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<body>

<h1 id="in-depth-1-comparison-of-point-estimates">In-Depth 1: Comparison of Point-Estimates</h1>
<ul>
<li><a href="#effect-point-estimates-in-the-bayesian-framework">Effect Point-Estimates in the Bayesian Framework</a>
<ul>
<li><a href="#introduction">Introduction</a></li>
<li><a href="#experiment-1-relationship-with-error-noise-and-sample-size">Experiment 1: Relationship with Error (Noise) and Sample Size</a>
<ul>
<li><a href="#methods">Methods</a></li>
<li><a href="#results">Results</a></li>
</ul></li>
<li><a href="#experiment-2-relationship-with-sampling-characteristics">Experiment 2: Relationship with Sampling Characteristics</a>
<ul>
<li><a href="#methods-1">Methods</a></li>
<li><a href="#results-1">Results</a></li>
</ul></li>
<li><a href="#experiment-3-relationship-with-priors-specification">Experiment 3: Relationship with Priors Specification</a></li>
<li><a href="#discussion">Discussion</a></li>
</ul></li>
</ul>
<p>This vignette can be referred to by citing the package:</p>
<ul>
<li>Makowski, D., Ben-Shachar, M. S., &amp; Lüdecke, D. (2019). <em>bayestestR: Describing Effects and their Uncertainty, Existence and Significance within the Bayesian Framework</em>. Journal of Open Source Software, 4(40), 1541. <a href="https://doi.org/10.21105/joss.01541">https://doi.org/10.21105/joss.01541</a></li>
</ul>
<hr />
<h1 id="effect-point-estimates-in-the-bayesian-framework">Effect Point-Estimates in the Bayesian Framework</h1>
<h2 id="introduction">Introduction</h2>
<p>One of the main difference between the Bayesian and the frequentist frameworks is that the former returns a probability distribution of each effect (<em>i.e.</em>, parameter of interest of a model, such as a regression slope) instead of a single value. However, there is still a need and demand, for reporting or use in further analysis, for a single value (<strong>point-estimate</strong>) that best characterise the underlying posterior distribution.</p>
<p>There are three main indices used in the literature for effect estimation: the <strong>mean</strong>, the <strong>median</strong> or the <strong>MAP</strong> (Maximum A Posteriori) estimate (roughly corresponding to the mode (the “peak”) of the distribution). Unfortunately, there is no consensus about which one to use, as no systematic comparison has ever been done.</p>
<p>In the present work, we will compare these three point-estimates of effect between themselves, as well as with the widely known <strong>beta</strong>, extracted from a comparable frequentist model. With this comparison, we expect to draw bridges and relationships between the two frameworks, helping and easing the transition for the public.</p>
<h2 id="experiment-1-relationship-with-error-noise-and-sample-size">Experiment 1: Relationship with Error (Noise) and Sample Size</h2>
<h3 id="methods">Methods</h3>
<p>The simulation aimed at modulating the following characteristics:</p>
<ul>
<li><strong>Model type</strong>: linear or logistic.</li>
<li><strong>“True” effect</strong> (original regression coefficient from which data is drawn): Can be 1 or 0 (no effect).</li>
<li><strong>Sample size</strong>: From 20 to 100 by steps of 10.</li>
<li><strong>Error</strong>: Gaussian noise applied to the predictor with SD uniformly spread between 0.33 and 6.66 (with 1000 different values).</li>
</ul>
<p>We generated a dataset for each combination of these characteristics, resulting in a total of <code>2 * 2 * 9 * 1000 = 36000</code> Bayesian and frequentist models. The code used for generation is avaible <a href="https://easystats.github.io/circus/articles/bayesian_indices.html">here</a> (please note that it takes usually several days/weeks to complete).</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">library</span>(ggplot2)</a>
<a class="sourceLine" id="cb1-2" title="2"><span class="kw">library</span>(dplyr)</a>
<a class="sourceLine" id="cb1-3" title="3"><span class="kw">library</span>(tidyr)</a>
<a class="sourceLine" id="cb1-4" title="4"><span class="kw">library</span>(see)</a>
<a class="sourceLine" id="cb1-5" title="5"></a>
<a class="sourceLine" id="cb1-6" title="6">df &lt;-<span class="st"> </span><span class="kw">read.csv</span>(<span class="st">&quot;https://raw.github.com/easystats/circus/master/data/bayesSim_study1.csv&quot;</span>)</a></code></pre></div>
<h3 id="results">Results</h3>
<h4 id="sensitivity-to-noise">Sensitivity to Noise</h4>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" title="1">df <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb2-2" title="2"><span class="st">  </span><span class="kw">select</span>(error, true_effect, outcome_type, Coefficient, Median, Mean, MAP) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb2-3" title="3"><span class="st">  </span><span class="kw">gather</span>(estimate, value, <span class="op">-</span>error, <span class="op">-</span>true_effect, <span class="op">-</span>outcome_type) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb2-4" title="4"><span class="st">  </span><span class="kw">mutate</span>(<span class="dt">temp =</span> <span class="kw">as.factor</span>(<span class="kw">cut</span>(error, <span class="dv">10</span>, <span class="dt">labels =</span> <span class="ot">FALSE</span>))) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb2-5" title="5"><span class="st">  </span><span class="kw">group_by</span>(temp) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb2-6" title="6"><span class="st">  </span><span class="kw">mutate</span>(<span class="dt">error_group =</span> <span class="kw">round</span>(<span class="kw">mean</span>(error), <span class="dv">1</span>)) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb2-7" title="7"><span class="st">  </span><span class="kw">ungroup</span>() <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb2-8" title="8"><span class="st">  </span><span class="kw">filter</span>(value <span class="op">&lt;</span><span class="st"> </span><span class="dv">6</span>) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb2-9" title="9"><span class="st">  </span><span class="kw">ggplot</span>(<span class="kw">aes</span>(<span class="dt">x =</span> error_group, <span class="dt">y =</span> value, <span class="dt">fill =</span> estimate, <span class="dt">group =</span> <span class="kw">interaction</span>(estimate, error_group))) <span class="op">+</span></a>
<a class="sourceLine" id="cb2-10" title="10"><span class="st">  </span><span class="co"># geom_hline(yintercept = 0) +</span></a>
<a class="sourceLine" id="cb2-11" title="11"><span class="st">  </span><span class="co"># geom_point(alpha=0.05, size=2, stroke = 0, shape=16) +</span></a>
<a class="sourceLine" id="cb2-12" title="12"><span class="st">  </span><span class="co"># geom_smooth(method=&quot;loess&quot;) +</span></a>
<a class="sourceLine" id="cb2-13" title="13"><span class="st">  </span><span class="kw">geom_boxplot</span>(<span class="dt">outlier.shape=</span><span class="ot">NA</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb2-14" title="14"><span class="st">  </span><span class="kw">theme_modern</span>() <span class="op">+</span></a>
<a class="sourceLine" id="cb2-15" title="15"><span class="st">  </span><span class="kw">scale_fill_manual</span>(<span class="dt">values =</span> <span class="kw">c</span>(<span class="st">&quot;Coefficient&quot;</span> =<span class="st"> &quot;#607D8B&quot;</span>, <span class="st">&quot;MAP&quot;</span> =<span class="st"> &quot;#795548&quot;</span>, <span class="st">&quot;Mean&quot;</span> =<span class="st"> &quot;#FF9800&quot;</span>, <span class="st">&quot;Median&quot;</span> =<span class="st"> &quot;#FFEB3B&quot;</span>),</a>
<a class="sourceLine" id="cb2-16" title="16">                    <span class="dt">name =</span> <span class="st">&quot;Index&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb2-17" title="17"><span class="st">  </span><span class="kw">ylab</span>(<span class="st">&quot;Point-estimate&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb2-18" title="18"><span class="st">  </span><span class="kw">xlab</span>(<span class="st">&quot;Noise&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb2-19" title="19"><span class="st">  </span><span class="kw">facet_wrap</span>(<span class="op">~</span><span class="st"> </span>outcome_type <span class="op">*</span><span class="st"> </span>true_effect, <span class="dt">scales=</span><span class="st">&quot;free&quot;</span>) </a></code></pre></div>
<p><img 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" /><!-- --></p>
<h4 id="sensitivity-to-sample-size">Sensitivity to Sample Size</h4>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb3-1" title="1">df <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb3-2" title="2"><span class="st">  </span><span class="kw">select</span>(sample_size, true_effect, outcome_type, Coefficient, Median, Mean, MAP) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb3-3" title="3"><span class="st">  </span><span class="kw">gather</span>(estimate, value, <span class="op">-</span>sample_size, <span class="op">-</span>true_effect, <span class="op">-</span>outcome_type) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb3-4" title="4"><span class="st">  </span><span class="kw">mutate</span>(<span class="dt">temp =</span> <span class="kw">as.factor</span>(<span class="kw">cut</span>(sample_size, <span class="dv">10</span>, <span class="dt">labels =</span> <span class="ot">FALSE</span>))) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb3-5" title="5"><span class="st">  </span><span class="kw">group_by</span>(temp) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb3-6" title="6"><span class="st">  </span><span class="kw">mutate</span>(<span class="dt">size_group =</span> <span class="kw">round</span>(<span class="kw">mean</span>(sample_size))) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb3-7" title="7"><span class="st">  </span><span class="kw">ungroup</span>() <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb3-8" title="8"><span class="st">  </span><span class="kw">filter</span>(value <span class="op">&lt;</span><span class="st"> </span><span class="dv">6</span>) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb3-9" title="9"><span class="st">  </span><span class="kw">ggplot</span>(<span class="kw">aes</span>(<span class="dt">x =</span> size_group, <span class="dt">y =</span> value, <span class="dt">fill =</span> estimate, <span class="dt">group =</span> <span class="kw">interaction</span>(estimate, size_group))) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-10" title="10"><span class="st">  </span><span class="co"># geom_hline(yintercept = 0) +</span></a>
<a class="sourceLine" id="cb3-11" title="11"><span class="st">  </span><span class="co"># geom_point(alpha=0.05, size=2, stroke = 0, shape=16) +</span></a>
<a class="sourceLine" id="cb3-12" title="12"><span class="st">  </span><span class="co"># geom_smooth(method=&quot;loess&quot;) +</span></a>
<a class="sourceLine" id="cb3-13" title="13"><span class="st">  </span><span class="kw">geom_boxplot</span>(<span class="dt">outlier.shape=</span><span class="ot">NA</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-14" title="14"><span class="st">  </span><span class="kw">theme_modern</span>() <span class="op">+</span></a>
<a class="sourceLine" id="cb3-15" title="15"><span class="st">  </span><span class="kw">scale_fill_manual</span>(<span class="dt">values =</span> <span class="kw">c</span>(<span class="st">&quot;Coefficient&quot;</span> =<span class="st"> &quot;#607D8B&quot;</span>, <span class="st">&quot;MAP&quot;</span> =<span class="st"> &quot;#795548&quot;</span>, <span class="st">&quot;Mean&quot;</span> =<span class="st"> &quot;#FF9800&quot;</span>, <span class="st">&quot;Median&quot;</span> =<span class="st"> &quot;#FFEB3B&quot;</span>),</a>
<a class="sourceLine" id="cb3-16" title="16">                    <span class="dt">name =</span> <span class="st">&quot;Index&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-17" title="17"><span class="st">  </span><span class="kw">ylab</span>(<span class="st">&quot;Point-estimate&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-18" title="18"><span class="st">  </span><span class="kw">xlab</span>(<span class="st">&quot;Sample size&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-19" title="19"><span class="st">  </span><span class="kw">facet_wrap</span>(<span class="op">~</span><span class="st"> </span>outcome_type <span class="op">*</span><span class="st"> </span>true_effect, <span class="dt">scales=</span><span class="st">&quot;free&quot;</span>)</a></code></pre></div>
<p><img 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" /><!-- --></p>
<h4 id="statistical-modelling">Statistical Modelling</h4>
<p>We fitted a (frequentist) multiple linear regression to statistically test the the predict the presence or absence of effect with the estimates as well as their interaction with noise and sample size.</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" title="1">df <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb4-2" title="2"><span class="st">  </span><span class="kw">select</span>(sample_size, error, true_effect, outcome_type, Coefficient, Median, Mean, MAP) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb4-3" title="3"><span class="st">  </span><span class="kw">gather</span>(estimate, value, <span class="op">-</span>sample_size, <span class="op">-</span>error, <span class="op">-</span>true_effect, <span class="op">-</span>outcome_type) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb4-4" title="4"><span class="st">  </span><span class="kw">glm</span>(true_effect <span class="op">~</span><span class="st"> </span>outcome_type <span class="op">/</span><span class="st"> </span>estimate <span class="op">/</span><span class="st"> </span>value, <span class="dt">data=</span>., <span class="dt">family=</span><span class="st">&quot;binomial&quot;</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb4-5" title="5"><span class="st">  </span>broom<span class="op">::</span><span class="kw">tidy</span>() <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb4-6" title="6"><span class="st">  </span><span class="kw">select</span>(term, estimate, <span class="dt">p=</span>p.value) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb4-7" title="7"><span class="st">  </span><span class="kw">filter</span>(stringr<span class="op">::</span><span class="kw">str_detect</span>(term, <span class="st">&#39;outcome_type&#39;</span>),</a>
<a class="sourceLine" id="cb4-8" title="8">         stringr<span class="op">::</span><span class="kw">str_detect</span>(term, <span class="st">&#39;:value&#39;</span>)) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb4-9" title="9"><span class="st">  </span><span class="kw">arrange</span>(<span class="kw">desc</span>(estimate)) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb4-10" title="10"><span class="st">  </span>knitr<span class="op">::</span><span class="kw">kable</span>(<span class="dt">digits=</span><span class="dv">2</span>) </a></code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">term</th>
<th align="right">estimate</th>
<th align="right">p</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">outcome_typelinear:estimateMean:value</td>
<td align="right">10.8</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typelinear:estimateMedian:value</td>
<td align="right">10.8</td>
<td align="right">0</td>
</tr>
<tr class="odd">
<td align="left">outcome_typelinear:estimateMAP:value</td>
<td align="right">10.7</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typelinear:estimateCoefficient:value</td>
<td align="right">10.5</td>
<td align="right">0</td>
</tr>
<tr class="odd">
<td align="left">outcome_typebinary:estimateMAP:value</td>
<td align="right">4.4</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typebinary:estimateMedian:value</td>
<td align="right">4.3</td>
<td align="right">0</td>
</tr>
<tr class="odd">
<td align="left">outcome_typebinary:estimateMean:value</td>
<td align="right">4.2</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typebinary:estimateCoefficient:value</td>
<td align="right">3.9</td>
<td align="right">0</td>
</tr>
</tbody>
</table>
<p>This suggests that, in order to delineate between the presence and the absence of an effect, compared to the frequentist’s beta:</p>
<ul>
<li>For linear models, the <strong>Mean</strong> was the better predictor, closely followed by the <strong>Median</strong>, the <strong>MAP</strong> and the frequentist <strong>Coefficient</strong>.</li>
<li>For logistic models, the <strong>MAP</strong> was the better predictor, followed by the <strong>Median</strong>, the <strong>Mean</strong> and, behind, the frequentist <strong>Coefficient</strong>.</li>
</ul>
<p>Overall, the <strong>median</strong> seems to be appears as a safe and approriate choice, maintaining a a high performance accross different types of models.</p>
<!-- ```{r, message=FALSE, warning=FALSE} -->

<!-- df %>% -->

<!--   select(sample_size, error, true_effect, outcome_type, beta, Median, Mean, MAP) %>% -->

<!--   gather(estimate, value, -sample_size, -error, -true_effect, -outcome_type) %>% -->

<!--   glm(true_effect ~ outcome_type / value * estimate * sample_size * error, data=., family="binomial") %>% -->

<!--   broom::tidy() %>% -->

<!--   select(term, estimate, p=p.value) %>% -->

<!--   filter(stringr::str_detect(term, 'outcome_type'), -->

<!--          stringr::str_detect(term, ':value')) %>% -->

<!--   mutate( -->

<!--     sample_size = stringr::str_detect(term, 'sample_size'), -->

<!--     error = stringr::str_detect(term, 'error'), -->

<!--     term = stringr::str_remove(term, "estimate"), -->

<!--     term = stringr::str_remove(term, "outcome_type"), -->

<!--     p = paste0(sprintf("%.2f", p), ifelse(p < .001, "***", ifelse(p < .01, "**", ifelse(p < .05, "*", ""))))) %>% -->

<!--   arrange(sample_size, error, term) %>%  -->

<!--   select(-sample_size, -error) %>%  -->

<!--   knitr::kable(digits=2)  -->

<!-- ``` -->

<!-- This suggests that, in order to delineate between the presence and the absence of an effect, compared to the frequentist's beta: -->

<!-- - For linear Models; -->

<!--   - The **mean**, followed closely by the **median**, and the **MAP** estimate had a superior performance, altough not significantly. -->

<!--   - The **mean**, followed closely by the **median**, and the **MAP** estimate, were less affected by noise, altough not significantly. -->

<!--   - No difference for the sensitivity to sample size was found. -->

<!-- - For logistic models: -->

<!--   - The **MAP** estimate, followed by the **median** and the **mean**, estimate had a superior performance. -->

<!--   - The **MAP** estimate, followed by the **median**, and the **mean**, were less affected by noise, altough not significantly. -->

<!--   - The **MAP** estimate, followed by the **mean**, and the **median**, were less affected by sample size, altough not significantly. -->

<h2 id="experiment-2-relationship-with-sampling-characteristics">Experiment 2: Relationship with Sampling Characteristics</h2>
<h3 id="methods-1">Methods</h3>
<p>The simulation aimed at modulating the following characteristics:</p>
<ul>
<li><strong>Model type</strong>: linear or logistic.</li>
<li><strong>“True” effect</strong> (original regression coefficient from which data is drawn): Can be 1 or 0 (no effect).</li>
<li><strong>draws</strong>: from 10 to 5000 by step of 5 (1000 iterations).</li>
<li><strong>warmup</strong>: Ratio of warmup iterations. from 1/10 to 9/10 by step of 0.1 (9 iterations).</li>
</ul>
<p>We generated 3 datasets for each combination of these characteristics, resulting in a total of <code>2 * 2 * 8 * 40 * 9 * 3 = 34560</code> Bayesian and frequentist models. The code used for generation is avaible <a href="https://easystats.github.io/circus/articles/bayesian_indices.html">here</a> (please note that it takes usually several days/weeks to complete).</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" title="1">df &lt;-<span class="st"> </span><span class="kw">read.csv</span>(<span class="st">&quot;https://raw.github.com/easystats/circus/master/data/bayesSim_study2.csv&quot;</span>)</a></code></pre></div>
<h3 id="results-1">Results</h3>
<h4 id="sensitivity-to-number-of-iterations">Sensitivity to number of iterations</h4>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" title="1">df <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb6-2" title="2"><span class="st">  </span><span class="kw">select</span>(iterations, true_effect, outcome_type, beta, Median, Mean, MAP) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb6-3" title="3"><span class="st">  </span><span class="kw">gather</span>(estimate, value, <span class="op">-</span>iterations, <span class="op">-</span>true_effect, <span class="op">-</span>outcome_type) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb6-4" title="4"><span class="st">  </span><span class="kw">mutate</span>(<span class="dt">temp =</span> <span class="kw">as.factor</span>(<span class="kw">cut</span>(iterations, <span class="dv">5</span>, <span class="dt">labels =</span> <span class="ot">FALSE</span>))) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb6-5" title="5"><span class="st">  </span><span class="kw">group_by</span>(temp) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb6-6" title="6"><span class="st">  </span><span class="kw">mutate</span>(<span class="dt">iterations_group =</span> <span class="kw">round</span>(<span class="kw">mean</span>(iterations), <span class="dv">1</span>)) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb6-7" title="7"><span class="st">  </span><span class="kw">ungroup</span>() <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb6-8" title="8"><span class="st">  </span><span class="kw">filter</span>(value <span class="op">&lt;</span><span class="st"> </span><span class="dv">6</span>) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb6-9" title="9"><span class="st">  </span><span class="kw">ggplot</span>(<span class="kw">aes</span>(<span class="dt">x =</span> iterations_group, <span class="dt">y =</span> value, <span class="dt">fill =</span> estimate, <span class="dt">group =</span> <span class="kw">interaction</span>(estimate, iterations_group))) <span class="op">+</span></a>
<a class="sourceLine" id="cb6-10" title="10"><span class="st">  </span><span class="kw">geom_boxplot</span>(<span class="dt">outlier.shape=</span><span class="ot">NA</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb6-11" title="11"><span class="st">  </span><span class="kw">theme_classic</span>() <span class="op">+</span></a>
<a class="sourceLine" id="cb6-12" title="12"><span class="st">  </span><span class="kw">scale_fill_manual</span>(<span class="dt">values =</span> <span class="kw">c</span>(<span class="st">&quot;beta&quot;</span> =<span class="st"> &quot;#607D8B&quot;</span>, <span class="st">&quot;MAP&quot;</span> =<span class="st"> &quot;#795548&quot;</span>, <span class="st">&quot;Mean&quot;</span> =<span class="st"> &quot;#FF9800&quot;</span>, <span class="st">&quot;Median&quot;</span> =<span class="st"> &quot;#FFEB3B&quot;</span>),</a>
<a class="sourceLine" id="cb6-13" title="13">                    <span class="dt">name =</span> <span class="st">&quot;Index&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb6-14" title="14"><span class="st">  </span><span class="kw">ylab</span>(<span class="st">&quot;Point-estimate of the true value 0</span><span class="ch">\n</span><span class="st">&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb6-15" title="15"><span class="st">  </span><span class="kw">xlab</span>(<span class="st">&quot;</span><span class="ch">\n</span><span class="st">Number of Iterations&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb6-16" title="16"><span class="st">  </span><span class="kw">facet_wrap</span>(<span class="op">~</span><span class="st"> </span>outcome_type <span class="op">*</span><span class="st"> </span>true_effect, <span class="dt">scales=</span><span class="st">&quot;free&quot;</span>) </a></code></pre></div>
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" /><!-- --></p>
<h4 id="sensitivity-to-warmup-ratio">Sensitivity to warmup ratio</h4>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" title="1">df <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb7-2" title="2"><span class="st">  </span><span class="kw">mutate</span>(<span class="dt">warmup =</span> warmup <span class="op">/</span><span class="st"> </span>iterations) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb7-3" title="3"><span class="st">  </span><span class="kw">select</span>(warmup, true_effect, outcome_type, beta, Median, Mean, MAP) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb7-4" title="4"><span class="st">  </span><span class="kw">gather</span>(estimate, value, <span class="op">-</span>warmup, <span class="op">-</span>true_effect, <span class="op">-</span>outcome_type) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb7-5" title="5"><span class="st">  </span><span class="kw">mutate</span>(<span class="dt">temp =</span> <span class="kw">as.factor</span>(<span class="kw">cut</span>(warmup, <span class="dv">3</span>, <span class="dt">labels =</span> <span class="ot">FALSE</span>))) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb7-6" title="6"><span class="st">  </span><span class="kw">group_by</span>(temp) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb7-7" title="7"><span class="st">  </span><span class="kw">mutate</span>(<span class="dt">warmup_group =</span> <span class="kw">round</span>(<span class="kw">mean</span>(warmup), <span class="dv">1</span>)) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb7-8" title="8"><span class="st">  </span><span class="kw">ungroup</span>() <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb7-9" title="9"><span class="st">  </span><span class="kw">filter</span>(value <span class="op">&lt;</span><span class="st"> </span><span class="dv">6</span>) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb7-10" title="10"><span class="st">  </span><span class="kw">ggplot</span>(<span class="kw">aes</span>(<span class="dt">x =</span> warmup_group, <span class="dt">y =</span> value, <span class="dt">fill =</span> estimate, <span class="dt">group =</span> <span class="kw">interaction</span>(estimate, warmup_group))) <span class="op">+</span></a>
<a class="sourceLine" id="cb7-11" title="11"><span class="st">  </span><span class="kw">geom_boxplot</span>(<span class="dt">outlier.shape=</span><span class="ot">NA</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb7-12" title="12"><span class="st">  </span><span class="kw">theme_classic</span>() <span class="op">+</span></a>
<a class="sourceLine" id="cb7-13" title="13"><span class="st">  </span><span class="kw">scale_fill_manual</span>(<span class="dt">values =</span> <span class="kw">c</span>(<span class="st">&quot;beta&quot;</span> =<span class="st"> &quot;#607D8B&quot;</span>, <span class="st">&quot;MAP&quot;</span> =<span class="st"> &quot;#795548&quot;</span>, <span class="st">&quot;Mean&quot;</span> =<span class="st"> &quot;#FF9800&quot;</span>, <span class="st">&quot;Median&quot;</span> =<span class="st"> &quot;#FFEB3B&quot;</span>),</a>
<a class="sourceLine" id="cb7-14" title="14">                    <span class="dt">name =</span> <span class="st">&quot;Index&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb7-15" title="15"><span class="st">  </span><span class="kw">ylab</span>(<span class="st">&quot;Point-estimate of the true value 0</span><span class="ch">\n</span><span class="st">&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb7-16" title="16"><span class="st">  </span><span class="kw">xlab</span>(<span class="st">&quot;</span><span class="ch">\n</span><span class="st">Number of Iterations&quot;</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb7-17" title="17"><span class="st">  </span><span class="kw">facet_wrap</span>(<span class="op">~</span><span class="st"> </span>outcome_type <span class="op">*</span><span class="st"> </span>true_effect, <span class="dt">scales=</span><span class="st">&quot;free&quot;</span>) </a></code></pre></div>
<p><img 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" /><!-- --></p>
<h2 id="experiment-3-relationship-with-priors-specification">Experiment 3: Relationship with Priors Specification</h2>
<h2 id="discussion">Discussion</h2>
<p>Conclusions can be found in the <a href="https://easystats.github.io/bayestestR/articles/guidelines.html">guidelines section</a>.</p>

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