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<h1 class="title toc-ignore">Assignment 03 - Fitting and Validating
Poisson Point Process Models</h1>

</div>


<hr />
<p>Complete the following exercises before the submission deadline. In
addition to the points detailed below, 5 points are assigned to the
quality of the annotation, as well as to the ‘cleanliness’ of the code
and resulting pdf document.</p>
<div id="exercise-1-1-point" class="section level2">
<h2>Exercise 1 – 1 point</h2>
<p>We will again be working with the BC Parks dataset, which contains
information on the locations of Provincial Parks in British Columbia.
The parks belong to 5 different regions. There is also information on
elevation (in m) and percent forest cover contained within the
dataset.</p>
<ul>
<li>Import the BC park locations dataset and convert the data to a
<code>ppp</code> object (for today you can exclude information on
regions). – 1 point(s)</li>
</ul>
<p>Note: You will need to load the <code>maptools</code> package and
make use of the <code>as.owin()</code> function.</p>
</div>
<div id="exercise-2-4-points" class="section level2">
<h2>Exercise 2 – 4 points</h2>
<ul>
<li>Estimate and plot <span class="math inline">\(\rho\)</span> for the
locations of parks as a function of both elevation and forest cover (be
sure that the x-axis for elevation does not go below 0). – 2
point(s)</li>
<li>Check for collinearity between elevation and forest cover (you will
need to consider NA values). – 1 point(s)</li>
<li>Based on these initial analyses, write down the expected form of the
model. Provide justification for this starting point. – 1 point(s)</li>
</ul>
<p>Note: Estimating rho can be slow (<span
class="math inline">\(\sim\)</span> 1-2 min). Be sure to leave enough
time for the document to knit.</p>
</div>
<div id="exercise-3-4-points" class="section level2">
<h2>Exercise 3 – 4 points</h2>
<ul>
<li>Fit the model you have defined in exercise 2 and inspect the model
output. – 1 point(s)</li>
<li>Fit a null, intercept only model. – 1 point(s)</li>
<li>Use AIC and a likelihood ratio test to determine if the model you
defined is a better fit than the intercept only model. – 1 point(s)</li>
<li>Write down the equation for the selected model. – 0.5 point(s)</li>
<li>Use this equation to estimate the intensity of parks at 500m
elevation and 50% forest cover.</li>
</ul>
</div>
<div id="exercise-4-4-points" class="section level2">
<h2>Exercise 4 – 4 points</h2>
<ul>
<li>Visualise the fitted model. Note: log scale the estimated intensity
when plotting, ignore the standard error. You can use the <code>n</code>
argument to adjust the resolution – 1 point(s)</li>
<li>Plot the effects of the individual coefficients. Note: use the
median value(s) of the other coefficients. – 2 point(s)</li>
<li>Visually, do you think the model predictions are a good match to the
data? – 1 point(s)</li>
</ul>
</div>
<div id="exercise-5-1-point" class="section level2">
<h2>Exercise 5 – 1 point</h2>
<ul>
<li>Test whether the observed data deviate significantly from the model
predictions. – 1 point(s)</li>
</ul>
</div>
<div id="exercise-5-2-points" class="section level2">
<h2>Exercise 5 – 2 points</h2>
<ul>
<li>Calculate and plot the model residuals. – 1 point(s)</li>
<li>Based on the residuals, do you think the model performing well? – 1
point(s)</li>
</ul>
</div>
<div id="exercise-6-3-points" class="section level2">
<h2>Exercise 6 – 3 points</h2>
<ul>
<li>Calculate the partial residuals as a function of both elevation and
forest cover. – 1 point(s)</li>
<li>Do you think that the terms are accurately capturing trends in the
data? – 1 point(s)</li>
<li>Do you have enough information to further refine the model and
improve it’s accuracy? – 1 point(s)</li>
</ul>
</div>
<div id="exercise-7-1-points" class="section level2">
<h2>Exercise 7 – 1 points</h2>
<ul>
<li>Based on these analyses, what have you learned about the spatial
distribution of parks in BC? – 1 point(s)</li>
</ul>
</div>


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