\)</span>-point means</a></li>
</ul></li>
<li class="chapter" data-level="32" data-path="activity-15-spatially-continuous-data-i.html"><a href="activity-15-spatially-continuous-data-i.html"><i class="fa fa-check"></i><b>32</b> Activity 15: Spatially Continuous Data I</a>
<ul>
<li class="chapter" data-level="32.1" data-path="activity-15-spatially-continuous-data-i.html"><a href="activity-15-spatially-continuous-data-i.html#practice-questions-12"><i class="fa fa-check"></i><b>32.1</b> Practice questions</a></li>
<li class="chapter" data-level="32.2" data-path="activity-15-spatially-continuous-data-i.html"><a href="activity-15-spatially-continuous-data-i.html#learning-objectives-31"><i class="fa fa-check"></i><b>32.2</b> Learning objectives</a></li>
<li class="chapter" data-level="32.3" data-path="activity-15-spatially-continuous-data-i.html"><a href="activity-15-spatially-continuous-data-i.html#suggested-reading-13"><i class="fa fa-check"></i><b>32.3</b> Suggested reading</a></li>
<li class="chapter" data-level="32.4" data-path="activity-15-spatially-continuous-data-i.html"><a href="activity-15-spatially-continuous-data-i.html#preliminaries-29"><i class="fa fa-check"></i><b>32.4</b> Preliminaries</a></li>
<li class="chapter" data-level="32.5" data-path="activity-15-spatially-continuous-data-i.html"><a href="activity-15-spatially-continuous-data-i.html#activity-14"><i class="fa fa-check"></i><b>32.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="33" data-path="spatially-continuous-data-ii.html"><a href="spatially-continuous-data-ii.html"><i class="fa fa-check"></i><b>33</b> Spatially Continuous Data II</a>
<ul>
<li class="chapter" data-level="33.1" data-path="spatially-continuous-data-ii.html"><a href="spatially-continuous-data-ii.html#learning-objectives-32"><i class="fa fa-check"></i><b>33.1</b> Learning objectives</a></li>
<li class="chapter" data-level="33.2" data-path="spatially-continuous-data-ii.html"><a href="spatially-continuous-data-ii.html#suggested-readings-15"><i class="fa fa-check"></i><b>33.2</b> Suggested readings</a></li>
<li class="chapter" data-level="33.3" data-path="spatially-continuous-data-ii.html"><a href="spatially-continuous-data-ii.html#preliminaries-30"><i class="fa fa-check"></i><b>33.3</b> Preliminaries</a></li>
<li class="chapter" data-level="33.4" data-path="spatially-continuous-data-ii.html"><a href="spatially-continuous-data-ii.html#uncertainty-in-the-predictions"><i class="fa fa-check"></i><b>33.4</b> Uncertainty in the predictions</a></li>
<li class="chapter" data-level="33.5" data-path="spatially-continuous-data-ii.html"><a href="spatially-continuous-data-ii.html#trend-surface-analysis-1"><i class="fa fa-check"></i><b>33.5</b> Trend surface analysis</a></li>
<li class="chapter" data-level="33.6" data-path="spatially-continuous-data-ii.html"><a href="spatially-continuous-data-ii.html#accuracy-and-precision"><i class="fa fa-check"></i><b>33.6</b> Accuracy and precision</a></li>
</ul></li>
<li class="chapter" data-level="34" data-path="activity-16-spatially-continuous-data-ii.html"><a href="activity-16-spatially-continuous-data-ii.html"><i class="fa fa-check"></i><b>34</b> Activity 16: Spatially Continuous Data II</a>
<ul>
<li class="chapter" data-level="34.1" data-path="activity-16-spatially-continuous-data-ii.html"><a href="activity-16-spatially-continuous-data-ii.html#practice-questions-13"><i class="fa fa-check"></i><b>34.1</b> Practice questions</a></li>
<li class="chapter" data-level="34.2" data-path="activity-16-spatially-continuous-data-ii.html"><a href="activity-16-spatially-continuous-data-ii.html#learning-objectives-33"><i class="fa fa-check"></i><b>34.2</b> Learning objectives</a></li>
<li class="chapter" data-level="34.3" data-path="activity-16-spatially-continuous-data-ii.html"><a href="activity-16-spatially-continuous-data-ii.html#suggested-reading-14"><i class="fa fa-check"></i><b>34.3</b> Suggested reading</a></li>
<li class="chapter" data-level="34.4" data-path="activity-16-spatially-continuous-data-ii.html"><a href="activity-16-spatially-continuous-data-ii.html#preliminaries-31"><i class="fa fa-check"></i><b>34.4</b> Preliminaries</a></li>
<li class="chapter" data-level="34.5" data-path="activity-16-spatially-continuous-data-ii.html"><a href="activity-16-spatially-continuous-data-ii.html#activity-15"><i class="fa fa-check"></i><b>34.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="35" data-path="spatially-continuous-data-iii.html"><a href="spatially-continuous-data-iii.html"><i class="fa fa-check"></i><b>35</b> Spatially Continuous Data III</a>
<ul>
<li class="chapter" data-level="35.1" data-path="spatially-continuous-data-iii.html"><a href="spatially-continuous-data-iii.html#learning-objectives-34"><i class="fa fa-check"></i><b>35.1</b> Learning objectives</a></li>
<li class="chapter" data-level="35.2" data-path="spatially-continuous-data-iii.html"><a href="spatially-continuous-data-iii.html#suggested-reading-15"><i class="fa fa-check"></i><b>35.2</b> Suggested reading</a></li>
<li class="chapter" data-level="35.3" data-path="spatially-continuous-data-iii.html"><a href="spatially-continuous-data-iii.html#preliminaries-32"><i class="fa fa-check"></i><b>35.3</b> Preliminaries</a></li>
<li class="chapter" data-level="35.4" data-path="spatially-continuous-data-iii.html"><a href="spatially-continuous-data-iii.html#residual-spatial-pattern"><i class="fa fa-check"></i><b>35.4</b> Residual spatial pattern</a></li>
<li class="chapter" data-level="35.5" data-path="spatially-continuous-data-iii.html"><a href="spatially-continuous-data-iii.html#measuring-spatial-dependence-in-spatially-continuous-data"><i class="fa fa-check"></i><b>35.5</b> Measuring spatial dependence in spatially continuous data</a></li>
<li class="chapter" data-level="35.6" data-path="spatially-continuous-data-iii.html"><a href="spatially-continuous-data-iii.html#variographic-analyisis"><i class="fa fa-check"></i><b>35.6</b> Variographic analyisis</a></li>
</ul></li>
<li class="chapter" data-level="36" data-path="activity-17-spatially-continuous-data-iii.html"><a href="activity-17-spatially-continuous-data-iii.html"><i class="fa fa-check"></i><b>36</b> Activity 17: Spatially Continuous Data III</a>
<ul>
<li class="chapter" data-level="36.1" data-path="activity-17-spatially-continuous-data-iii.html"><a href="activity-17-spatially-continuous-data-iii.html#practice-questions-14"><i class="fa fa-check"></i><b>36.1</b> Practice questions</a></li>
<li class="chapter" data-level="36.2" data-path="activity-17-spatially-continuous-data-iii.html"><a href="activity-17-spatially-continuous-data-iii.html#learning-objectives-35"><i class="fa fa-check"></i><b>36.2</b> Learning objectives</a></li>
<li class="chapter" data-level="36.3" data-path="activity-17-spatially-continuous-data-iii.html"><a href="activity-17-spatially-continuous-data-iii.html#suggested-reading-16"><i class="fa fa-check"></i><b>36.3</b> Suggested reading</a></li>
<li class="chapter" data-level="36.4" data-path="activity-17-spatially-continuous-data-iii.html"><a href="activity-17-spatially-continuous-data-iii.html#preliminaries-33"><i class="fa fa-check"></i><b>36.4</b> Preliminaries</a></li>
<li class="chapter" data-level="36.5" data-path="activity-17-spatially-continuous-data-iii.html"><a href="activity-17-spatially-continuous-data-iii.html#activity-16"><i class="fa fa-check"></i><b>36.5</b> Activity</a></li>
</ul></li>
<li class="chapter" data-level="37" data-path="spatially-continuous-data-iv.html"><a href="spatially-continuous-data-iv.html"><i class="fa fa-check"></i><b>37</b> Spatially Continuous Data IV</a>
<ul>
<li class="chapter" data-level="37.1" data-path="spatially-continuous-data-iv.html"><a href="spatially-continuous-data-iv.html#learning-objectives-36"><i class="fa fa-check"></i><b>37.1</b> Learning objectives</a></li>
<li class="chapter" data-level="37.2" data-path="spatially-continuous-data-iv.html"><a href="spatially-continuous-data-iv.html#suggested-reading-17"><i class="fa fa-check"></i><b>37.2</b> Suggested reading</a></li>
<li class="chapter" data-level="37.3" data-path="spatially-continuous-data-iv.html"><a href="spatially-continuous-data-iv.html#preliminaries-34"><i class="fa fa-check"></i><b>37.3</b> Preliminaries</a></li>
<li class="chapter" data-level="37.4" data-path="spatially-continuous-data-iv.html"><a href="spatially-continuous-data-iv.html#using-residual-spatial-pattern-to-estimate-prediction-errors"><i class="fa fa-check"></i><b>37.4</b> Using residual spatial pattern to estimate prediction errors</a></li>
<li class="chapter" data-level="37.5" data-path="spatially-continuous-data-iv.html"><a href="spatially-continuous-data-iv.html#kriging-a-method-for-optimal-prediction."><i class="fa fa-check"></i><b>37.5</b> Kriging: a method for optimal prediction.</a></li>
</ul></li>
<li class="chapter" data-level="38" data-path="activity-18-spatially-continuous-data-iv.html"><a href="activity-18-spatially-continuous-data-iv.html"><i class="fa fa-check"></i><b>38</b> Activity 18: Spatially Continuous Data IV</a>
<ul>
<li class="chapter" data-level="38.1" data-path="activity-18-spatially-continuous-data-iv.html"><a href="activity-18-spatially-continuous-data-iv.html#practice-questions-15"><i class="fa fa-check"></i><b>38.1</b> Practice questions</a></li>
<li class="chapter" data-level="38.2" data-path="activity-18-spatially-continuous-data-iv.html"><a href="activity-18-spatially-continuous-data-iv.html#learning-objectives-37"><i class="fa fa-check"></i><b>38.2</b> Learning objectives</a></li>
<li class="chapter" data-level="38.3" data-path="activity-18-spatially-continuous-data-iv.html"><a href="activity-18-spatially-continuous-data-iv.html#suggested-reading-18"><i class="fa fa-check"></i><b>38.3</b> Suggested reading</a></li>
<li class="chapter" data-level="38.4" data-path="activity-18-spatially-continuous-data-iv.html"><a href="activity-18-spatially-continuous-data-iv.html#preliminaries-35"><i class="fa fa-check"></i><b>38.4</b> Preliminaries</a></li>
<li class="chapter" data-level="38.5" data-path="activity-18-spatially-continuous-data-iv.html"><a href="activity-18-spatially-continuous-data-iv.html#activity-17"><i class="fa fa-check"></i><b>38.5</b> Activity</a></li>
</ul></li>
<li class="divider"></li>
<li><a href="https://github.com/paezha/spatial-analysis-R" target="blank">Published with bookdown</a></li>
</ul>
</nav>
</div>
<div class="book-body">
<div class="body-inner">
<div class="book-header" role="navigation">
<h1>
<i class="fa fa-circle-o-notch fa-spin"></i><a href="./">An Introduction to Spatial Data Analysis and Statistics: A Course in <code>R</code></a>
</h1>
</div>
<div class="page-wrapper" tabindex="-1" role="main">
<div class="page-inner">
<section class="normal" id="section-">
<div id="activity-4-point-pattern-analysis-i" class="section level1" number="10">
<h1><span class="header-section-number">Chapter 10</span> Activity 4: Point Pattern Analysis I</h1>
<p>Remember, you can download the source file for this activity from <a href="https://github.com/paezha/Spatial-Statistics-Course">here</a>.</p>
<div id="practice-questions-1" class="section level2" number="10.1">
<h2><span class="header-section-number">10.1</span> Practice questions</h2>
<p>Answer the following questions:</p>
<ol style="list-style-type: decimal">
<li>What is a random process?</li>
<li>What is a deterministic process?</li>
<li>What is a stochastic process?</li>
<li>What is a pattern?</li>
<li>What is the usefulness of a null landscape?</li>
</ol>
</div>
<div id="learning-objectives-9" class="section level2" number="10.2">
<h2><span class="header-section-number">10.2</span> Learning objectives</h2>
<p>In this activity, you will:</p>
<ol style="list-style-type: decimal">
<li>Use the concept of quadrats to analyze a real dataset.</li>
<li>Learn about a quadrat-based test for randomness in point patterns.</li>
<li>Learn how to use the p-value of a statistical test to make a decision.</li>
<li>Think about the distribution of events in a null landscape.</li>
<li>Think about ways to decide whether a landscape is random.</li>
</ol>
</div>
<div id="suggested-reading-2" class="section level2" number="10.3">
<h2><span class="header-section-number">10.3</span> Suggested reading</h2>
<p>O’Sullivan D and Unwin D (2010) Geographic Information Analysis, 2nd Edition, Chapter 5. John Wiley & Sons: New Jersey.</p>
</div>
<div id="preliminaries-7" class="section level2" number="10.4">
<h2><span class="header-section-number">10.4</span> Preliminaries</h2>
<p>For this activity you will need the following:</p>
<ul>
<li><p>An R markdown notebook version of this document (the source file).</p></li>
<li><p>A package called <code>geog4ga3</code>.</p></li>
</ul>
<p>It is good practice to clear the working space to make sure that you do not have extraneous items there when you begin your work. The command in R to clear the workspace is <code>rm</code> (for “remove”), followed by a list of items to be removed. To clear the workspace from <em>all</em> objects, do the following:</p>
<div class="sourceCode" id="cb207"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb207-1"><a href="activity-4-point-pattern-analysis-i.html#cb207-1" aria-hidden="true" tabindex="-1"></a><span class="fu">rm</span>(<span class="at">list =</span> <span class="fu">ls</span>())</span></code></pre></div>
<p>Note that <code>ls()</code> lists all objects currently on the workspace.</p>
<p>Load the libraries you will use in this activity. In addition to <code>tidyverse</code>, you will need <code>spatstat</code>, a package designed for the analysis of point patterns (you can learn about <code>spatstat</code> <a href="https://cran.r-project.org/web/packages/spatstat/vignettes/getstart.pdf">here</a> and <a href="http://spatstat.org/resources/spatstatJSSpaper.pdf">here</a>):</p>
<div class="sourceCode" id="cb208"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb208-1"><a href="activity-4-point-pattern-analysis-i.html#cb208-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(geog4ga3)</span>
<span id="cb208-2"><a href="activity-4-point-pattern-analysis-i.html#cb208-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(maptools) <span class="co"># Needed to convert a `Spatial Polygons` object into an `owin` object</span></span>
<span id="cb208-3"><a href="activity-4-point-pattern-analysis-i.html#cb208-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(sf)</span>
<span id="cb208-4"><a href="activity-4-point-pattern-analysis-i.html#cb208-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(spatstat)</span>
<span id="cb208-5"><a href="activity-4-point-pattern-analysis-i.html#cb208-5" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidyverse)</span></code></pre></div>
<p>In the practice that preceded this activity, you learned about the concepts of intensity and density, about quadrats, and also how to create density maps.
Begin by loading the data that you will use in this activity:</p>
<div class="sourceCode" id="cb209"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb209-1"><a href="activity-4-point-pattern-analysis-i.html#cb209-1" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(<span class="st">"Fast_Food"</span>)</span>
<span id="cb209-2"><a href="activity-4-point-pattern-analysis-i.html#cb209-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(<span class="st">"Gas_Stands"</span>)</span>
<span id="cb209-3"><a href="activity-4-point-pattern-analysis-i.html#cb209-3" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(<span class="st">"Paez_Mart"</span>)</span></code></pre></div>
<p>Next the geospatial files need to be read. For this example, the city boundary of Toronto is provided in two different formats, as a dataframe (which can be used to plot using <code>ggplot2</code>) and as a <code>SpatialPolygons</code> object, a format widely used in R for spatial analysis. The :</p>
<div class="sourceCode" id="cb210"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb210-1"><a href="activity-4-point-pattern-analysis-i.html#cb210-1" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(<span class="st">"Toronto"</span>)</span></code></pre></div>
<p>If you inspect your workspace, you will see that the following dataframes are there:</p>
<ul>
<li><code>Fast_Food</code></li>
<li><code>Gas_Stands</code></li>
<li><code>Paez_Mart</code></li>
</ul>
<p>These are locations of a selection of fast food restaurants, and also of gas stands in Toronto (data are from 2008). Paez Mart on the other hand is a project to cover Toronto with convenience stores. The points are the planned locations of the stores.</p>
<p>Also, there should be an object of class <code>sf</code>. This dataframe contains the city boundary of Toronto:</p>
<div class="sourceCode" id="cb211"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb211-1"><a href="activity-4-point-pattern-analysis-i.html#cb211-1" aria-hidden="true" tabindex="-1"></a><span class="fu">class</span>(Toronto)</span></code></pre></div>
<pre><code>## [1] "sf" "data.frame"</code></pre>
<p>Try plotting the following:</p>
<div class="sourceCode" id="cb213"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb213-1"><a href="activity-4-point-pattern-analysis-i.html#cb213-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>() <span class="sc">+</span></span>
<span id="cb213-2"><a href="activity-4-point-pattern-analysis-i.html#cb213-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_sf</span>(<span class="at">data =</span> Toronto, <span class="at">color =</span> <span class="st">"black"</span>, <span class="at">fill =</span> <span class="cn">NA</span>, <span class="at">alpha =</span> <span class="dv">1</span>, <span class="at">size =</span> .<span class="dv">3</span>) <span class="sc">+</span></span>
<span id="cb213-3"><a href="activity-4-point-pattern-analysis-i.html#cb213-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_sf</span>(<span class="at">data =</span> Paez_Mart) <span class="sc">+</span></span>
<span id="cb213-4"><a href="activity-4-point-pattern-analysis-i.html#cb213-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">coord_sf</span>()</span></code></pre></div>
<p><img src="spatial-analysis-R_files/figure-html/unnamed-chunk-146-1.png" width="672" /></p>
<p>As discussed in the preceding chapter, the package <code>spatstat</code> offers a very rich collection of tools to do point pattern analysis. To convert the three sets of events (i.e., the fast food establishments, gas stands, and Paez Mart) into <code>ppp</code> objects we first must define a region or <em>window</em>. To do this we take the <code>sf</code> and convert to an <code>owin</code> (a window object) for use with the package <code>spatstat</code> (this is done via <code>SpatialPolygons</code>, hence <code>as(x, "Spatial")</code>:</p>
<div class="sourceCode" id="cb214"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb214-1"><a href="activity-4-point-pattern-analysis-i.html#cb214-1" aria-hidden="true" tabindex="-1"></a><span class="co"># `as.owin()` will take a "foreign" object (foreign to `spatstat`) and convert it into an `owin` object. Here, there are two steps involved: first, we take the `sf` object with the boundaries of Toronto and convert it into a "Spatial" object, and then the "Spatial" object is passed on to `as.owin()`</span></span>
<span id="cb214-2"><a href="activity-4-point-pattern-analysis-i.html#cb214-2" aria-hidden="true" tabindex="-1"></a>Toronto.owin <span class="ot"><-</span> <span class="fu">as</span>(Toronto, <span class="st">"Spatial"</span>) <span class="sc">%>%</span> <span class="fu">as.owin</span>() <span class="co"># Requires `maptools` package</span></span></code></pre></div>
<p>And, then convert the dataframes to <code>ppp</code> objects (this necessitates that we extract the coordinates of the events by means of <code>st_coordinates</code>):</p>
<div class="sourceCode" id="cb215"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb215-1"><a href="activity-4-point-pattern-analysis-i.html#cb215-1" aria-hidden="true" tabindex="-1"></a>Fast_Food.ppp <span class="ot"><-</span> <span class="fu">as.ppp</span>(<span class="fu">st_coordinates</span>(Fast_Food), <span class="at">W =</span> Toronto.owin)</span>
<span id="cb215-2"><a href="activity-4-point-pattern-analysis-i.html#cb215-2" aria-hidden="true" tabindex="-1"></a>Gas_Stands.ppp <span class="ot"><-</span> <span class="fu">as.ppp</span>(<span class="fu">st_coordinates</span>(Gas_Stands), <span class="at">W =</span> Toronto.owin)</span>
<span id="cb215-3"><a href="activity-4-point-pattern-analysis-i.html#cb215-3" aria-hidden="true" tabindex="-1"></a>Paez_Mart.ppp <span class="ot"><-</span> <span class="fu">as.ppp</span>(<span class="fu">st_coordinates</span>(Paez_Mart), <span class="at">W =</span> Toronto.owin)</span></code></pre></div>
<p>These objects can now be used with the functions of the <code>spatstat</code> package. For instance, you can calculate the counts of events by quadrat by means of <code>quadrat.count</code>. The input must be a <code>ppp</code> object, and the number of quadrats on the horizontal (nx) and vertical (ny) direction (notice how I use the function <code>table</code> to present the frequency of quadrats with number of events):</p>
<div class="sourceCode" id="cb216"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb216-1"><a href="activity-4-point-pattern-analysis-i.html#cb216-1" aria-hidden="true" tabindex="-1"></a>q_count <span class="ot"><-</span> <span class="fu">quadratcount</span>(Fast_Food.ppp, <span class="at">nx =</span> <span class="dv">3</span>, <span class="at">ny =</span> <span class="dv">3</span>)</span>
<span id="cb216-2"><a href="activity-4-point-pattern-analysis-i.html#cb216-2" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(q_count)</span></code></pre></div>
<pre><code>## q_count
## 0 6 44 48 60 64 85 144 163
## 1 1 1 1 1 1 1 1 1</code></pre>
<p>As you see from the table, there is one quadrat with zero events, one quadrat with six events, one quadrat with forty-four events, and so on.</p>
<p>You can also plot the results of the <code>quadratcount()</code> function!</p>
<div class="sourceCode" id="cb218"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb218-1"><a href="activity-4-point-pattern-analysis-i.html#cb218-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(q_count)</span></code></pre></div>
<p><img src="spatial-analysis-R_files/figure-html/unnamed-chunk-150-1.png" width="672" /></p>
<p>A useful function in the <code>spatstat</code> package is <code>quadrat.test</code>. This function implements a statistical test that compares the empirical distribution of events by quadrats to the distribution of events as expected under the hypothesis that the underlying process is <em>random</em>.</p>
<p>This is implemented as follows:</p>
<div class="sourceCode" id="cb219"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb219-1"><a href="activity-4-point-pattern-analysis-i.html#cb219-1" aria-hidden="true" tabindex="-1"></a>q_test <span class="ot"><-</span> <span class="fu">quadrat.test</span>(Fast_Food.ppp, <span class="at">nx =</span> <span class="dv">3</span>, <span class="at">ny =</span> <span class="dv">3</span>)</span></code></pre></div>
<pre><code>## Warning: Some expected counts are small; chi^2 approximation may be inaccurate</code></pre>
<div class="sourceCode" id="cb221"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb221-1"><a href="activity-4-point-pattern-analysis-i.html#cb221-1" aria-hidden="true" tabindex="-1"></a>q_test</span></code></pre></div>
<pre><code>##
## Chi-squared test of CSR using quadrat counts
##
## data: Fast_Food.ppp
## X2 = 213.74, df = 8, p-value < 2.2e-16
## alternative hypothesis: two.sided
##
## Quadrats: 9 tiles (irregular windows)</code></pre>
<p>The quadrat test reports a <span class="math inline">\(p\)</span>-value which can be used to make a decision. The <span class="math inline">\(p\)</span>-value is the probability that you will be mistaken if you reject the null hypothesis. To make a decision, you need to know what is the null hypothesis, and your own tolerance for making a mistake. In the case above, the <span class="math inline">\(p\)</span>-value is very, very small (2.2e-16 = 0.00000000000000022). Since the null hypothesis is spatial randomness, you can reject this hypothesis and the probability that this decision is mistaken is vanishingly small.</p>
<p>Try plotting the results of <code>quadrat.test</code>:</p>
<div class="sourceCode" id="cb223"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb223-1"><a href="activity-4-point-pattern-analysis-i.html#cb223-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(q_test)</span></code></pre></div>
<p><img src="spatial-analysis-R_files/figure-html/unnamed-chunk-152-1.png" width="672" /></p>
<p>Now that you have seen how to do some analysis using quadrats, you are ready for the next activity.</p>
</div>
<div id="activity-3" class="section level2" number="10.5">
<h2><span class="header-section-number">10.5</span> Activity</h2>
<p><strong>NOTE</strong>: Activities include technical “how to” tasks/questions. Usually, these ask you to organize data, create a plot, and so on in support of analysis and interpretation. These tasks are indicated by a star (*).</p>
<ol style="list-style-type: decimal">
<li><p>(*)Use <code>Fast_Food</code>, <code>Gas_Stands</code>, <code>Paez_Mart</code>, and <code>Toronto</code> to create density maps for the three point patterns. Select a quadrat size that you think is appropriate.</p></li>
<li><p>(*)Use <code>Fast_Food.ppp</code>, <code>Gas_Stands</code>, and <code>Paez_Mart</code>, and the function <code>quadratcount</code> to calculate the number of events per quadrat. Remember that you need to select the number of quadrats in the horizontal and vertical directions!</p></li>
<li><p>(*)Use the function <code>table()</code> to examine the frequency of events per quadrat for each of the point patterns.</p></li>
<li><p>Show your density maps to a fellow student. Did they select the same quadrat size? If not, what was their rationale for their size?</p></li>
<li><p>Again, use the function <code>table()</code> to examine the frequency of events per quadrat for each of the point patterns. What are the differences among these point patterns? What would you expect the frequency of events per quadrat to be in a null landscape?</p></li>
<li><p>Use <code>Fast_Food.ppp</code>, <code>Gas_Stands</code>, and <code>Paez_Mart</code>, and the function <code>quadrat.test</code> to calculate the test of spatial independence for these point patterns. What is your decision in each case? Explain.</p></li>
</ol>
</div>
</div>
</section>
</div>
</div>
</div>
<a href="point-pattern-analysis-i.html" class="navigation navigation-prev " aria-label="Previous page"><i class="fa fa-angle-left"></i></a>
<a href="point-pattern-analysis-ii.html" class="navigation navigation-next " aria-label="Next page"><i class="fa fa-angle-right"></i></a>
</div>
</div>
<script src="libs/gitbook-2.6.7/js/app.min.js"></script>
<script src="libs/gitbook-2.6.7/js/clipboard.min.js"></script>
<script src="libs/gitbook-2.6.7/js/plugin-search.js"></script>
<script src="libs/gitbook-2.6.7/js/plugin-sharing.js"></script>
<script src="libs/gitbook-2.6.7/js/plugin-fontsettings.js"></script>
<script src="libs/gitbook-2.6.7/js/plugin-bookdown.js"></script>
<script src="libs/gitbook-2.6.7/js/jquery.highlight.js"></script>
<script src="libs/gitbook-2.6.7/js/plugin-clipboard.js"></script>
<script>
gitbook.require(["gitbook"], function(gitbook) {
gitbook.start({
"sharing": {
"github": false,
"facebook": true,
"twitter": true,
"linkedin": false,
"weibo": false,
"instapaper": false,
"vk": false,
"whatsapp": false,
"all": ["facebook", "twitter", "linkedin", "weibo", "instapaper"]
},
"fontsettings": {
"theme": "white",
"family": "sans",
"size": 2
},
"edit": {
"link": "https://github.com/paezha/spatial-analysis-R/edit/main/10-Activity-Point-Pattern-Analysis-I.Rmd",
"text": "Edit"
},
"history": {
"link": null,
"text": null
},
"view": {
"link": null,
"text": null
},
"download": ["spatial-analysis-R.pdf", "spatial-analysis-R.epub"],
"search": {
"engine": "fuse",
"options": null
},
"toc": {
"collapse": "subsection"
}
});
});
</script>
<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
(function () {
var script = document.createElement("script");
script.type = "text/javascript";
var src = "true";
if (src === "" || src === "true") src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-MML-AM_CHTML";
if (location.protocol !== "file:")
if (/^https?:/.test(src))
src = src.replace(/^https?:/, '');
script.src = src;
document.getElementsByTagName("head")[0].appendChild(script);
})();
</script>
</body>
</html>
此处可能存在不合适展示的内容，页面不予展示。您可通过相关编辑功能自查并修改。
如您确认内容无涉及 不当用语 / 纯广告导流 / 暴力 / 低俗色情 / 侵权 / 盗版 / 虚假 / 无价值内容或违法国家有关法律法规的内容，可点击提交进行申诉，我们将尽快为您处理。
马建仓 AI 助手