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<h1 class="title">Uncertainty with Palmer Penguins</h1>
</div>
<div class="quarto-title-meta">
</div>
</header>
<section id="setup" class="level2">
<h2 class="anchored" data-anchor-id="setup">Setup</h2>
<p>The following libraries are needed:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(palmerpenguins) <span class="co"># the data</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2) <span class="co"># for plotting</span></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(dplyr) <span class="co"># for data cleaning</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stderr">
<pre><code>
Attaching package: 'dplyr'</code></pre>
</div>
<div class="cell-output cell-output-stderr">
<pre><code>The following objects are masked from 'package:stats':
filter, lag</code></pre>
</div>
<div class="cell-output cell-output-stderr">
<pre><code>The following objects are masked from 'package:base':
intersect, setdiff, setequal, union</code></pre>
</div>
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggdist) <span class="co"># for visualizing distributions and uncertainty</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(distributional) <span class="co"># for creating distributions, e.g. dist_normal()</span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(broom) <span class="co"># for tidying model output: augment()</span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a><span class="co"># a nicer ggplot theme...</span></span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a><span class="fu">theme_set</span>(<span class="fu">theme_ggdist</span>())</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="the-data-penguins" class="level2">
<h2 class="anchored" data-anchor-id="the-data-penguins">The data — Penguins!</h2>
<p>We’ll be using the Palmer Penguins dataset, which you can learn more about <a href="https://allisonhorst.github.io/palmerpenguins/">here</a>.</p>
<p>It contains data on several species of penguins who live in Antarctica, and includes data on their body mass, sex, and dimensions of their bills and flippers:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">glimpse</span>(penguins)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>Rows: 344
Columns: 8
$ species <fct> Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adel…
$ island <fct> Torgersen, Torgersen, Torgersen, Torgersen, Torgerse…
$ bill_length_mm <dbl> 39.1, 39.5, 40.3, NA, 36.7, 39.3, 38.9, 39.2, 34.1, …
$ bill_depth_mm <dbl> 18.7, 17.4, 18.0, NA, 19.3, 20.6, 17.8, 19.6, 18.1, …
$ flipper_length_mm <int> 181, 186, 195, NA, 193, 190, 181, 195, 193, 190, 186…
$ body_mass_g <int> 3750, 3800, 3250, NA, 3450, 3650, 3625, 4675, 3475, …
$ sex <fct> male, female, female, NA, female, male, female, male…
$ year <int> 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007…</code></pre>
</div>
</div>
<p>For example, here is a simple scatter plot of body mass by sex and species:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>penguins <span class="sc">|></span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> body_mass_g, <span class="at">y =</span> species, <span class="at">color =</span> sex)) <span class="sc">+</span></span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_point</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stderr">
<pre><code>Warning: Removed 2 rows containing missing values (`geom_point()`).</code></pre>
</div>
<div class="cell-output-display">
<p><img src="penguins_files/figure-html/unnamed-chunk-3-1.png" class="img-fluid" width="672"></p>
</div>
</div>
<p>As you can see, it’s a bit hard to see what’s going on just using a scatterplot, because of the overlap between points.</p>
<p>Let’s use <code>ggdist::geom_dots()</code> with <code>position_dodge()</code> to make it easier to see…</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>penguins <span class="sc">|></span></span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> body_mass_g, <span class="at">y =</span> species, <span class="at">fill =</span> sex)) <span class="sc">+</span></span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_dots</span>(<span class="at">position =</span> <span class="st">"dodge"</span>, <span class="at">linewidth =</span> <span class="dv">0</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stderr">
<pre><code>Warning: Removed 2 rows containing missing values (`geom_dotsinterval()`).</code></pre>
</div>
<div class="cell-output-display">
<p><img src="penguins_files/figure-html/unnamed-chunk-4-1.png" class="img-fluid" width="672"></p>
</div>
</div>
<p>We can see a few missing data values in <code>sex</code> that we will remove for now:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>penguins_clean <span class="ot">=</span> penguins <span class="sc">|></span></span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(<span class="sc">!</span><span class="fu">is.na</span>(sex))</span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a>penguins_clean <span class="sc">|></span></span>
<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> body_mass_g, <span class="at">y =</span> species, <span class="at">fill =</span> sex)) <span class="sc">+</span></span>
<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_dots</span>(<span class="at">position =</span> <span class="st">"dodge"</span>, <span class="at">linewidth =</span> <span class="dv">0</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<p><img src="penguins_files/figure-html/unnamed-chunk-5-1.png" class="img-fluid" width="672"></p>
</div>
</div>
</section>
<section id="adding-a-model-and-showing-uncertainty" class="level2">
<h2 class="anchored" data-anchor-id="adding-a-model-and-showing-uncertainty">Adding a model and showing uncertainty</h2>
<p>Say we want an estimate of the average mass of a penguin, given its species and sex. We could fit a linear model to estimate this:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>m <span class="ot">=</span> <span class="fu">lm</span>(body_mass_g <span class="sc">~</span> species <span class="sc">*</span> sex, <span class="at">data =</span> penguins_clean)</span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>m</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>
Call:
lm(formula = body_mass_g ~ species * sex, data = penguins_clean)
Coefficients:
(Intercept) speciesChinstrap speciesGentoo
3368.8 158.4 1310.9
sexmale speciesChinstrap:sexmale speciesGentoo:sexmale
674.7 -262.9 130.4 </code></pre>
</div>
</div>
<p>Then, we can use the <code>broom</code> package to get estimates of the body mass for each combination of species and sex in the data. To do that, we’ll first create a prediction grid containing all combinations of the predictors we want to estimate mean body mass for:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>grid <span class="ot">=</span> penguins_clean <span class="sc">|></span></span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(species, sex) <span class="sc">|></span></span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">unique</span>()</span>
<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a>grid</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code># A tibble: 6 × 2
species sex
<fct> <fct>
1 Adelie male
2 Adelie female
3 Gentoo female
4 Gentoo male
5 Chinstrap female
6 Chinstrap male </code></pre>
</div>
</div>
<p>Then, we’ll use <code>broom::augment()</code> to get means (<code>.fitted</code>) and standard errors (<code>.se.fit</code>) for each combination of species and sex:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>predictions <span class="ot">=</span> <span class="fu">augment</span>(m, <span class="at">newdata =</span> grid, <span class="at">se_fit =</span> <span class="cn">TRUE</span>)</span>
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>predictions</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code># A tibble: 6 × 4
species sex .fitted .se.fit
<fct> <fct> <dbl> <dbl>
1 Adelie male 4043. 36.2
2 Adelie female 3369. 36.2
3 Gentoo female 4680. 40.6
4 Gentoo male 5485. 39.6
5 Chinstrap female 3527. 53.1
6 Chinstrap male 3939. 53.1</code></pre>
</div>
</div>
<p>Finally, since we’ll be using a Student t distribution to calculate intervals, we need the degrees of freedom of the fit:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>dof <span class="ot">=</span> <span class="fu">df.residual</span>(m)</span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a>dof</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code>[1] 327</code></pre>
</div>
</div>
<p>Now, we can generate a visulization of uncertainty in the mean body mass conditional on sex and speciies:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb21"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a>predictions <span class="sc">|></span></span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">y =</span> species, <span class="at">fill =</span> sex)) <span class="sc">+</span></span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">stat_halfeye</span>(<span class="fu">aes</span>(<span class="at">xdist =</span> <span class="fu">dist_student_t</span>(dof, .fitted, .se.fit)), <span class="at">scale =</span> <span class="fl">0.5</span>) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<p><img src="penguins_files/figure-html/unnamed-chunk-10-1.png" class="img-fluid" width="672"></p>
</div>
</div>
<p>We can combine the estimate of the mean with the raw data to see how they line up:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb22"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a>predictions <span class="sc">|></span></span>
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">y =</span> species, <span class="at">fill =</span> sex)) <span class="sc">+</span></span>
<span id="cb22-3"><a href="#cb22-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_swarm</span>(<span class="fu">aes</span>(<span class="at">x =</span> body_mass_g), <span class="at">data =</span> penguins_clean, <span class="at">position =</span> <span class="st">"dodge"</span>, <span class="at">linewidth =</span> <span class="dv">0</span>, <span class="at">height =</span> <span class="fl">0.7</span>, <span class="at">alpha =</span> <span class="fl">0.5</span>) <span class="sc">+</span></span>
<span id="cb22-4"><a href="#cb22-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">stat_pointinterval</span>(<span class="fu">aes</span>(<span class="at">xdist =</span> <span class="fu">dist_student_t</span>(dof, .fitted, .se.fit)), <span class="at">position =</span> <span class="st">"dodge"</span>, <span class="at">scale =</span> <span class="fl">0.5</span>, <span class="at">height =</span> <span class="fl">0.7</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<p><img src="penguins_files/figure-html/unnamed-chunk-11-1.png" class="img-fluid" width="672"></p>
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