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      <h1>Using maxcovr</h1>
                        <h4 class="author">Nicholas Tierney</h4>
            
            <h4 class="date">2019-06-13</h4>
      
      <small class="dont-index">Source: <a href="https://github.com/njtierney/maxcovr/blob/master/vignettes/intro_to_maxcovr.Rmd"><code>vignettes/intro_to_maxcovr.Rmd</code></a></small>
      <div class="hidden name"><code>intro_to_maxcovr.Rmd</code></div>

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<p>maxcovr provides tools to make it easy to solve the “maximum covering location problem”, a binary optimisation problem described by <a href="http://www.geog.ucsb.edu/~forest/G294download/MAX_COVER_RLC_CSR.pdf">Church</a>.</p>
<p><code>maxcovr</code> aims to provide researchers and analysts with an easy to user, fast, accurate and (eventually) extensible implementation of Church’s maximal covering location problem, while adhering as best as it can to <a href="http://www.tidyverse.org"><code>tidyverse</code></a> principles.</p>
<p>This vignette aims to get users started with using maxcovr. In this vignette you will learn about:</p>
<ul>
<li>The motivation behind <code>maxcovr</code>
</li>
<li>How to assess current coverage of facilities</li>
<li>How to maximise coverage using some new proposed facilities</li>
<li>Explore results of the new locations</li>
<li>How to explore the new locations proposed</li>
</ul>
<p>Other vignettes provided in the package include:</p>
<ul>
<li>“Cross Validation with maxcovr”, which explains how to perform and interpret cross validation results in a maximum covering location framework</li>
<li>“Performing the maximal coverage relocation problem”</li>
</ul>
<div id="the-moviation-why-maxcovr" class="section level1">
<h1 class="hasAnchor">
<a href="#the-moviation-why-maxcovr" class="anchor"></a>The moviation: Why <code>maxcovr</code>
</h1>
<p><code>maxcovr</code> was created to make it easy for a non expert to correctly solve the maximum covering location problem. This problem is beginning to be applied in problems in <a href="">AED placement</a>, but has been applied in <a href="">many different areas</a>. Many implementations in papers apply commercial software such as AMPL, Gurobi, or CPLEX. Additionally, the code that they use in the paper to implement the optimisation is not provided, and has to be requested. As a result, these analyses are more difficult to implement, and more difficult to reproduce.</p>
<p><code>maxcovr</code> was created to address these shortcomings, using:</p>
<ul>
<li>R, a free and open source language</li>
<li>Open source solvers, lpSolve, and glpk, that can be used on Linux, Windows, and OSX.</li>
<li>Real-world, open source example data.</li>
<li>Tidyverse principles to design it for humans make it easy to use, code, and extend.</li>
</ul>
<p>This means results are easy to implement, reproduce, and extend.</p>
</div>
<div id="the-problem" class="section level1">
<h1 class="hasAnchor">
<a href="#the-problem" class="anchor"></a>The problem</h1>
<p>Consider the toy example where we want to place crime surveillance towers to detect crime. We have two datasets, <code>york</code>, and <code>york_crime</code>:</p>
<ul>
<li>
<code>york</code> contains listed building GPS locations in the city of York, provided by the city of york</li>
<li>
<code>york_crime</code> contains a set of crime data from the <a href="https://www.github.com/njtierney/ukpolice"><code>ukpolice</code> package</a>, containing crime data from September 2016.</li>
</ul>
<p>We already have a few surveillance towers built, which are placed on top of the listed buildings with a grade of I. We will call this dataset <code>york_existing</code>, and the remaining building locations <code>york_proposed</code>. Here, <code>york_existing</code> is the currently locations of facilities, and <code>york_proposed</code> is the potential facility locations.</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/library">library</a></span>(maxcovr)</a>
<a class="sourceLine" id="cb1-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/library">library</a></span>(dplyr)</a></code></pre></div>
<pre><code>## 
## Attaching package: 'dplyr'</code></pre>
<pre><code>## The following objects are masked from 'package:stats':
## 
##     filter, lag</code></pre>
<pre><code>## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union</code></pre>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" title="1"><span class="co"># subset to be the places with towers built on them.</span></a>
<a class="sourceLine" id="cb5-2" title="2">york_existing &lt;-<span class="st"> </span>york <span class="op">%&gt;%</span><span class="st"> </span><span class="kw"><a href="https://dplyr.tidyverse.org/reference/filter.html">filter</a></span>(grade <span class="op">==</span><span class="st"> "I"</span>)</a>
<a class="sourceLine" id="cb5-3" title="3"></a>
<a class="sourceLine" id="cb5-4" title="4">york_proposed &lt;-<span class="st"> </span>york <span class="op">%&gt;%</span><span class="st"> </span><span class="kw"><a href="https://dplyr.tidyverse.org/reference/filter.html">filter</a></span>(grade <span class="op">!=</span><span class="st"> "I"</span>)</a></code></pre></div>
<p>We are interested in placing surveillance towers so that they are within 100m of the largest number of crimes. We are going to use the crime data that we have to help us choose ideal locations to place towers.</p>
<p>This can be illustrated with the following graphic, where the red circles indicate the current coverage of the building locations, so those blue crimes within the circles are within the coverage.</p>
<pre><code>## Assuming "long" and "lat" are longitude and latitude, respectively
## Assuming "long" and "lat" are longitude and latitude, respectively</code></pre>
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the coverage looks OK, but to get a better estimate, we can verify the coverage using the <code><a href="../reference/nearest.html">nearest()</a></code> function.</p>
<p><code><a href="../reference/nearest.html">nearest()</a></code> takes two dataframes and returns the nearest lat/long coords from the first dataframe to the second dataframe, along with the distances between them and the appropriate columns from the building dataframe. You can think of reading this as “What is the nearest (nearest_df) to (to_df)”.</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" title="1">dat_dist &lt;-<span class="st"> </span><span class="kw"><a href="../reference/nearest.html">nearest</a></span>(<span class="dt">nearest_df =</span> york_proposed, </a>
<a class="sourceLine" id="cb7-2" title="2">                    <span class="dt">to_df =</span> york_crime)</a>
<a class="sourceLine" id="cb7-3" title="3"></a>
<a class="sourceLine" id="cb7-4" title="4"><span class="kw"><a href="https://www.rdocumentation.org/packages/utils/topics/head">head</a></span>(dat_dist)</a></code></pre></div>
<pre><code>## # A tibble: 6 x 22
##   to_id nearest_id distance category persistent_id date  lat_to long_to
##   &lt;dbl&gt;      &lt;dbl&gt;    &lt;dbl&gt; &lt;chr&gt;    &lt;chr&gt;         &lt;chr&gt;  &lt;dbl&gt;   &lt;dbl&gt;
## 1     1       1787   18.2   anti-so… 62299914865f… 2016…   54.0   -1.08
## 2     2        794  512.    anti-so… 4e34f53d247f… 2016…   54.0   -1.12
## 3     3        350    0.993 anti-so… 2a0062f3dfac… 2016…   54.0   -1.08
## 4     4        327   20.5   anti-so… eb53e09ae46a… 2016…   54.0   -1.09
## 5     5       1860  135.    anti-so… 6139f131b724… 2016…   54.0   -1.08
## 6     6        404   22.8   anti-so… d8de26d5af47… 2016…   54.0   -1.08
## # … with 14 more variables: street_id &lt;chr&gt;, street_name &lt;chr&gt;,
## #   context &lt;chr&gt;, id &lt;chr&gt;, location_type &lt;chr&gt;, location_subtype &lt;chr&gt;,
## #   outcome_status &lt;chr&gt;, long_nearest &lt;dbl&gt;, lat_nearest &lt;dbl&gt;,
## #   object_id &lt;int&gt;, desig_id &lt;chr&gt;, pref_ref &lt;int&gt;, name &lt;chr&gt;,
## #   grade &lt;chr&gt;</code></pre>
<blockquote>
<p>Note that <code>maxcovr</code> records the positions of locations must be named “lat” and “long” for latitude and longitude, respectively.</p>
</blockquote>
<p>The dataframe <code>dat_dist</code> contains the nearest proposed facility to each crime. This means that we have a dataframe that contains “to_id” - the ID number (labelled from 1 to the number of rows in the to dataset), “nearest_id” describes the row numer of “nearest_df” that corresponds to the row location of that data.frame. We also have the rest of the columns of <code>york_crime</code>. These are returned to make it easy to do other data manipulation / exploration tasks, if you wish.</p>
<p>You can instead return a dataframe which has every building in the rows, and the nearest crime to the building, by simply changing the order.</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" title="1">dat_dist_bldg &lt;-<span class="st"> </span><span class="kw"><a href="../reference/nearest.html">nearest</a></span>(york_crime,york_existing)</a>
<a class="sourceLine" id="cb9-2" title="2"></a>
<a class="sourceLine" id="cb9-3" title="3"><span class="kw"><a href="https://www.rdocumentation.org/packages/utils/topics/head">head</a></span>(dat_dist_bldg)</a></code></pre></div>
<pre><code>## # A tibble: 6 x 22
##   to_id nearest_id distance long_to lat_to object_id desig_id pref_ref
##   &lt;dbl&gt;      &lt;dbl&gt;    &lt;dbl&gt;   &lt;dbl&gt;  &lt;dbl&gt;     &lt;int&gt; &lt;chr&gt;       &lt;int&gt;
## 1     1         33     36.0   -1.09   54.0      6144 DYO1195    463280
## 2     2        183     35.8   -1.09   54.0      6142 DYO1373    462942
## 3     3        503     95.3   -1.08   54.0      3463 DYO365     464845
## 4     4        273     44.3   -1.08   54.0      3461 DYO583     464427
## 5     5        908     26.5   -1.08   54.0      3460 DYO916     463764
## 6     6        495    326.    -1.13   54.0      3450 DYO1525    328614
## # … with 14 more variables: name &lt;chr&gt;, grade &lt;chr&gt;, category &lt;chr&gt;,
## #   persistent_id &lt;chr&gt;, date &lt;chr&gt;, lat_nearest &lt;dbl&gt;,
## #   long_nearest &lt;dbl&gt;, street_id &lt;chr&gt;, street_name &lt;chr&gt;, context &lt;chr&gt;,
## #   id &lt;chr&gt;, location_type &lt;chr&gt;, location_subtype &lt;chr&gt;,
## #   outcome_status &lt;chr&gt;</code></pre>
<p>To evaluate the coverage we use <code>coverage</code>, specifying the distance cutoff in <code>distance_cutoff</code> to be 100m.</p>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb11-1" title="1"><span class="kw"><a href="../reference/coverage.html">coverage</a></span>(york_proposed, </a>
<a class="sourceLine" id="cb11-2" title="2">         york_crime,</a>
<a class="sourceLine" id="cb11-3" title="3">         <span class="dt">distance_cutoff =</span> <span class="dv">100</span>)</a></code></pre></div>
<pre><code>## # A tibble: 1 x 7
##   distance_within n_cov n_not_cov prop_cov prop_not_cov dist_avg dist_sd
##             &lt;dbl&gt; &lt;int&gt;     &lt;int&gt;    &lt;dbl&gt;        &lt;dbl&gt;    &lt;dbl&gt;   &lt;dbl&gt;
## 1             100   685      1129    0.378        0.622     355.    422.</code></pre>
<p>This contains useful summary information:</p>
<ul>
<li>distance_within - this is the distance used to determine coverae</li>
<li>n_cov - this is the number of events that are covered</li>
<li>n_not_cov - the number of events not covered</li>
<li>pct_cov - the proportion of events covered</li>
<li>pct_not_cov - the proportion of events not covered</li>
<li>dist_avg - the average distance from the rows to the nearest facility or user</li>
<li>dist_avg - the standard deviation of the distance from the rows to the nearest facility or user.</li>
</ul>
<p>This tells us that out of all the crime, 37.76% of it is within 100m, 339 crimes are covered, but the mean distance to the surveillance camera is 1400m.</p>
</div>
<div id="using-max_coverage" class="section level1">
<h1 class="hasAnchor">
<a href="#using-max_coverage" class="anchor"></a>using max_coverage</h1>
<p>Knowing this information, you might be interested in improving this coverage. To do so we can use the <code>max_coverage</code> function.</p>
<p>This function takes 5 arguments:</p>
<ul>
<li>existing_facility = the facilities currently installed</li>
<li>proposed_facility = the facilities proposed to install</li>
<li>user = the users that you want to maximise coverage over</li>
<li>n_added = the number of new facilities that you can install</li>
<li>distance_cutoff = the distance that we consider coverage to be within.</li>
</ul>
<p>Similar to using <code>nearest</code> - the data frames for existing_facility, proposed_facility, and user need to contain columns of latitude and longitude, and they must be named “lat”, and “long”, respectively. These are used to calculate the distance.</p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1"><span class="co"># mc_20 &lt;- max_coverage(A = dat_dist_indic,</span></a>
<a class="sourceLine" id="cb13-2" title="2">mc_<span class="dv">20</span> &lt;-<span class="st"> </span><span class="kw"><a href="../reference/max_coverage.html">max_coverage</a></span>(<span class="dt">existing_facility =</span> york_existing,</a>
<a class="sourceLine" id="cb13-3" title="3">                      <span class="dt">proposed_facility =</span> york_proposed,</a>
<a class="sourceLine" id="cb13-4" title="4">                      <span class="dt">user =</span> york_crime,</a>
<a class="sourceLine" id="cb13-5" title="5">                      <span class="dt">n_added =</span> <span class="dv">20</span>,</a>
<a class="sourceLine" id="cb13-6" title="6">                      <span class="dt">distance_cutoff =</span> <span class="dv">100</span>)</a></code></pre></div>
<p>We can look at a quick summary of the model with summary</p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb14-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mc_<span class="dv">20</span>)</a></code></pre></div>
<pre><code>## 
## ------------------------------------------- 
## Model Fit: maxcovr fixed location model 
## ------------------------------------------- 
## Distance Cutoff: 100m 
## Facilities: 
##     Added:       20 
## Coverage (Previous): 
##     # Users:     540    (339) 
##     Proportion:  0.2977 (0.1869) 
## Distance (m) to Facility (Previous): 
##     Avg:         886 (1400) 
##     SD:          986 (1597) 
## -------------------------------------------</code></pre>
<p>Here this tells us useful information about the distance cutoff, the number of facilities added, and the number of users covered, and previousl, and the proportion of events covered.</p>
<p>To get this information out we can use the information in each of the columns below. The information each of these is a list, which might seem strange, but it becomes very useful when you are assessing different levels of <code>n_added</code>. We will go into more detail for this soon.</p>
<p>Firstly, we have the data input into <code>n_added</code> and <code>distance_cutoff</code> - the same information that we entered.</p>
<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb16-1" title="1">mc_<span class="dv">20</span><span class="op">$</span>n_added[[<span class="dv">1</span>]]</a></code></pre></div>
<pre><code>## [1] 20</code></pre>
<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb18-1" title="1">mc_<span class="dv">20</span><span class="op">$</span>distance_cutoff[[<span class="dv">1</span>]]</a></code></pre></div>
<pre><code>## [1] 100</code></pre>
<p>We can then get summary information about the model coverage. We can first get the existing, or previous coverage with <code>existing_coverage</code></p>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb20-1" title="1">mc_<span class="dv">20</span><span class="op">$</span>existing_coverage[[<span class="dv">1</span>]]</a></code></pre></div>
<pre><code>## # A tibble: 1 x 8
##   n_added distance_within n_cov pct_cov n_not_cov pct_not_cov dist_avg
##     &lt;dbl&gt;           &lt;dbl&gt; &lt;int&gt;   &lt;dbl&gt;     &lt;int&gt;       &lt;dbl&gt;    &lt;dbl&gt;
## 1       0             100   339   0.187      1475       0.813    1400.
## # … with 1 more variable: dist_sd &lt;dbl&gt;</code></pre>
<p>This provides us with the information that we saw previously with <code>summarise_coverage</code>.</p>
<p>We can then get the information of the coverage from the model with the added additional AEDs with <code>model_coverage</code>.</p>
<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb22-1" title="1">mc_<span class="dv">20</span><span class="op">$</span>model_coverage[[<span class="dv">1</span>]]</a></code></pre></div>
<pre><code>## # A tibble: 1 x 8
##   n_added distance_within n_cov pct_cov n_not_cov pct_not_cov dist_avg
##     &lt;dbl&gt;           &lt;dbl&gt; &lt;int&gt;   &lt;dbl&gt;     &lt;int&gt;       &lt;dbl&gt;    &lt;dbl&gt;
## 1      20             100   540   0.298      1274       0.702     886.
## # … with 1 more variable: dist_sd &lt;dbl&gt;</code></pre>
<p>We can then get both pieces of information from <code>summary</code></p>
<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb24-1" title="1">mc_<span class="dv">20</span><span class="op">$</span>summary[[<span class="dv">1</span>]]</a></code></pre></div>
<pre><code>## # A tibble: 2 x 8
##   n_added distance_within n_cov pct_cov n_not_cov pct_not_cov dist_avg
##     &lt;dbl&gt;           &lt;dbl&gt; &lt;int&gt;   &lt;dbl&gt;     &lt;int&gt;       &lt;dbl&gt;    &lt;dbl&gt;
## 1       0             100   339   0.187      1475       0.813    1400.
## 2      20             100   540   0.298      1274       0.702     886.
## # … with 1 more variable: dist_sd &lt;dbl&gt;</code></pre>
<p>You can drill deeper, and get more information about the facilities using <code>facility_selected</code>, which returns facilities selected from the <code>proposed_facility</code> data.</p>
<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb26-1" title="1">mc_<span class="dv">20</span><span class="op">$</span>facility_selected[[<span class="dv">1</span>]]</a></code></pre></div>
<pre><code>## # A tibble: 20 x 7
##     long   lat object_id desig_id pref_ref name                       grade
##    &lt;dbl&gt; &lt;dbl&gt;     &lt;int&gt; &lt;chr&gt;       &lt;int&gt; &lt;chr&gt;                      &lt;chr&gt;
##  1 -1.09  54.0      5978 DYO1383    462917 &lt;NA&gt;                       II   
##  2 -1.08  54.0      5909 DYO1297    463072 &lt;NA&gt;                       II   
##  3 -1.08  54.0      5872 DYO1244    463186 &lt;NA&gt;                       II   
##  4 -1.08  54.0      5847 DYO1216    463242 &lt;NA&gt;                       II   
##  5 -1.12  54.0      5759 DYO1108    463434 FORMER JUNIOR SCHOOL BUIL… II   
##  6 -1.08  54.0      5748 DYO1096    463469 &lt;NA&gt;                       II   
##  7 -1.08  54.0      5745 DYO1093    463465 &lt;NA&gt;                       II   
##  8 -1.08  54.0      5739 DYO1086    463457 CHURCH OF ST GEORGE AND A… II   
##  9 -1.10  54.0      5642 DYO960     463695 &lt;NA&gt;                       II   
## 10 -1.09  53.9      5606 DYO920     463771 PRESS STAND AT YORK RACEC… II   
## 11 -1.06  54.0      5592 DYO903     463788 &lt;NA&gt;                       II   
## 12 -1.07  54.0      5588 DYO899     463782 &lt;NA&gt;                       II   
## 13 -1.08  54.0      5529 DYO829     463938 CHURCH OF ST THOMAS        II   
## 14 -1.08  54.0      5454 DYO705     464133 NUMBERS 45-51 (ODD) AND A… II   
## 15 -1.03  54.0      5373 DYO1644        NA War Memorial               II   
## 16 -1.12  54.0      5349 DYO572     464451 POPPLETON ROAD SCHOOL      II   
## 17 -1.08  54.0      5328 DYO544     464508 WOODS MILL                 II   
## 18 -1.00  54.0      3215 DYO1581    491367 STOCKTON GRANGE AND ATTAC… II   
## 19 -1.08  54.0      3213 DYO1580    490659 NEW CHAPEL AT ST JOHN'S C… II   
## 20 -1.08  54.0      4803 DYO1734        NA The Swan Public House      II</code></pre>
<p>We can then get information about the users with <code>augmented_users</code></p>
<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb28-1" title="1">mc_<span class="dv">20</span><span class="op">$</span>augmented_users[[<span class="dv">1</span>]]</a></code></pre></div>
<pre><code>## # A tibble: 1,814 x 19
##    to_id nearest_id distance user_id category persistent_id date  lat_to
##    &lt;dbl&gt;      &lt;dbl&gt;    &lt;dbl&gt;   &lt;int&gt; &lt;chr&gt;    &lt;chr&gt;         &lt;chr&gt;  &lt;dbl&gt;
##  1     1          3     84.3       1 anti-so… 62299914865f… 2016…   54.0
##  2     2         16    512.        2 anti-so… 4e34f53d247f… 2016…   54.0
##  3     3          3     65.2       3 anti-so… 2a0062f3dfac… 2016…   54.0
##  4     4         31    286.        4 anti-so… eb53e09ae46a… 2016…   54.0
##  5     5         20    231.        5 anti-so… 6139f131b724… 2016…   54.0
##  6     6          8     22.8       6 anti-so… d8de26d5af47… 2016…   54.0
##  7     7         22   2136.        7 anti-so… 5b742b1cb918… 2016…   54.0
##  8     8         26   2329.        8 anti-so… d2112b4fd0a0… 2016…   54.0
##  9     9         49     37.4       9 anti-so… 30bf5bfa97c5… 2016…   54.0
## 10    10          5   3150.       10 anti-so… d75bbe6c18bf… 2016…   54.0
## # … with 1,804 more rows, and 11 more variables: long_to &lt;dbl&gt;,
## #   street_id &lt;chr&gt;, street_name &lt;chr&gt;, context &lt;chr&gt;, id &lt;chr&gt;,
## #   location_type &lt;chr&gt;, location_subtype &lt;chr&gt;, outcome_status &lt;chr&gt;,
## #   lat_nearest &lt;dbl&gt;, long_nearest &lt;dbl&gt;, type &lt;chr&gt;</code></pre>
<p>This returns the dataframe of users, with the distance to their nearest AED, and at the end, provides information about the <code>type</code> of AED that is used.</p>
<p>Now try and run the code for n_added = 40, and call it “mc_40”</p>
</div>
<div id="interpreting-results" class="section level1">
<h1 class="hasAnchor">
<a href="#interpreting-results" class="anchor"></a>Interpreting results</h1>
<p>We can assess what happens if we add 100 facilities.</p>
<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb30-1" title="1">mc_<span class="dv">100</span> &lt;-<span class="st"> </span><span class="kw"><a href="../reference/max_coverage.html">max_coverage</a></span>(<span class="dt">existing_facility =</span> york_existing,</a>
<a class="sourceLine" id="cb30-2" title="2">                      <span class="dt">proposed_facility =</span> york_proposed,</a>
<a class="sourceLine" id="cb30-3" title="3">                      <span class="dt">user =</span> york_crime,</a>
<a class="sourceLine" id="cb30-4" title="4">                      <span class="dt">n_added =</span> <span class="dv">100</span>,</a>
<a class="sourceLine" id="cb30-5" title="5">                      <span class="dt">distance_cutoff =</span> <span class="dv">100</span>)</a></code></pre></div>
<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb31-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mc_<span class="dv">100</span>)</a></code></pre></div>
<pre><code>## 
## ------------------------------------------- 
## Model Fit: maxcovr fixed location model 
## ------------------------------------------- 
## Distance Cutoff: 100m 
## Facilities: 
##     Added:       100 
## Coverage (Previous): 
##     # Users:     693    (339) 
##     Proportion:  0.382 (0.1869) 
## Distance (m) to Facility (Previous): 
##     Avg:         555 (1400) 
##     SD:          696 (1597) 
## -------------------------------------------</code></pre>
<p>So then, if we want to add information to discover the differences between 20 and 100, we can bind these two pieces together using <code>bind_rows</code>.</p>
<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb33-1" title="1">mc_<span class="dv">20</span>_<span class="dv">100</span> &lt;-<span class="st"> </span><span class="kw"><a href="https://dplyr.tidyverse.org/reference/bind.html">bind_rows</a></span>(mc_<span class="dv">20</span>, mc_<span class="dv">100</span>)</a></code></pre></div>
<p>We can then look at the summary row, and expand the information out here using <code><a href="https://tidyr.tidyverse.org/reference/unnest.html">tidyr::unnest()</a></code></p>
<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb34-1" title="1">mc_<span class="dv">20</span>_<span class="dv">100</span>_sum &lt;-<span class="st"> </span>mc_<span class="dv">20</span>_<span class="dv">100</span> <span class="op">%&gt;%</span><span class="st"> </span><span class="kw"><a href="https://dplyr.tidyverse.org/reference/select.html">select</a></span>(summary) <span class="op">%&gt;%</span><span class="st"> </span>tidyr<span class="op">::</span><span class="kw"><a href="https://tidyr.tidyverse.org/reference/unnest.html">unnest</a></span>()</a>
<a class="sourceLine" id="cb34-2" title="2">mc_<span class="dv">20</span>_<span class="dv">100</span>_sum</a></code></pre></div>
<pre><code>## # A tibble: 4 x 8
##   n_added distance_within n_cov pct_cov n_not_cov pct_not_cov dist_avg
##     &lt;dbl&gt;           &lt;dbl&gt; &lt;int&gt;   &lt;dbl&gt;     &lt;int&gt;       &lt;dbl&gt;    &lt;dbl&gt;
## 1       0             100   339   0.187      1475       0.813    1400.
## 2      20             100   540   0.298      1274       0.702     886.
## 3       0             100   339   0.187      1475       0.813    1400.
## 4     100             100   693   0.382      1121       0.618     555.
## # … with 1 more variable: dist_sd &lt;dbl&gt;</code></pre>
<p>This information can then be plotted, for example, like so:</p>
<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb36-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/library">library</a></span>(ggplot2)</a>
<a class="sourceLine" id="cb36-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/ggplot2/topics/ggplot">ggplot</a></span>(mc_<span class="dv">20</span>_<span class="dv">100</span>_sum,</a>
<a class="sourceLine" id="cb36-3" title="3">       <span class="kw"><a href="https://www.rdocumentation.org/packages/ggplot2/topics/aes">aes</a></span>(<span class="dt">x =</span> n_added,</a>
<a class="sourceLine" id="cb36-4" title="4">           <span class="dt">y =</span> pct_cov)) <span class="op">+</span><span class="st"> </span></a>
<a class="sourceLine" id="cb36-5" title="5"><span class="st">    </span><span class="kw"><a href="https://www.rdocumentation.org/packages/ggplot2/topics/geom_point">geom_point</a></span>() <span class="op">+</span><span class="st"> </span></a>
<a class="sourceLine" id="cb36-6" title="6"><span class="st">    </span><span class="kw"><a href="https://www.rdocumentation.org/packages/ggplot2/topics/geom_path">geom_line</a></span>()</a></code></pre></div>
<p><img src="intro_to_maxcovr_files/figure-html/unnamed-chunk-16-1.png" width="672"></p>
<p>You can then produce a plot of the average distances.</p>
<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb37-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/library">library</a></span>(ggplot2)</a>
<a class="sourceLine" id="cb37-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/ggplot2/topics/ggplot">ggplot</a></span>(mc_<span class="dv">20</span>_<span class="dv">100</span>_sum,</a>
<a class="sourceLine" id="cb37-3" title="3">       <span class="kw"><a href="https://www.rdocumentation.org/packages/ggplot2/topics/aes">aes</a></span>(<span class="dt">x =</span> n_added,</a>
<a class="sourceLine" id="cb37-4" title="4">           <span class="dt">y =</span> dist_avg)) <span class="op">+</span><span class="st"> </span></a>
<a class="sourceLine" id="cb37-5" title="5"><span class="st">    </span><span class="kw"><a href="https://www.rdocumentation.org/packages/ggplot2/topics/geom_point">geom_point</a></span>() <span class="op">+</span><span class="st"> </span></a>
<a class="sourceLine" id="cb37-6" title="6"><span class="st">    </span><span class="kw"><a href="https://www.rdocumentation.org/packages/ggplot2/topics/geom_path">geom_line</a></span>()</a></code></pre></div>
<p><img src="intro_to_maxcovr_files/figure-html/unnamed-chunk-17-1.png" width="672"></p>
<p>If you would like to calculate your own summaries on the distances, I would recommend something like:</p>
<div class="sourceCode" id="cb38"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb38-1" title="1">mc_<span class="dv">20</span><span class="op">$</span>augmented_users[[<span class="dv">1</span>]] <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb38-2" title="2"><span class="st">    </span><span class="kw"><a href="https://dplyr.tidyverse.org/reference/summarise.html">summarise</a></span>(<span class="dt">mean_dist =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/mean">mean</a></span>(distance),</a>
<a class="sourceLine" id="cb38-3" title="3">              <span class="dt">sd_dist =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/sd">sd</a></span>(distance),</a>
<a class="sourceLine" id="cb38-4" title="4">              <span class="dt">median_dist =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(distance),</a>
<a class="sourceLine" id="cb38-5" title="5">              <span class="dt">lower_975_dist =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/quantile">quantile</a></span>(distance, <span class="dt">probs =</span> <span class="fl">0.025</span>),</a>
<a class="sourceLine" id="cb38-6" title="6">              <span class="dt">upper_975_dist =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/quantile">quantile</a></span>(distance, <span class="dt">probs =</span> <span class="fl">0.975</span>))</a></code></pre></div>
<pre><code>## # A tibble: 1 x 5
##   mean_dist sd_dist median_dist lower_975_dist upper_975_dist
##       &lt;dbl&gt;   &lt;dbl&gt;       &lt;dbl&gt;          &lt;dbl&gt;          &lt;dbl&gt;
## 1      886.    986.        613.           17.1          3526.</code></pre>
<p>You can then package this up in a function and apply it to all rows</p>
<div class="sourceCode" id="cb40"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb40-1" title="1">my_dist_summary &lt;-<span class="st">  </span><span class="cf">function</span>(data){</a>
<a class="sourceLine" id="cb40-2" title="2">    data <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb40-3" title="3"><span class="st">    </span><span class="kw"><a href="https://dplyr.tidyverse.org/reference/summarise.html">summarise</a></span>(<span class="dt">mean_dist =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/mean">mean</a></span>(distance),</a>
<a class="sourceLine" id="cb40-4" title="4">              <span class="dt">sd_dist =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/sd">sd</a></span>(distance),</a>
<a class="sourceLine" id="cb40-5" title="5">              <span class="dt">median_dist =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(distance),</a>
<a class="sourceLine" id="cb40-6" title="6">              <span class="dt">lower_975_dist =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/quantile">quantile</a></span>(distance, <span class="dt">probs =</span> <span class="fl">0.025</span>),</a>
<a class="sourceLine" id="cb40-7" title="7">              <span class="dt">upper_975_dist =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/quantile">quantile</a></span>(distance, <span class="dt">probs =</span> <span class="fl">0.975</span>))</a>
<a class="sourceLine" id="cb40-8" title="8">}</a></code></pre></div>
<p>This can then be used to create a new column with <code><a href="https://purrr.tidyverse.org/reference/map.html">purrr::map()</a></code>.</p>
<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb41-1" title="1">mc_<span class="dv">20</span>_<span class="dv">100</span> <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb41-2" title="2"><span class="st">    </span><span class="kw"><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate</a></span>(<span class="dt">new_summary =</span> purrr<span class="op">::</span><span class="kw"><a href="https://purrr.tidyverse.org/reference/map.html">map</a></span>(augmented_users,</a>
<a class="sourceLine" id="cb41-3" title="3">                                    my_dist_summary)) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb41-4" title="4"><span class="st">    </span><span class="kw"><a href="https://dplyr.tidyverse.org/reference/select.html">select</a></span>(new_summary) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb41-5" title="5"><span class="st">    </span>tidyr<span class="op">::</span><span class="kw"><a href="https://tidyr.tidyverse.org/reference/unnest.html">unnest</a></span>()</a></code></pre></div>
<pre><code>## # A tibble: 2 x 5
##   mean_dist sd_dist median_dist lower_975_dist upper_975_dist
##       &lt;dbl&gt;   &lt;dbl&gt;       &lt;dbl&gt;          &lt;dbl&gt;          &lt;dbl&gt;
## 1      886.    986.        613.           17.1          3526.
## 2      555.    696.        307.           16.2          2277.</code></pre>
</div>
<div id="other-graphics-options" class="section level1">
<h1 class="hasAnchor">
<a href="#other-graphics-options" class="anchor"></a>Other graphics options</h1>
<p>You might be interested in plotting the existing users, the proposed facilities, and the coverage.</p>
<p>You can plot the existing facilities with leaflet.</p>
<div class="sourceCode" id="cb43"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb43-1" title="1">york_existing <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb43-2" title="2"><span class="st">    </span><span class="kw">leaflet</span>() <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb43-3" title="3"><span class="st">    </span><span class="kw">addTiles</span>() <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb43-4" title="4"><span class="st">    </span><span class="kw">addCircles</span>(<span class="dt">color =</span> <span class="st">"steelblue"</span>) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb43-5" title="5"><span class="st">    </span><span class="kw">setView</span>(<span class="dt">lng =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(york_existing<span class="op">$</span>long),</a>
<a class="sourceLine" id="cb43-6" title="6">            <span class="dt">lat =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(york_existing<span class="op">$</span>lat),</a>
<a class="sourceLine" id="cb43-7" title="7">            <span class="dt">zoom =</span> <span class="dv">12</span>)</a></code></pre></div>
<pre><code>## Assuming "long" and "lat" are longitude and latitude, respectively</code></pre>
<div id="htmlwidget-2f5581f5e03066e54aec" style="width:672px;height:480px;" class="leaflet html-widget"></div>
<script type="application/json" data-for="htmlwidget-2f5581f5e03066e54aec">{"x":{"options":{"crs":{"crsClass":"L.CRS.EPSG3857","code":null,"proj4def":null,"projectedBounds":null,"options":{}}},"calls":[{"method":"addTiles","args":["//{s}.tile.openstreetmap.org/{z}/{x}/{y}.png",null,null,{"minZoom":0,"maxZoom":18,"tileSize":256,"subdomains":"abc","errorTileUrl":"","tms":false,"noWrap":false,"zoomOffset":0,"zoomReverse":false,"opacity":1,"zIndex":1,"detectRetina":false,"attribution":"&copy; <a href=\"http://openstreetmap.org\">OpenStreetMap<\/a> contributors, <a href=\"http://creativecommons.org/licenses/by-sa/2.0/\">CC-BY-SA<\/a>"}]},{"method":"addCircles","args":[[53.9596508907596,53.9677564882369,53.9613148671082,53.9581772382319,53.9568594545915,54.00190351476,53.8864514211043,53.9621413468314,53.9619141135335,53.9610311094279,53.9550853795,53.9548812827909,53.9572022633226,53.9567095186753,53.9567679914352,53.9549214230194,53.9551530962012,53.9557704838986,53.9554957484559,53.953847326884,53.9642651931427,53.9616621953769,53.9606843980898,53.9573256867742,53.9552832184138,53.9623334690796,53.9631810722954,53.9634462525789,53.9623858215608,53.9623637265149,53.9579984495218,53.9614033037429,53.9616095278682,53.9609922552611,53.9610129118402,53.9542071359681,53.9606187708284,53.9622211642985,53.9575014516572,53.957036374116,53.9570997944319,53.9564946365779,53.9630295134081,53.9632362043567,53.9623292428585,53.9618220980056,53.9620531924554,53.9618056106727,53.9619572057287,53.9612597685256,53.9618143118863,53.9611378455884,53.9602467168394,53.9584333524427,53.9585804758401,53.9608933308177,53.9621686363612,53.9616730746285,53.9578300037296,53.9402584126711,53.9564777958943,53.9565938954867,53.9567028218865,53.9558970981207,53.9617319142055,53.9604926872793,53.896743403682,53.9053014675519,53.9294414427806,53.9231183858955,53.9598873773357],[-1.08564690097183,-1.08543294587906,-1.08308086305074,-1.08067825836393,-1.08269707398103,-1.13419801897719,-1.08916174344548,-1.0775141711116,-1.07718386582876,-1.08512897647179,-1.09044049040063,-1.07898497912229,-1.08042737201173,-1.08063633340091,-1.08005592360874,-1.0783592760631,-1.0792685364235,-1.08007787649931,-1.07823994006268,-1.07660000547084,-1.08255836915638,-1.08656312583665,-1.08681312099624,-1.09193100084883,-1.08100297055658,-1.08029922569387,-1.08300895065045,-1.08242391560264,-1.08598336028082,-1.08662400672101,-1.07876389006008,-1.07972527407815,-1.07965976260535,-1.08003915418572,-1.08038925565428,-1.06848487243362,-1.08527517341871,-1.08915728982939,-1.08784279407337,-1.08933123791529,-1.0870285946683,-1.08900776307917,-1.0808173886299,-1.08081284238164,-1.08209787394751,-1.08631576675556,-1.08952675811234,-1.09006561700215,-1.08872103189743,-1.08683103394326,-1.08765721709806,-1.08616306870545,-1.08717323366321,-1.08628315611027,-1.07965025425549,-1.07534694183706,-1.08578996328984,-1.08327066894096,-1.08259293490607,-1.1040469712115,-1.08797181720659,-1.07260742563499,-1.07624736878836,-1.0872529800169,-1.08273591377721,-1.0758435281912,-0.961850613180836,-1.09774757158968,-1.15813181157224,-1.09210995120073,-1.08483394971923],10,null,null,{"interactive":true,"className":"","stroke":true,"color":"steelblue","weight":5,"opacity":0.5,"fill":true,"fillColor":"steelblue","fillOpacity":0.2},null,null,null,{"interactive":false,"permanent":false,"direction":"auto","opacity":1,"offset":[0,0],"textsize":"10px","textOnly":false,"className":"","sticky":true},null,null]}],"limits":{"lat":[53.8864514211043,54.00190351476],"lng":[-1.15813181157224,-0.961850613180836]},"setView":[[53.9602467168394,-1.08308086305074],12,[]]},"evals":[],"jsHooks":[]}</script><p>You might want to then add the user information to this plot. You can add new circles based on new datasets, and then change the colour, so that they are visible.</p>
<div class="sourceCode" id="cb45"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb45-1" title="1"><span class="kw">leaflet</span>() <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb45-2" title="2"><span class="st">    </span><span class="kw">addCircles</span>(<span class="dt">data =</span> york_crime, </a>
<a class="sourceLine" id="cb45-3" title="3">               <span class="dt">color =</span> <span class="st">"steelblue"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb45-4" title="4"><span class="st">    </span><span class="kw">addCircles</span>(<span class="dt">data =</span> york_existing, </a>
<a class="sourceLine" id="cb45-5" title="5">               <span class="dt">color =</span> <span class="st">"coral"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb45-6" title="6"><span class="st">    </span><span class="kw">addTiles</span>() <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb45-7" title="7"><span class="st">    </span><span class="kw">setView</span>(<span class="dt">lng =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(york<span class="op">$</span>long),</a>
<a class="sourceLine" id="cb45-8" title="8">            <span class="dt">lat =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(york<span class="op">$</span>lat),</a>
<a class="sourceLine" id="cb45-9" title="9">            <span class="dt">zoom =</span> <span class="dv">15</span>)</a></code></pre></div>
<pre><code>## Assuming "long" and "lat" are longitude and latitude, respectively
## Assuming "long" and "lat" are longitude and latitude, respectively</code></pre>
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<a href=\"http://openstreetmap.org\">OpenStreetMap<\/a> contributors, <a href=\"http://creativecommons.org/licenses/by-sa/2.0/\">CC-BY-SA<\/a>"}]}],"limits":{"lat":[53.862931,54.053155],"lng":[-1.237961,-0.885483]},"setView":[[53.9594376386842,-1.082764565677],15,[]]},"evals":[],"jsHooks":[]}</script><p>With leaflet you can also specify the radius in metres of the circles. This means that we can set the radius of the circles to be 100, and this is 100m.</p>
<div class="sourceCode" id="cb47"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb47-1" title="1"><span class="kw">leaflet</span>() <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb47-2" title="2"><span class="st">    </span><span class="kw">addCircles</span>(<span class="dt">data =</span> york_crime, </a>
<a class="sourceLine" id="cb47-3" title="3">               <span class="dt">color =</span> <span class="st">"steelblue"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb47-4" title="4"><span class="st">    </span><span class="kw">addCircles</span>(<span class="dt">data =</span> york_existing, </a>
<a class="sourceLine" id="cb47-5" title="5">               <span class="dt">radius =</span> <span class="dv">100</span>,</a>
<a class="sourceLine" id="cb47-6" title="6">               <span class="dt">color =</span> <span class="st">"coral"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb47-7" title="7"><span class="st">    </span><span class="kw">addTiles</span>() <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb47-8" title="8"><span class="st">    </span><span class="kw">setView</span>(<span class="dt">lng =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(york<span class="op">$</span>long),</a>
<a class="sourceLine" id="cb47-9" title="9">            <span class="dt">lat =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(york<span class="op">$</span>lat),</a>
<a class="sourceLine" id="cb47-10" title="10">            <span class="dt">zoom =</span> <span class="dv">15</span>)</a></code></pre></div>
<pre><code>## Assuming "long" and "lat" are longitude and latitude, respectively
## Assuming "long" and "lat" are longitude and latitude, respectively</code></pre>
<div id="htmlwidget-e1dda077f7ec1378f6fc" style="width:672px;height:480px;" class="leaflet html-widget"></div>
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<a href=\"http://openstreetmap.org\">OpenStreetMap<\/a> contributors, <a href=\"http://creativecommons.org/licenses/by-sa/2.0/\">CC-BY-SA<\/a>"}]}],"limits":{"lat":[53.862931,54.053155],"lng":[-1.237961,-0.885483]},"setView":[[53.9594376386842,-1.082764565677],15,[]]},"evals":[],"jsHooks":[]}</script><p>to make this a bit clearer we can remove the fill (<code>fill = FALSE</code>), and also change the map that is used with <code>addProviderTiles("CartoDB.Positron")</code>.</p>
<div class="sourceCode" id="cb49"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb49-1" title="1"><span class="kw">leaflet</span>() <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb49-2" title="2"><span class="st">    </span><span class="kw">addCircles</span>(<span class="dt">data =</span> york_crime, </a>
<a class="sourceLine" id="cb49-3" title="3">               <span class="dt">color =</span> <span class="st">"steelblue"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb49-4" title="4"><span class="st">    </span><span class="kw">addCircles</span>(<span class="dt">data =</span> york_existing, </a>
<a class="sourceLine" id="cb49-5" title="5">               <span class="dt">radius =</span> <span class="dv">100</span>,</a>
<a class="sourceLine" id="cb49-6" title="6">               <span class="dt">fill =</span> <span class="ot">FALSE</span>,</a>
<a class="sourceLine" id="cb49-7" title="7">               <span class="dt">color =</span> <span class="st">"coral"</span>,</a>
<a class="sourceLine" id="cb49-8" title="8">               <span class="dt">weight =</span> <span class="dv">3</span>,</a>
<a class="sourceLine" id="cb49-9" title="9">               <span class="dt">dashArray =</span> <span class="st">"1,5"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb49-10" title="10"><span class="st">    </span><span class="kw">addProviderTiles</span>(<span class="st">"CartoDB.Positron"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb49-11" title="11"><span class="st">    </span><span class="kw">setView</span>(<span class="dt">lng =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(york<span class="op">$</span>long),</a>
<a class="sourceLine" id="cb49-12" title="12">            <span class="dt">lat =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(york<span class="op">$</span>lat),</a>
<a class="sourceLine" id="cb49-13" title="13">            <span class="dt">zoom =</span> <span class="dv">15</span>)</a></code></pre></div>
<pre><code>## Assuming "long" and "lat" are longitude and latitude, respectively
## Assuming "long" and "lat" are longitude and latitude, respectively</code></pre>
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id="applying-this-to-the-coverage-data" class="section level2">
<h2 class="hasAnchor">
<a href="#applying-this-to-the-coverage-data" class="anchor"></a>Applying this to the coverage data</h2>
<p>So using this knowledge, we can visualise:</p>
<ul>
<li>crime (<code>york_crime</code>)</li>
<li>existing facilities (<code>york_existing</code>)</li>
<li>newly placed facilities (<code>mc_20$facility_selected[[1]]</code>)</li>
</ul>
<div class="sourceCode" id="cb51"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb51-1" title="1"><span class="kw">leaflet</span>() <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb51-2" title="2"><span class="st">    </span><span class="kw">addCircles</span>(<span class="dt">data =</span> york_crime, </a>
<a class="sourceLine" id="cb51-3" title="3">               <span class="dt">color =</span> <span class="st">"steelblue"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb51-4" title="4"><span class="st">    </span><span class="kw">addCircles</span>(<span class="dt">data =</span> york_existing, </a>
<a class="sourceLine" id="cb51-5" title="5">               <span class="dt">radius =</span> <span class="dv">100</span>,</a>
<a class="sourceLine" id="cb51-6" title="6">               <span class="dt">fill =</span> <span class="ot">FALSE</span>,</a>
<a class="sourceLine" id="cb51-7" title="7">               <span class="dt">weight =</span> <span class="dv">3</span>,</a>
<a class="sourceLine" id="cb51-8" title="8">               <span class="dt">color =</span> <span class="st">"coral"</span>,</a>
<a class="sourceLine" id="cb51-9" title="9">               <span class="dt">dashArray =</span> <span class="st">"1,5"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb51-10" title="10"><span class="st">    </span><span class="kw">addCircles</span>(<span class="dt">data =</span> mc_<span class="dv">20</span><span class="op">$</span>facility_selected[[<span class="dv">1</span>]], </a>
<a class="sourceLine" id="cb51-11" title="11">               <span class="dt">radius =</span> <span class="dv">100</span>,</a>
<a class="sourceLine" id="cb51-12" title="12">               <span class="dt">fill =</span> <span class="ot">FALSE</span>,</a>
<a class="sourceLine" id="cb51-13" title="13">               <span class="dt">weight =</span> <span class="dv">3</span>,</a>
<a class="sourceLine" id="cb51-14" title="14">               <span class="dt">color =</span> <span class="st">"green"</span>,</a>
<a class="sourceLine" id="cb51-15" title="15">               <span class="dt">dashArray =</span> <span class="st">"1,5"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb51-16" title="16"><span class="st">    </span><span class="kw">addProviderTiles</span>(<span class="st">"CartoDB.Positron"</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb51-17" title="17"><span class="st">    </span><span class="kw">setView</span>(<span class="dt">lng =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(york<span class="op">$</span>long),</a>
<a class="sourceLine" id="cb51-18" title="18">            <span class="dt">lat =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/stats/topics/median">median</a></span>(york<span class="op">$</span>lat),</a>
<a class="sourceLine" id="cb51-19" title="19">            <span class="dt">zoom =</span> <span class="dv">15</span>)</a></code></pre></div>
<pre><code>## Assuming "long" and "lat" are longitude and latitude, respectively
## Assuming "long" and "lat" are longitude and latitude, respectively
## Assuming "long" and "lat" are longitude and latitude, respectively</code></pre>
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<div id="future-work" class="section level1">
<h1 class="hasAnchor">
<a href="#future-work" class="anchor"></a>Future work</h1>
<p>In the future <code>maxcovr</code> will be able to talk to commercial solvers like CPLEX and Gurobi, and will have a mechanism for extensions.</p>
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<a href="#tocnav" class="anchor"></a>Contents</h2>
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<li><a href="#the-moviation-why-maxcovr">The moviation: Why <code>maxcovr</code></a></li>
      <li><a href="#the-problem">The problem</a></li>
      <li><a href="#using-max_coverage">using max_coverage</a></li>
      <li><a href="#interpreting-results">Interpreting results</a></li>
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<a href="#other-graphics-options">Other graphics options</a><ul class="nav nav-pills nav-stacked">
<li><a href="#applying-this-to-the-coverage-data">Applying this to the coverage data</a></li>
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      <li><a href="#future-work">Future work</a></li>
      </ul>
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  <p>Developed by Nicholas Tierney.</p>
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