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graphical_data_exploration_exercise_solutions.html
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graphical_data_exploration_exercise_solutions.html
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<h1 class="title toc-ignore">Exercise Solutions</h1>
</div>
<p> </p>
<div id="exercise-graphical-data-exploration-using-r"
class="section level2">
<h2>Exercise: Graphical data exploration using R</h2>
<p> </p>
<p>1. As in previous exercises, either create a new R script (perhaps
call it graphical_data_exploration) or continue with your previous R
script in your RStudio Project. Again, make sure you include any
metadata you feel is appropriate (title, description of task, date of
creation etc) and don’t forget to comment out your metadata with a
<code>#</code> at the beginning of the line.</p>
<p> </p>
<p>2. If you haven’t already, download the data file
<em>‘loyn.xlsx’</em> from the <strong><a
href="data.html"><i class="fa fa-download"></i> Data</a></strong> link
and save it to the <code>data</code> directory you created during
Exercise 1. Open this file in Microsoft Excel (or even better use an
open source equivalent - <a
href="https://www.libreoffice.org/download/download/">LibreOffice</a> is
a good free alternative) and save it as a tab delimited file type. Name
the file <em>‘loyn.txt’</em> and also save it to the <code>data</code>
directory.</p>
<p> </p>
<p>3. These data are from a study originally conducted by Loyn
(1987)<sup>1</sup> and subsequently re-analysed by Quinn and Keough
(2002)<sup>2</sup> and Zuur et al (2009)<sup>3</sup>. The aim of the
study was to relate bird density in 67 forest patches to a number of
different environmental variables and management practices. A summary of
the variables is: <strong>ABUND</strong>: Density of birds, Continuous
response; <strong>AREA</strong>: Size of forest patch, Continuous
explanatory; <strong>DIST</strong>: Distance to nearest patch,
Continuous explanatory; <strong>LDIST</strong>: Distance to nearest
larger patch, Continuous explanatory; <strong>ALT</strong>: Mean
altitude of patch, Continuous explanatory; <strong>YR.ISOL</strong>:
Year of isolation of clearance, Continuous explanatory;
<strong>GRAZE</strong>: Index of livestock grazing intensity, 5 level
Categorical explanatory 1= low graze, 5 = high graze. Add a description
of your variables to the metadata you created previously. Clearly
highlight which variable is the response variable and which variables
are potential explanatory variables.</p>
<p> </p>
<p>4. Import your <em>‘loyn.txt’</em> file into R using the
<code>read.table()</code> function and assign it to an object called
<code>loyn</code> (checkout <a
href="https://intro2r.com/importing-data.html#import_fnc">Section
3.3.2</a> if you need a reminder). Use the <code>str()</code> function
to display the structure of the dataset and the <code>summary()</code>
function to summarise the dataset. Copy and paste the output of
<code>str()</code> and <code>Summary()</code> to your R code as a
record. Don’t forget to comment this code with a <code>#</code> at the
beginning of each line (can you remember the keyboard <a
href="https://intro2r.com/proj_doc.html#proj_doc">shortcut</a>?). How
many observations are in this dataset? How many variables does the
dataframe contain? Are there any missing values (coded as
<code>NA</code>) in any variable? How is the variable <code>GRAZE</code>
coded? (as a number or a string?). If you think this will cause a
problem (hint: it will!), create a new variable called
<code>FGRAZE</code> <strong>in</strong> the dataframe with
<code>GRAZE</code> recoded as a factor.</p>
<p> </p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a>loyn <span class="ot"><-</span> <span class="fu">read.table</span>(<span class="st">"./data/loyn.txt"</span>, <span class="at">header =</span> <span class="cn">TRUE</span>, </span>
<span id="cb1-2"><a href="#cb1-2" tabindex="-1"></a> <span class="at">stringsAsFactors =</span> <span class="cn">TRUE</span>)</span>
<span id="cb1-3"><a href="#cb1-3" tabindex="-1"></a><span class="fu">str</span>(loyn)</span>
<span id="cb1-4"><a href="#cb1-4" tabindex="-1"></a><span class="do">## 'data.frame': 67 obs. of 8 variables:</span></span>
<span id="cb1-5"><a href="#cb1-5" tabindex="-1"></a><span class="do">## $ SITE : int 1 60 2 3 61 4 5 6 7 8 ...</span></span>
<span id="cb1-6"><a href="#cb1-6" tabindex="-1"></a><span class="do">## $ ABUND : num 5.3 10 2 1.5 13 17.1 13.8 14.1 3.8 2.2 ...</span></span>
<span id="cb1-7"><a href="#cb1-7" tabindex="-1"></a><span class="do">## $ AREA : num 0.1 0.2 0.5 0.5 0.6 1 1 1 1 1 ...</span></span>
<span id="cb1-8"><a href="#cb1-8" tabindex="-1"></a><span class="do">## $ DIST : int 39 142 234 104 191 66 246 234 467 284 ...</span></span>
<span id="cb1-9"><a href="#cb1-9" tabindex="-1"></a><span class="do">## $ LDIST : int 39 142 234 311 357 66 246 285 467 1829 ...</span></span>
<span id="cb1-10"><a href="#cb1-10" tabindex="-1"></a><span class="do">## $ YR.ISOL: int 1968 1961 1920 1900 1957 1966 1918 1965 1955 1920 ...</span></span>
<span id="cb1-11"><a href="#cb1-11" tabindex="-1"></a><span class="do">## $ GRAZE : int 2 2 5 5 2 3 5 3 5 5 ...</span></span>
<span id="cb1-12"><a href="#cb1-12" tabindex="-1"></a><span class="do">## $ ALT : int 160 180 60 140 185 160 140 130 90 60 ...</span></span>
<span id="cb1-13"><a href="#cb1-13" tabindex="-1"></a></span>
<span id="cb1-14"><a href="#cb1-14" tabindex="-1"></a><span class="co"># 67 observations and 8 variables (from str())</span></span>
<span id="cb1-15"><a href="#cb1-15" tabindex="-1"></a></span>
<span id="cb1-16"><a href="#cb1-16" tabindex="-1"></a><span class="fu">summary</span>(loyn)</span>
<span id="cb1-17"><a href="#cb1-17" tabindex="-1"></a><span class="do">## SITE ABUND AREA DIST LDIST YR.ISOL GRAZE </span></span>
<span id="cb1-18"><a href="#cb1-18" tabindex="-1"></a><span class="do">## Min. : 1.0 Min. : 1.50 Min. : 0.1 Min. : 26.0 Min. : 26.0 Min. :1890 Min. :1.00 </span></span>
<span id="cb1-19"><a href="#cb1-19" tabindex="-1"></a><span class="do">## 1st Qu.:17.5 1st Qu.:12.10 1st Qu.: 2.0 1st Qu.: 112.0 1st Qu.: 157.5 1st Qu.:1946 1st Qu.:2.00 </span></span>
<span id="cb1-20"><a href="#cb1-20" tabindex="-1"></a><span class="do">## Median :34.0 Median :19.40 Median : 7.0 Median : 208.0 Median : 345.0 Median :1963 Median :3.00 </span></span>
<span id="cb1-21"><a href="#cb1-21" tabindex="-1"></a><span class="do">## Mean :34.0 Mean :18.76 Mean : 58.7 Mean : 241.8 Mean : 678.0 Mean :1952 Mean :3.03 </span></span>
<span id="cb1-22"><a href="#cb1-22" tabindex="-1"></a><span class="do">## 3rd Qu.:50.5 3rd Qu.:27.45 3rd Qu.: 20.5 3rd Qu.: 334.5 3rd Qu.: 826.0 3rd Qu.:1966 3rd Qu.:4.00 </span></span>
<span id="cb1-23"><a href="#cb1-23" tabindex="-1"></a><span class="do">## Max. :67.0 Max. :39.60 Max. :1771.0 Max. :1427.0 Max. :4426.0 Max. :1976 Max. :5.00 </span></span>
<span id="cb1-24"><a href="#cb1-24" tabindex="-1"></a><span class="do">## ALT </span></span>
<span id="cb1-25"><a href="#cb1-25" tabindex="-1"></a><span class="do">## Min. : 60.0 </span></span>
<span id="cb1-26"><a href="#cb1-26" tabindex="-1"></a><span class="do">## 1st Qu.:120.0 </span></span>
<span id="cb1-27"><a href="#cb1-27" tabindex="-1"></a><span class="do">## Median :150.0 </span></span>
<span id="cb1-28"><a href="#cb1-28" tabindex="-1"></a><span class="do">## Mean :150.4 </span></span>
<span id="cb1-29"><a href="#cb1-29" tabindex="-1"></a><span class="do">## 3rd Qu.:187.5 </span></span>
<span id="cb1-30"><a href="#cb1-30" tabindex="-1"></a><span class="do">## Max. :260.0</span></span>
<span id="cb1-31"><a href="#cb1-31" tabindex="-1"></a></span>
<span id="cb1-32"><a href="#cb1-32" tabindex="-1"></a><span class="co"># GRAZE is coded as numeric (i.e. 1,2,3,5)</span></span>
<span id="cb1-33"><a href="#cb1-33" tabindex="-1"></a></span>
<span id="cb1-34"><a href="#cb1-34" tabindex="-1"></a><span class="co"># create a new factor variable variable FGRAZE which is a factor of GRAZE</span></span>
<span id="cb1-35"><a href="#cb1-35" tabindex="-1"></a>loyn<span class="sc">$</span>FGRAZE <span class="ot"><-</span> <span class="fu">factor</span>(loyn<span class="sc">$</span>GRAZE)</span></code></pre></div>
<p> </p>
<p>5. Use the function <code>table()</code> (or <code>xtabs()</code>) to
determine how many observations are in each <code>FGRAZE</code> level.
See <a href="https://intro2r.com/summarising-data-frames.html">section
3.5</a> of the Introduction to R book to remind yourself how to do
this.</p>
<p> </p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a><span class="fu">table</span>(loyn<span class="sc">$</span>FGRAZE)</span>
<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a><span class="do">## </span></span>
<span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a><span class="do">## 1 2 3 4 5 </span></span>
<span id="cb2-4"><a href="#cb2-4" tabindex="-1"></a><span class="do">## 13 11 17 13 13</span></span>
<span id="cb2-5"><a href="#cb2-5" tabindex="-1"></a></span>
<span id="cb2-6"><a href="#cb2-6" tabindex="-1"></a><span class="co"># or use xtabs function</span></span>
<span id="cb2-7"><a href="#cb2-7" tabindex="-1"></a><span class="fu">xtabs</span>(<span class="sc">~</span> FGRAZE, <span class="at">data =</span> loyn)</span>
<span id="cb2-8"><a href="#cb2-8" tabindex="-1"></a><span class="do">## FGRAZE</span></span>
<span id="cb2-9"><a href="#cb2-9" tabindex="-1"></a><span class="do">## 1 2 3 4 5 </span></span>
<span id="cb2-10"><a href="#cb2-10" tabindex="-1"></a><span class="do">## 13 11 17 13 13</span></span></code></pre></div>
<p> </p>
<p>6. Using the <code>tapply()</code> function what is the mean bird
abundance (<code>ABUND</code>) for each levels of <code>FGRAZE</code>?
Can you determine the variance, the minimum and maximum for each
<code>FGRAZE</code> level? Again see <a
href="https://intro2r.com/summarising-data-frames.html">section 3.5</a>
of the Introduction to R book to remind yourself how to do this.</p>
<p> </p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a><span class="co"># mean abundance of birds for each level of FGRAZE</span></span>
<span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a><span class="fu">tapply</span>(loyn<span class="sc">$</span>ABUND, loyn<span class="sc">$</span>FGRAZE, mean, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
<span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a><span class="do">## 1 2 3 4 5 </span></span>
<span id="cb3-4"><a href="#cb3-4" tabindex="-1"></a><span class="do">## 28.623077 19.418182 20.164706 18.961538 6.292308</span></span>
<span id="cb3-5"><a href="#cb3-5" tabindex="-1"></a></span>
<span id="cb3-6"><a href="#cb3-6" tabindex="-1"></a><span class="co"># variance in the abundance of birds for each level of FGRAZE</span></span>
<span id="cb3-7"><a href="#cb3-7" tabindex="-1"></a><span class="fu">tapply</span>(loyn<span class="sc">$</span>ABUND, loyn<span class="sc">$</span>FGRAZE, var, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
<span id="cb3-8"><a href="#cb3-8" tabindex="-1"></a><span class="do">## 1 2 3 4 5 </span></span>
<span id="cb3-9"><a href="#cb3-9" tabindex="-1"></a><span class="do">## 32.63859 73.13364 89.42243 50.62923 23.10744</span></span>
<span id="cb3-10"><a href="#cb3-10" tabindex="-1"></a></span>
<span id="cb3-11"><a href="#cb3-11" tabindex="-1"></a><span class="co"># minimum abundance of birds for each level of FGRAZE</span></span>
<span id="cb3-12"><a href="#cb3-12" tabindex="-1"></a><span class="fu">tapply</span>(loyn<span class="sc">$</span>ABUND, loyn<span class="sc">$</span>FGRAZE, min, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
<span id="cb3-13"><a href="#cb3-13" tabindex="-1"></a><span class="do">## 1 2 3 4 5 </span></span>
<span id="cb3-14"><a href="#cb3-14" tabindex="-1"></a><span class="do">## 14.6 5.3 2.9 3.3 1.5</span></span>
<span id="cb3-15"><a href="#cb3-15" tabindex="-1"></a></span>
<span id="cb3-16"><a href="#cb3-16" tabindex="-1"></a><span class="co"># maximum abundance of birds for each level of FGRAZE</span></span>
<span id="cb3-17"><a href="#cb3-17" tabindex="-1"></a><span class="fu">tapply</span>(loyn<span class="sc">$</span>ABUND, loyn<span class="sc">$</span>FGRAZE, max, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
<span id="cb3-18"><a href="#cb3-18" tabindex="-1"></a><span class="do">## 1 2 3 4 5 </span></span>
<span id="cb3-19"><a href="#cb3-19" tabindex="-1"></a><span class="do">## 39.6 34.4 37.7 27.8 13.8</span></span>
<span id="cb3-20"><a href="#cb3-20" tabindex="-1"></a></span>
<span id="cb3-21"><a href="#cb3-21" tabindex="-1"></a><span class="co"># OR use the summary function</span></span>
<span id="cb3-22"><a href="#cb3-22" tabindex="-1"></a><span class="fu">tapply</span>(loyn<span class="sc">$</span>ABUND, loyn<span class="sc">$</span>FGRAZE, summary, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
<span id="cb3-23"><a href="#cb3-23" tabindex="-1"></a><span class="do">## $`1`</span></span>
<span id="cb3-24"><a href="#cb3-24" tabindex="-1"></a><span class="do">## Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb3-25"><a href="#cb3-25" tabindex="-1"></a><span class="do">## 14.60 27.30 29.50 28.62 30.90 39.60 </span></span>
<span id="cb3-26"><a href="#cb3-26" tabindex="-1"></a><span class="do">## </span></span>
<span id="cb3-27"><a href="#cb3-27" tabindex="-1"></a><span class="do">## $`2`</span></span>
<span id="cb3-28"><a href="#cb3-28" tabindex="-1"></a><span class="do">## Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb3-29"><a href="#cb3-29" tabindex="-1"></a><span class="do">## 5.30 14.00 19.40 19.42 25.20 34.40 </span></span>
<span id="cb3-30"><a href="#cb3-30" tabindex="-1"></a><span class="do">## </span></span>
<span id="cb3-31"><a href="#cb3-31" tabindex="-1"></a><span class="do">## $`3`</span></span>
<span id="cb3-32"><a href="#cb3-32" tabindex="-1"></a><span class="do">## Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb3-33"><a href="#cb3-33" tabindex="-1"></a><span class="do">## 2.90 14.10 19.50 20.16 27.60 37.70 </span></span>
<span id="cb3-34"><a href="#cb3-34" tabindex="-1"></a><span class="do">## </span></span>
<span id="cb3-35"><a href="#cb3-35" tabindex="-1"></a><span class="do">## $`4`</span></span>
<span id="cb3-36"><a href="#cb3-36" tabindex="-1"></a><span class="do">## Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb3-37"><a href="#cb3-37" tabindex="-1"></a><span class="do">## 3.30 15.00 19.90 18.96 25.00 27.80 </span></span>
<span id="cb3-38"><a href="#cb3-38" tabindex="-1"></a><span class="do">## </span></span>
<span id="cb3-39"><a href="#cb3-39" tabindex="-1"></a><span class="do">## $`5`</span></span>
<span id="cb3-40"><a href="#cb3-40" tabindex="-1"></a><span class="do">## Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb3-41"><a href="#cb3-41" tabindex="-1"></a><span class="do">## 1.500 2.200 3.800 6.292 11.500 13.800</span></span></code></pre></div>
<p> </p>
<p>7. Now onto some plotting action. Plot a Cleveland dotchart (<a
href="https://intro2r.com/simple-base-r-plots.html#dotcharts">Section
4.2.4</a>) of each variable separately to assess whether there are any
outliers (unusually large or small values) in the response variable
(<code>ABUND</code>) or any of the explanatory variables (see Q3).
Produce a Cleveland dotchart of each variable separately to assess this.
If you feel in the mood, output these plots to an external PDF file in
the output directory you created in Exercise 1.</p>
<p> </p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" tabindex="-1"></a><span class="co"># first split the plotting device into 2 rows</span></span>
<span id="cb4-2"><a href="#cb4-2" tabindex="-1"></a><span class="co"># and 3 columns</span></span>
<span id="cb4-3"><a href="#cb4-3" tabindex="-1"></a><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">2</span>,<span class="dv">3</span>))</span>
<span id="cb4-4"><a href="#cb4-4" tabindex="-1"></a></span>
<span id="cb4-5"><a href="#cb4-5" tabindex="-1"></a><span class="co"># now produce the plots</span></span>
<span id="cb4-6"><a href="#cb4-6" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>AREA, <span class="at">main =</span> <span class="st">"Area"</span>)</span>
<span id="cb4-7"><a href="#cb4-7" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>DIST, <span class="at">main =</span> <span class="st">"Distance"</span>)</span>
<span id="cb4-8"><a href="#cb4-8" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>LDIST, <span class="at">main =</span> <span class="st">"Distance to larger patch"</span>)</span>
<span id="cb4-9"><a href="#cb4-9" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>YR.ISOL, <span class="at">main =</span> <span class="st">"Year of isolation"</span>)</span>
<span id="cb4-10"><a href="#cb4-10" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>ALT, <span class="at">main =</span> <span class="st">"Altitude"</span>)</span>
<span id="cb4-11"><a href="#cb4-11" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>GRAZE, <span class="at">main =</span> <span class="st">"Grazing levels"</span>)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q7a-1.png" width="672" /></p>
<p> </p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a><span class="co"># A fancier version of a dotplot - just for fun!</span></span>
<span id="cb5-2"><a href="#cb5-2" tabindex="-1"></a>Z <span class="ot"><-</span> <span class="fu">cbind</span>(loyn<span class="sc">$</span>ABUND, loyn<span class="sc">$</span>AREA, loyn<span class="sc">$</span>DIST,</span>
<span id="cb5-3"><a href="#cb5-3" tabindex="-1"></a> loyn<span class="sc">$</span>LDIST,loyn<span class="sc">$</span>YR.ISOL,loyn<span class="sc">$</span>ALT,</span>
<span id="cb5-4"><a href="#cb5-4" tabindex="-1"></a> loyn<span class="sc">$</span>GRAZE)</span>
<span id="cb5-5"><a href="#cb5-5" tabindex="-1"></a></span>
<span id="cb5-6"><a href="#cb5-6" tabindex="-1"></a><span class="fu">colnames</span>(Z) <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"Abundance"</span>, <span class="st">"Area"</span>,<span class="st">"Distance"</span>,</span>
<span id="cb5-7"><a href="#cb5-7" tabindex="-1"></a> <span class="st">"larger dist"</span>,<span class="st">"year of isolation"</span>,</span>
<span id="cb5-8"><a href="#cb5-8" tabindex="-1"></a> <span class="st">"Altitude"</span>, <span class="st">"Grazing"</span>)</span>
<span id="cb5-9"><a href="#cb5-9" tabindex="-1"></a> </span>
<span id="cb5-10"><a href="#cb5-10" tabindex="-1"></a><span class="fu">library</span>(lattice)</span>
<span id="cb5-11"><a href="#cb5-11" tabindex="-1"></a><span class="fu">dotplot</span>(<span class="fu">as.matrix</span>(Z),</span>
<span id="cb5-12"><a href="#cb5-12" tabindex="-1"></a> <span class="at">groups=</span><span class="cn">FALSE</span>,</span>
<span id="cb5-13"><a href="#cb5-13" tabindex="-1"></a> <span class="at">strip =</span> <span class="fu">strip.custom</span>(<span class="at">bg =</span> <span class="st">'white'</span>,</span>
<span id="cb5-14"><a href="#cb5-14" tabindex="-1"></a> <span class="at">par.strip.text =</span> <span class="fu">list</span>(<span class="at">cex =</span> <span class="fl">0.8</span>)),</span>
<span id="cb5-15"><a href="#cb5-15" tabindex="-1"></a> <span class="at">scales =</span> <span class="fu">list</span>(<span class="at">x =</span> <span class="fu">list</span>(<span class="at">relation =</span> <span class="st">"free"</span>),</span>
<span id="cb5-16"><a href="#cb5-16" tabindex="-1"></a> <span class="at">y =</span> <span class="fu">list</span>(<span class="at">relation =</span> <span class="st">"free"</span>),</span>
<span id="cb5-17"><a href="#cb5-17" tabindex="-1"></a> <span class="at">draw =</span> <span class="cn">FALSE</span>),</span>
<span id="cb5-18"><a href="#cb5-18" tabindex="-1"></a> <span class="at">col=</span><span class="dv">1</span>, <span class="at">cex =</span><span class="fl">0.5</span>, <span class="at">pch =</span> <span class="dv">16</span>,</span>
<span id="cb5-19"><a href="#cb5-19" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">"Value of the variable"</span>,</span>
<span id="cb5-20"><a href="#cb5-20" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">"Order of the data from text file"</span>)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q7b-1.png" width="672" /></p>
<p>8. If you do spot any variables with unusual observations you will
need to have a think about what you want to do with them (NOTE: do
<strong>not</strong> just remove them without justification!). If you’re
unsure, be sure to speak to an instructor to discuss your options during
our synchronous practical sessions. One option is to apply a data
transformation to see if this reduces the magnitude of any outlier. The
best thing to do here is to play around with different transformations
(i.e. <code>log10()</code>, <code>sqrt()</code>) to see which one does
what you want it to do. Best practice is to create new variables in your
dataframe to store these transformed variables. After you have applied
these data transformations make sure you re-plot your dotcharts with any
transformed variable to double check what the transformation is doing.
Hint: a log<sub>10</sub> transformation might help reduce the magnitude
of the outliers for some of the variables.</p>
<p> </p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a><span class="co"># There appears to be two unusually large forest patches compared to the rest</span></span>
<span id="cb6-2"><a href="#cb6-2" tabindex="-1"></a><span class="co"># Also one potentially large distance in DIST</span></span>
<span id="cb6-3"><a href="#cb6-3" tabindex="-1"></a><span class="co"># One option would be to log10 transform AREA, DIST </span></span>
<span id="cb6-4"><a href="#cb6-4" tabindex="-1"></a><span class="co"># log base 10 transform variables </span></span>
<span id="cb6-5"><a href="#cb6-5" tabindex="-1"></a></span>
<span id="cb6-6"><a href="#cb6-6" tabindex="-1"></a>loyn<span class="sc">$</span>LOGAREA <span class="ot"><-</span> <span class="fu">log10</span>(loyn<span class="sc">$</span>AREA)</span>
<span id="cb6-7"><a href="#cb6-7" tabindex="-1"></a>loyn<span class="sc">$</span>LOGDIST <span class="ot"><-</span> <span class="fu">log10</span>(loyn<span class="sc">$</span>DIST)</span>
<span id="cb6-8"><a href="#cb6-8" tabindex="-1"></a></span>
<span id="cb6-9"><a href="#cb6-9" tabindex="-1"></a><span class="co"># check the dataframe</span></span>
<span id="cb6-10"><a href="#cb6-10" tabindex="-1"></a><span class="fu">str</span>(loyn)</span>
<span id="cb6-11"><a href="#cb6-11" tabindex="-1"></a><span class="do">## 'data.frame': 67 obs. of 11 variables:</span></span>
<span id="cb6-12"><a href="#cb6-12" tabindex="-1"></a><span class="do">## $ SITE : int 1 60 2 3 61 4 5 6 7 8 ...</span></span>
<span id="cb6-13"><a href="#cb6-13" tabindex="-1"></a><span class="do">## $ ABUND : num 5.3 10 2 1.5 13 17.1 13.8 14.1 3.8 2.2 ...</span></span>
<span id="cb6-14"><a href="#cb6-14" tabindex="-1"></a><span class="do">## $ AREA : num 0.1 0.2 0.5 0.5 0.6 1 1 1 1 1 ...</span></span>
<span id="cb6-15"><a href="#cb6-15" tabindex="-1"></a><span class="do">## $ DIST : int 39 142 234 104 191 66 246 234 467 284 ...</span></span>
<span id="cb6-16"><a href="#cb6-16" tabindex="-1"></a><span class="do">## $ LDIST : int 39 142 234 311 357 66 246 285 467 1829 ...</span></span>
<span id="cb6-17"><a href="#cb6-17" tabindex="-1"></a><span class="do">## $ YR.ISOL: int 1968 1961 1920 1900 1957 1966 1918 1965 1955 1920 ...</span></span>
<span id="cb6-18"><a href="#cb6-18" tabindex="-1"></a><span class="do">## $ GRAZE : int 2 2 5 5 2 3 5 3 5 5 ...</span></span>
<span id="cb6-19"><a href="#cb6-19" tabindex="-1"></a><span class="do">## $ ALT : int 160 180 60 140 185 160 140 130 90 60 ...</span></span>
<span id="cb6-20"><a href="#cb6-20" tabindex="-1"></a><span class="do">## $ FGRAZE : Factor w/ 5 levels "1","2","3","4",..: 2 2 5 5 2 3 5 3 5 5 ...</span></span>
<span id="cb6-21"><a href="#cb6-21" tabindex="-1"></a><span class="do">## $ LOGAREA: num -1 -0.699 -0.301 -0.301 -0.222 ...</span></span>
<span id="cb6-22"><a href="#cb6-22" tabindex="-1"></a><span class="do">## $ LOGDIST: num 1.59 2.15 2.37 2.02 2.28 ...</span></span></code></pre></div>
<p> </p>
<p>9. Next, check if there is any potential collinearity between any of
the <strong>explanatory variables</strong>. Remember, collinearity is a
<em>strong</em> relationship between your explanatory variables. Plot
these variables using the <code>pairs()</code> function (<a
href="https://intro2r.com/simple-base-r-plots.html#pairs-plots">Section
4.2.5</a>). You will need to extract your explanatory variables from the
<code>loyn</code> dataframe (using <code>[]</code>) either before you
use the <code>pairs()</code> function or whilst using it. Optionally,
include the correlation coefficient between variables in the upper panel
of the pairs plot (see <a
href="https://intro2r.com/simple-base-r-plots.html#pairs-plots">section
4.2.5</a> of the introduction to R book for details) to help you decide
whether collinearity is an issue.</p>
<p> </p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" tabindex="-1"></a><span class="co"># Vanilla pairs plot</span></span>
<span id="cb7-2"><a href="#cb7-2" tabindex="-1"></a></span>
<span id="cb7-3"><a href="#cb7-3" tabindex="-1"></a><span class="fu">pairs</span>(loyn[,<span class="fu">c</span>(<span class="st">"LOGAREA"</span>,<span class="st">"LOGDIST"</span>,<span class="st">"LDIST"</span>,</span>
<span id="cb7-4"><a href="#cb7-4" tabindex="-1"></a> <span class="st">"YR.ISOL"</span>,<span class="st">"ALT"</span>,<span class="st">"GRAZE"</span>)])</span>
<span id="cb7-5"><a href="#cb7-5" tabindex="-1"></a></span>
<span id="cb7-6"><a href="#cb7-6" tabindex="-1"></a><span class="co"># or first create a new dataframe and then use this </span></span>
<span id="cb7-7"><a href="#cb7-7" tabindex="-1"></a><span class="co"># data frame with the pairs function</span></span>
<span id="cb7-8"><a href="#cb7-8" tabindex="-1"></a></span>
<span id="cb7-9"><a href="#cb7-9" tabindex="-1"></a>explan_vars <span class="ot"><-</span> loyn[,<span class="fu">c</span>(<span class="st">"LOGAREA"</span>,<span class="st">"LOGDIST"</span>,<span class="st">"LDIST"</span>,</span>
<span id="cb7-10"><a href="#cb7-10" tabindex="-1"></a> <span class="st">"YR.ISOL"</span>,<span class="st">"ALT"</span>,<span class="st">"GRAZE"</span>)]</span>
<span id="cb7-11"><a href="#cb7-11" tabindex="-1"></a><span class="fu">pairs</span>(explan_vars)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q9a-1.png" width="672" /></p>
<p> </p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a><span class="co"># And with correlations in the upper panel</span></span>
<span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a></span>
<span id="cb8-3"><a href="#cb8-3" tabindex="-1"></a><span class="co"># first need to define the panel.cor function</span></span>
<span id="cb8-4"><a href="#cb8-4" tabindex="-1"></a>panel.cor <span class="ot"><-</span> <span class="cf">function</span>(x, y, <span class="at">digits =</span> <span class="dv">2</span>, <span class="at">prefix =</span> <span class="st">""</span>, cex.cor, ...){</span>
<span id="cb8-5"><a href="#cb8-5" tabindex="-1"></a> usr <span class="ot"><-</span> <span class="fu">par</span>(<span class="st">"usr"</span>)</span>
<span id="cb8-6"><a href="#cb8-6" tabindex="-1"></a> <span class="co">#on.exit(par(usr))</span></span>
<span id="cb8-7"><a href="#cb8-7" tabindex="-1"></a> <span class="fu">par</span>(<span class="at">usr =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>, <span class="dv">0</span>, <span class="dv">1</span>))</span>
<span id="cb8-8"><a href="#cb8-8" tabindex="-1"></a> r <span class="ot"><-</span> <span class="fu">abs</span>(<span class="fu">cor</span>(x, y))</span>
<span id="cb8-9"><a href="#cb8-9" tabindex="-1"></a> txt <span class="ot"><-</span> <span class="fu">format</span>(<span class="fu">c</span>(r, <span class="fl">0.123456789</span>), <span class="at">digits =</span> digits)[<span class="dv">1</span>]</span>
<span id="cb8-10"><a href="#cb8-10" tabindex="-1"></a> txt <span class="ot"><-</span> <span class="fu">paste0</span>(prefix, txt)</span>
<span id="cb8-11"><a href="#cb8-11" tabindex="-1"></a> <span class="cf">if</span>(<span class="fu">missing</span>(cex.cor)) cex.cor <span class="ot"><-</span> <span class="fl">0.8</span><span class="sc">/</span><span class="fu">strwidth</span>(txt)</span>
<span id="cb8-12"><a href="#cb8-12" tabindex="-1"></a> <span class="fu">text</span>(<span class="fl">0.5</span>, <span class="fl">0.5</span>, txt, <span class="at">cex =</span> cex.cor <span class="sc">*</span> r)</span>
<span id="cb8-13"><a href="#cb8-13" tabindex="-1"></a>}</span>
<span id="cb8-14"><a href="#cb8-14" tabindex="-1"></a></span>
<span id="cb8-15"><a href="#cb8-15" tabindex="-1"></a><span class="co"># then use the panel.cor function when we use pairs</span></span>
<span id="cb8-16"><a href="#cb8-16" tabindex="-1"></a><span class="fu">pairs</span>(loyn[,<span class="fu">c</span>(<span class="st">"LOGAREA"</span>,<span class="st">"LOGDIST"</span>,<span class="st">"LDIST"</span>,</span>
<span id="cb8-17"><a href="#cb8-17" tabindex="-1"></a> <span class="st">"YR.ISOL"</span>,<span class="st">"ALT"</span>,<span class="st">"GRAZE"</span>)],</span>
<span id="cb8-18"><a href="#cb8-18" tabindex="-1"></a> <span class="at">upper.panel =</span> panel.cor)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q9b-1.png" width="672" /></p>
<p> </p>
<p>10. Now that we’ve checked for collinearity let’s assess whether
there are any clear relationships between the response variable
(<code>ABUND</code>) and individual explanatory variables. Use
appropriate plotting functions (<code>plot()</code>,
<code>boxplot()</code> etc) to visualise these relationships. Don’t
forget, if you have applied a data transformation to any of your
variables (Q8) you will need to plot these transformed variables instead
of the original variables. Also, don’t forget, you can split your
plotting device up to allow you to plot multiple graphs (<a
href="https://intro2r.com/mult_graphs.html#mult_graphs">Section 4.4</a>)
or again use a function like <code>pairs()</code> to create a
multi-panel plot. Output these plots to the output directory as PDFs.
Add some comments in your R code to summarise your findings.</p>
<p> </p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a><span class="fu">pairs</span>(loyn[,<span class="fu">c</span>(<span class="st">"ABUND"</span>,<span class="st">"LOGAREA"</span>,<span class="st">"LOGDIST"</span>,<span class="st">"LDIST"</span>,</span>
<span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a> <span class="st">"YR.ISOL"</span>,<span class="st">"ALT"</span>,<span class="st">"GRAZE"</span>)],</span>
<span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a> <span class="at">lower.panel =</span> panel.cor)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q10a-1.png" width="672" /></p>
<p> </p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a><span class="fu">plot</span>(loyn<span class="sc">$</span>LOGAREA, loyn<span class="sc">$</span>ABUND, <span class="at">xlab =</span> <span class="st">"log area"</span>, <span class="at">ylab =</span> <span class="st">"bird abundance"</span>)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q10b-1.png" width="672" /></p>
<p> </p>
<p>11. One of the main aims of this study was to determine whether
management practices such as grazing intensity (<code>GRAZE</code>) and
size of the forest (<code>AREA</code>) affected the abundance of birds
(<code>ABUND</code>). One hypothesis was that the size of the forest
affected the number of birds, but this was dependent of the intensity of
the grazing regime (in other words, there is an interaction between
<code>AREA</code> and <code>GRAZE</code>). Use an appropriate plotting
function to explore these data for such an interaction (perhaps a
<code>coplot()</code> or <code>xyplot()</code> in <a
href="https://intro2r.com/simple-base-r-plots.html#coplots">Section
4.2.6</a> might be helpful?). Again, don’t forget, if you have applied a
data transformation to your <code>AREA</code> variable you need to use
the transformed variable in this plot not the original <code>AREA</code>
variable. Output this plot as a PDF to your output directory and add
some comments to your R code to describe any patterns you observe.</p>
<p> </p>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" tabindex="-1"></a><span class="co"># Interaction between LOGAREA and FGRAZE? </span></span>
<span id="cb11-2"><a href="#cb11-2" tabindex="-1"></a><span class="co"># Do the slopes look similar or different? </span></span>
<span id="cb11-3"><a href="#cb11-3" tabindex="-1"></a><span class="fu">coplot</span>(ABUND <span class="sc">~</span> LOGAREA <span class="sc">|</span> FGRAZE, <span class="at">data =</span> loyn)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q11a-1.png" width="672" /></p>
<p> </p>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" tabindex="-1"></a><span class="co"># Fancier version of the above plot </span></span>
<span id="cb12-2"><a href="#cb12-2" tabindex="-1"></a><span class="co"># with a line of best fit included just for fun</span></span>
<span id="cb12-3"><a href="#cb12-3" tabindex="-1"></a><span class="fu">coplot</span>(ABUND <span class="sc">~</span> LOGAREA <span class="sc">|</span> FGRAZE,</span>
<span id="cb12-4"><a href="#cb12-4" tabindex="-1"></a> <span class="at">data =</span> loyn,</span>
<span id="cb12-5"><a href="#cb12-5" tabindex="-1"></a> <span class="at">panel =</span> <span class="cf">function</span>(x, y, ...) {</span>
<span id="cb12-6"><a href="#cb12-6" tabindex="-1"></a> tmp <span class="ot"><-</span> <span class="fu">lm</span>(y <span class="sc">~</span> x, <span class="at">na.action =</span> na.omit)</span>
<span id="cb12-7"><a href="#cb12-7" tabindex="-1"></a> <span class="fu">abline</span>(tmp)</span>
<span id="cb12-8"><a href="#cb12-8" tabindex="-1"></a> <span class="fu">points</span>(x, y) })</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q11b-1.png" width="672" /></p>
<p> </p>
<p>End of Graphical data exploration using R Exercise</p>
</div>
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