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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>Understand and Describe Bayesian Models and Posterior Distributions using bayestestR</em>. Available from <a href="https://github.com/easystats/bayestestR">https://github.com/easystats/bayestestR</a>. DOI: <a href="https://zenodo.org/record/2556486">10.5281/zenodo.2556486</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"></a>
<a class="sourceLine" id="cb1-5" title="5">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, beta, 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_classic</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;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="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 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="cb2-18" title="18"><span class="st">  </span><span class="kw">xlab</span>(<span class="st">&quot;</span><span class="ch">\n</span><span class="st">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, beta, 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_classic</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;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="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">xlab</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="cb3-18" title="18"><span class="st">  </span><span class="kw">ylab</span>(<span class="st">&quot;</span><span class="ch">\n</span><span class="st">Noise&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, beta, 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>value <span class="op">*</span><span class="st"> </span>estimate <span class="op">*</span><span class="st"> </span>sample_size <span class="op">*</span><span class="st"> </span>error, <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">mutate</span>(</a>
<a class="sourceLine" id="cb4-10" title="10">    <span class="dt">sample_size =</span> stringr<span class="op">::</span><span class="kw">str_detect</span>(term, <span class="st">&#39;sample_size&#39;</span>),</a>
<a class="sourceLine" id="cb4-11" title="11">    <span class="dt">error =</span> stringr<span class="op">::</span><span class="kw">str_detect</span>(term, <span class="st">&#39;error&#39;</span>),</a>
<a class="sourceLine" id="cb4-12" title="12">    <span class="dt">term =</span> stringr<span class="op">::</span><span class="kw">str_remove</span>(term, <span class="st">&quot;estimate&quot;</span>),</a>
<a class="sourceLine" id="cb4-13" title="13">    <span class="dt">term =</span> stringr<span class="op">::</span><span class="kw">str_remove</span>(term, <span class="st">&quot;outcome_type&quot;</span>),</a>
<a class="sourceLine" id="cb4-14" title="14">    <span class="dt">p =</span> <span class="kw">paste0</span>(<span class="kw">sprintf</span>(<span class="st">&quot;%.2f&quot;</span>, p), <span class="kw">ifelse</span>(p <span class="op">&lt;</span><span class="st"> </span><span class="fl">.001</span>, <span class="st">&quot;***&quot;</span>, <span class="kw">ifelse</span>(p <span class="op">&lt;</span><span class="st"> </span><span class="fl">.01</span>, <span class="st">&quot;**&quot;</span>, <span class="kw">ifelse</span>(p <span class="op">&lt;</span><span class="st"> </span><span class="fl">.05</span>, <span class="st">&quot;*&quot;</span>, <span class="st">&quot;&quot;</span>))))) <span class="op">%&gt;%</span></a>
<a class="sourceLine" id="cb4-15" title="15"><span class="st">  </span><span class="kw">arrange</span>(sample_size, error, term) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb4-16" title="16"><span class="st">  </span><span class="kw">select</span>(<span class="op">-</span>sample_size, <span class="op">-</span>error) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb4-17" title="17"><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="left">p</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">binary:value</td>
<td align="right">2.72</td>
<td align="left">0.05*</td>
</tr>
<tr class="even">
<td align="left">binary:value:Mean</td>
<td align="right">-0.18</td>
<td align="left">0.93</td>
</tr>
<tr class="odd">
<td align="left">binary:value:Median</td>
<td align="right">-0.08</td>
<td align="left">0.97</td>
</tr>
<tr class="even">
<td align="left">binary:value:beta</td>
<td align="right">-1.08</td>
<td align="left">0.56</td>
</tr>
<tr class="odd">
<td align="left">linear:value</td>
<td align="right">6.73</td>
<td align="left">0.03*</td>
</tr>
<tr class="even">
<td align="left">linear:value:Mean</td>
<td align="right">-0.31</td>
<td align="left">0.94</td>
</tr>
<tr class="odd">
<td align="left">linear:value:Median</td>
<td align="right">-0.39</td>
<td align="left">0.93</td>
</tr>
<tr class="even">
<td align="left">linear:value:beta</td>
<td align="right">-1.03</td>
<td align="left">0.81</td>
</tr>
<tr class="odd">
<td align="left">binary:value:Mean:error</td>
<td align="right">0.03</td>
<td align="left">0.94</td>
</tr>
<tr class="even">
<td align="left">binary:value:Median:error</td>
<td align="right">0.01</td>
<td align="left">0.98</td>
</tr>
<tr class="odd">
<td align="left">binary:value:beta:error</td>
<td align="right">0.19</td>
<td align="left">0.64</td>
</tr>
<tr class="even">
<td align="left">binary:value:error</td>
<td align="right">-0.74</td>
<td align="left">0.01*</td>
</tr>
<tr class="odd">
<td align="left">linear:value:Mean:error</td>
<td align="right">0.04</td>
<td align="left">0.96</td>
</tr>
<tr class="even">
<td align="left">linear:value:Median:error</td>
<td align="right">0.06</td>
<td align="left">0.95</td>
</tr>
<tr class="odd">
<td align="left">linear:value:beta:error</td>
<td align="right">0.17</td>
<td align="left">0.85</td>
</tr>
<tr class="even">
<td align="left">linear:value:error</td>
<td align="right">-1.91</td>
<td align="left">0.00**</td>
</tr>
<tr class="odd">
<td align="left">binary:value:Mean:sample_size</td>
<td align="right">0.00</td>
<td align="left">0.96</td>
</tr>
<tr class="even">
<td align="left">binary:value:Median:sample_size</td>
<td align="right">0.00</td>
<td align="left">0.97</td>
</tr>
<tr class="odd">
<td align="left">binary:value:beta:sample_size</td>
<td align="right">0.01</td>
<td align="left">0.87</td>
</tr>
<tr class="even">
<td align="left">binary:value:sample_size</td>
<td align="right">0.12</td>
<td align="left">0.00***</td>
</tr>
<tr class="odd">
<td align="left">linear:value:Mean:sample_size</td>
<td align="right">0.01</td>
<td align="left">0.93</td>
</tr>
<tr class="even">
<td align="left">linear:value:Median:sample_size</td>
<td align="right">0.01</td>
<td align="left">0.92</td>
</tr>
<tr class="odd">
<td align="left">linear:value:beta:sample_size</td>
<td align="right">0.02</td>
<td align="left">0.88</td>
</tr>
<tr class="even">
<td align="left">linear:value:sample_size</td>
<td align="right">0.26</td>
<td align="left">0.00***</td>
</tr>
<tr class="odd">
<td align="left">binary:value:Mean:sample_size:error</td>
<td align="right">0.00</td>
<td align="left">0.98</td>
</tr>
<tr class="even">
<td align="left">binary:value:Median:sample_size:error</td>
<td align="right">0.00</td>
<td align="left">0.97</td>
</tr>
<tr class="odd">
<td align="left">binary:value:beta:sample_size:error</td>
<td align="right">0.00</td>
<td align="left">0.86</td>
</tr>
<tr class="even">
<td align="left">binary:value:sample_size:error</td>
<td align="right">0.00</td>
<td align="left">0.64</td>
</tr>
<tr class="odd">
<td align="left">linear:value:Mean:sample_size:error</td>
<td align="right">0.00</td>
<td align="left">0.97</td>
</tr>
<tr class="even">
<td align="left">linear:value:Median:sample_size:error</td>
<td align="right">0.00</td>
<td align="left">0.96</td>
</tr>
<tr class="odd">
<td align="left">linear:value:beta:sample_size:error</td>
<td align="right">0.00</td>
<td align="left">0.91</td>
</tr>
<tr class="even">
<td align="left">linear:value:sample_size:error</td>
<td align="right">0.00</td>
<td align="left">0.93</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><p>For linear Models;</p>
<ul>
<li>The <strong>mean</strong>, followed closely by the <strong>median</strong>, and the <strong>MAP</strong> estimate had a superior performance, altough not significantly.</li>
<li>The <strong>mean</strong>, followed closely by the <strong>median</strong>, and the <strong>MAP</strong> estimate, were less affected by noise, altough not significantly.</li>
<li>No difference for the sensitivity to sample size was found.</li>
</ul></li>
<li><p>For logistic models:</p>
<ul>
<li>The <strong>MAP</strong> estimate, followed by the <strong>median</strong> and the <strong>mean</strong>, estimate had a superior performance.</li>
<li>The <strong>MAP</strong> estimate, followed by the <strong>median</strong>, and the <strong>mean</strong>, were less affected by noise, altough not significantly.</li>
<li>The <strong>MAP</strong> estimate, followed by the <strong>mean</strong>, and the <strong>median</strong>, were less affected by sample size, altough not significantly.</li>
</ul></li>
</ul>
<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>
<p><img 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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 src="data:image/png;base64,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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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