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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"><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, 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_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;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&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, 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_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;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">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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IYBj2uTuUmLqOKxX3jQPnZVrzbhcezt49pkbtKi5t2J4/HsxOWxVlFLf7U29cnc3jws1j5ebYvnfo9bt8AKmh63qtDMvwOEGfvc6YfO08q0nmDi8RB2Hn/6dX0Tj71COR+IRpHWrJtmjZjpDZPMtOQTH/QcUC8pkx5rXS1nGPVYNI13DWSrneEwEE2PFfl3p0ibMXu2dRiqfBm417we7x/CqzYhHifDuPZxppt/DRqKx4NxVa+G2cHjQc+P+9oE0Xi8Wi6XRf90NqafC2YnRY8r+v7CMQeMxuMt6xHPnWAGekblxO9x9UF/3xQeZ/WKtP44ELBPXzSS8djKASP1+OqkKIZXuuMywTq9tSM8nnLA+Dx2kzj00NtbgcdTDojHMAu9Tw/i8LgHPPY8ceih92n+wBFKyXvcOC4ewxzojMoZk3/bN+f3WI/ZD+gGPI4WnVE5swszf1p+HtA0eBwtOqNy/PZ4dvB4/sShB51ROZ567AchnTwex4vGqBzzHoMT8Dhi+kflxFeIeszF4kHzo9Pr35tJG4+TAY8dM5/Hb+8vrv/h6W0zSeOxX+CxY2bz+OK9Z+fXv391y5TIeOwTeOyYwuOfn94+XSxKe4vX/1a8O18sFrly5+89ywvSke7Vg5sfI8s9Lv83Ah77BB47Rnic//P2/o1c42vPc4ML3XJ/i7Lz56c3xpfP9eAWN4PS4/wIRsBjn+jwWONDmIzwuDD1tKj1FpXs0031t3Du4r3/+atnI9OWy+MbpcdhdKLBQPDYMcLjvCguDCtK4azQ7aJ8U2p9urgxNm25fbx4kCd8vt8cN5E4OIZoOEb2uKz0lroJHrR2hOmy11+9WLw3tmzvSRzcQjQc01UeF+Rt59EtWp4fJwPRcIzkcaN9XNh8fu1/j+2uxuN0IBqOkTzOTnNzLxbVm6IH++39B9nF2AJZ6q/+S1HC018dJUTDMbLHxfPja/998/z4hvhQ/HgEeJwMRCNitsHNG9lbGM8VI0QjYtrKYyuJg2uIRsTY7eeCmSAaPmHTKVVw6xvl4+McU+1jAJgFyePi8fSN7NXoQZ4A4ITm9yQuiu9JjB7lCQAuaHr86s+fl/8DQDg0v39c9FnjMUBYSO3jYgDI6W1z8wgAwCzIfeSn179/e5/uaoDAYHAAwOwYn6rBD4+vTpbLZbH6weVx/mZ5r/cXBrFLdC1N6GyG9VLwxMbJv/ndd9UxxHnb+AP2IBoKzEUjTo+vTvLLsSquuVhbzDDbRBsLLBjk8tjKyV8el6szbc/b3h9Qg2gokzUWDbseuxrPtVtRbLc6oEE2iTYXPDJIuRqa8ZPP7/dFktvztvgH1CAa7ZiMhlWPxVx+zihubSsrYa0SbS5AaI43D49qxzHFenlUZsbtedv7A1oOTjRkTERDa734UTTHgTjkLL8iZ59VTTOjCVeJNhcENniEMk0LJy9yzua87f0B+xCNfSZH4/CLBsLjn59WXxW+EDPUZ6fV9qmoH2uMr2yOA3FHfr/LWyB3X+YRMHv1t4mKtoyFJtnl8VH9OAYpc8n2vK39AS0HJhr7TI6G2uONv+Xrq1/9lWjaihmo397vrydL7WOX35BY77oWbTXLrOWcepJmT96Vx0SjNWVrHv+H8qv/b//zfymNPb/2v8pZ+DYzyV/0T2HrRT9XJu7/G0TDwzB5otZqcmfFrX93HIMpO6pXE41W7NWrb5yWk2aK9Z7yzWqerspjMbdmJ570c63qLRlbjzts9ayIitzuOAaTdtPPRTTasdXPlVt7Uc68d7sUt5wDtyyCx5XH7vq5Vktx2xSXxvA9epuorScd1U3fxsmvHTx3IhoqJkdDXR4X3016+5fPTqvVnyoXN+3j/o4uL/q5xIOCgvKqGO5Z2SVqaeTBJkkLJ792MA6EaCiTnhoNtcc/P31QfPe/EFdMTF8sx7jpr9bQUu7n6q+HW2ElxtIVl+SsHFNnmG2iKyvDGrdVK/MnX5Un2/O28wfIEA0Vk6Oh9riYvCNvIxce1xZ80l8xUa5XL5ifC8AaHR6/+vN//q/PCnGrLi6xRvIojwHAJh0e//z0r/Mm8ulu3baipwuPAfxD3V9dLX58KprIBUUzGY8BPEYeV116fCEaxP9v20d1eu35CI/f3r/+e9rHAHMQ5/ePAdICjwHCx6rHxtdNBYBZwGOA8LG6/jEAzILV9Y8BoA36uQDCx67H5XjtxYJlYQCsYtfj02vPX93azEUAAJawPO/t7XJ0GP3VADaYb97b4lsWeAxgg8MfGijmvR1O0+NiGgLWTQWwgdpjad7bEcjt4+u/v3/D9XT0ALGi9Fie93YEjf7qxbXnqXVz/XjwOP/P9VmAIO5oKD2W5r093wzFOhWz+7y9/zf3yzcd8Pw44mwTIHFHQ2ve26KLqpxr7/SGmBXk7f3tRLhK8FiUAK/v/Przm3+fZa8/P/jgqyz7tzsH+da7R3925/3/4/oEkyLuaKjL4928t6JZe3HteTm8spj6svykZw5M2eO39xfX/+B0laf52eScD//9y/e/fX3n41++yV/+4qssf3n36P1vXZ9eYsQdDbXHu3lvxfxclbYXRX367f2ycq3vcZ7E+fXvxfy5ybDJOR8XeeXFza/Kqt0v//K3Bze/evfoI9dnlxpxR0Pt8W7e24vttLd5O7lc6Gmox8U4kOKZU1rPneScc1Dw8es7H/zjN1HknNCIOxodHm/nvd0uAlMWya9GeFyOAyk8TmocyF4JkFO8lDW54HNOaMQdjQ6Pt/PeboW9KDS8GFGvLov33GP9WfpiQMo5xUuebV4cPP7ToyhKgNCIOxo6896KnunT956Jonhxe0T7ePEg9/i851FVZEg5J/vxzsHNvEH25cHNvzt4HEHOCY1EoqGe97Z6flyUxfnre89yoQd7LFaG6V+kEQCmwDwCAOGDxwDhY91jV0unAsB48BggfPAYIHzwGGB2aB8DhA/91QDhwzptAOGDxwDBMsO8t6zTBmCZw58a9M97e1GNr+6BddoA5kLtsXLe2wu9rzvQzwUwF0qP1fPejvF4U7emfQxgAaXH7fPeFl9c/B+benX3JLjNddpm+GMAEmXgvLe5jheLyuOeSXCb8/okTjXRKvjBL18GP0WmhLo8bpn3VgzJquYR6JsEF4/rvHv00S/ffPhH16cBgj99fpCKxy3z3pbzc9X7q7smwW3Oz5U2xSSrP96kQPaDd49u3knF45Z5b88lj3smwW3OzzXTH+QppcdRr0wSEu/+4V+TqVe3zHsrlcd9k+DK9epF4v3VL/DYK9JpH7fMeysawefC475JcHl+XIfy2C+i83jIvLflm01/dd8kuHhch/axX8Tm8RateW+l58c9k+DicR36q/0iEY8NsPX47f3rv0++fczzY7/AY10ojwFmB48BYA/Z41e3WBcGIDwa40CKgZmJrdMGED5t4zLTWjcVYHbszs9VfU+C+bkArGLVY+PlMZ1oPkE0/MFuf7Xp9jE5xyeIhj9Yfu5kuL+anOMTRMM5M8x7awNyjk8QDecc/raB8LhlMaaLgXViPE4GouEcbY91pqyWqAX3fNEyD98kyDk+QTScM4fH22n6zEHO8Qmi4Rylx399azfVbf6m6Ke6/v1mqlsdauvClH3V2o+c1svlb76u3l8eL3PuNT4l5/gF0XCOop/r1a1NGbopTKWpbnWofW+xmm5T74zWua7rjbJvPv265VNyjl8QDecoy+OyDL32fCuhNNWtDk2PNfW/OjnK/z27J7bWn3zX8ml7zmntaTf+OA328cLjtCPd2T7O3dvOeStNdavDSI/fPHyS/7uq/F3da/sUj/0Cj52j8vhXz8S/2zlvpaludRjrcVmT3pTDZ5/lzeOj5qd47Bd47By98jgT/dXbqW51GOmxaARXTeHL47svc5mP5E+zTo8P2z4Em+Cxc7rbx7U5b6WpbnWoebxbx7y/s6tpbFYWw8M9brUarIDHzunqry6N3cx5W5Sq26ludRgZ3GYNOisbxwPq1Xg8O3jsD/JlEM+Py4J3M+dtsaL5ZqpbnQTHetzo0cpKtQf0c+Hx7OCxP/gyz570hEnomxfDA5474fHs4LE/+OKxPOKjNPfsSGscCB67Ao/9wRuPs5UYgXl1Ujq8XC6f1D7tSByPXYHHETP79xbx2BV4HDF4nAx4HDF4nAx4HDF4nAx4HDF4nAx4HDF4nAxeRINI2wGPk8GLaBBpO+BxMngRDSJtBzxOBi+iQaTtgMfJ4EU0iLQd8DgZvIgGkbYDHieDF9FoTZvwTwaPk8GLaBB+O+BxMngRDcJvBzxOhtHRMBkdwm8HPE4Gwx6Ps53w2wGPk2Gqx4ftm429eiD8dsDjZMDjiMHjZHDh8d6Hfjzoig88ToYkPFYdMHbwOC6kBahXm+kPS+bxuCewBsM/6ICxg8dRIU08vCo2diLjccTE73EigSyRFgKopiSevioAHvsPHseEtDAPHo9POzjwOCbkhfKoV49OOzhS87g7E4ZOY+HatZnVPfDYf0Ly2GK4I4m27PFZXi6/eXi0+SEeR4zXHh92bmqSksdSvdrYKrZ47D8heNzIQANJyuO6uo1KNh73fBg0eDwhae9oX5a6+mHSHps4oM+M9rjeh3J1slwuixx0eZy/WRpbxxyPhyIvS037GI97qGeYq5P8zarQV7TPOhMfkXPwWJ+9Zam3GuPx1AN2noZjRnrcUoErWmW7SpwycTx2RXgeH3ZsufO45zq4YaTHzb7QTJTQq3vSXnjsEwF5PD6T4PEg5IFDJUVr7OwzGzU5PDYCHuNxk+YzjaLf6yi7PL77MhfadM8KHhsBj/G4yZ7H610vtfEnHXhsBDzG4ybNevW6VpsWbWdV4njsCjzG4yaNfq5VTePawyc89gk8xuMm0nOnXGNRAlsaQYTHRsBjPN6jPg5kN2aoFHu2fq7WKzgpT/TgR8jGgsd4vE9t4FAxndtSbJ7ZmNmtx2ODeaIH83liTvAYj80ljseuwGM8Npc4HrsCj/HYXOJ47Ao8xmNziePxcHqugyZ4PDFmetfBDXjcdohJOcc8eGz7gFrgcQ0PPD4UtOyEx23p43HrL+Ox6qV7pwmBPJT5bYE1jw/btiZFG49tH7CVcdfBDf56fLgtNuWtgUmJ3/6h4PDwp4KZPDZYauOx7QN27az4KR4rX6SdhHs/SGVoq3xdSW1+G4/x2PAB8Vj5Um3U3ftBuPfTWI+/KMDjAjzGY3OJa3hcdw+P99Ow6nFv+8VTrfB43sTxeDizetx3nT3VqnYPGppJxh0wYY9r17l+2RsXH4+7UzTtsW5nvlceH7YyLpPo7oXHFcKqL7aXvV2rNDzWCn97GqY8HtgJWDu85YJPx2ODmUR3Lzyu2Hj8Q2fOwePupMx5POzi1D22KwweDwaPpd/CY8XFmbUCi8eDCdZjuam999KWFh43Uh/i8ZzC4PFgwvVY7JW1FRfNIxrxWO/GofpxsB6bfJpvcC88lgnd4+4uM6MeSzcOxU7KNML1WI4ZHuOxFY+7DTXvcTstaQ3KOVn7XpF5bLBKg8cyeCz2k197c46c1Ew5J3yPzVVp8FgGj8V+8utkj3sLbTxW7qWVFh7L4HHWHGa299KblKp7t+PGoZ9zdmcXmsd79y88tgYe706ruxDV81jq3p3mcaOnuKNs18Omx+3XThEz+e8dV1nBYxk81s6qeh5rVuRNZlVNrHo86OK02I7H0wjXY62Cz0JWHV1q4/GEi9N5nfEYj/dPa1DVEY/7khrpcU+pjccy/nvc3daa32P/ihxNAvFYus6zDMLX3QuPKzQ9HlTwde7keVY1VOSMjIavF8dgpS3DYxuJj/K4ClFUHhu8nzVYi3Uvt5zdfamKRtgXxwuP+6IxH6M9ljLMdkPORvRXdx+w29AxHteXpRbxwGP1y5C92sMwvnZkGBPrmO82GtkIj6eUtCPq1VcnxRry5WryJZfHaXusfSfU8FjrOjhjpMdShtluNLNRih5rGVphqMjZ8eZhsYj86pPvqu3V3X9K22O9TLINT03g9rtqbB5LGWa70cxGgXk8oHic6LHZqmMtLJ8WdaH1JgD5Ztrt42GZRGbUdXDGWI/rGWa70chGwXg8QD7vsqqEaNNsWjZF9QiPZ620OWOkx1KG2W7I2Sg4j4PMquqw5LXqlyM8HlWf9PTi4HEPcXkcRFZVVBMk9qtJeIzHHQRTr64Xtd6M5xr1/DhrDkBoC0u9g2K1FDxRRKPZLgz5JofH434tmH4u/Zav5ldsx7eih3asZarnIOps03xg0FMet+Kpx13XGY9Tee5kzmPVy5DT2hywJ63hHu+NA9HyuDpXXzwecO9tZpJRd9WUPR45DqSecQKsMhnzeJffDHtcVKaL6391Ut1MA+yv1qsmDLcdj9uQMsxqMxxz1T0uc8KtNiaPNdMa43EHJj0eIMwsnQd12alX205cr12Ix907ufF4dMFHP9cc+Ph9J70Q6RTt7jxuKScC9ar0LeYAAAlISURBVHhqwYfHcxCsx5nB5qp5j+Uf791e9NLyyuPRwuDxHOCxYY+3ynYbGo7HWhdnmMcaVXQ8HgYem/XY7F6xeazTFsLjMeDx/mkp2tp4bMrjQdHAYx2S9LhZAuyZO0QrPO5OKrL2cXdlwhmxe6y46gphxmiFx8qk2qvM/nmsVU3QahQ4I3KPdfcKwuOJzOFxdy4PymNFpY16NR4P38sk83vsvl6tY+iobnQ8xuP2D5QfmmKOddpakvLB4+66sNbYHTzeoRki3RpM0B7PT4oe6xhKf/XQxPVClIlcj8eGob9akd/weGDieOwSPMZjM4kP87i7zyRz53HrvkNPa35C8VirUTt/fzUebxnksfyy3zvh3GMVeDzJ43LHjpdqQ6sTZdAB9+4YIw7ojFA8rr927oXHKqLyOGuttHWW2mYOiMd47JYYPe7ZCY+tJG7H49bf6UlrnMd64HHMHndXAJwRj8cq8LgCj40e0KPIZng8KCk98BiPZydkj/XA4wo8xmMzieOxS/AYj80k7q/HJsFjPJ4dPDZOcB5rPIKNyuOWPmY8HpI4HrtE5XHWea5Tvu9kf1hGz06td6qWpPB4UOJ47BLVOm2ZAY+r3+oRRqsCsH8iEzzW+QtHHtCjyGZ4bIFgPM50zlUqaf2f3HtcUng8KPGNxw3weBbGeVxtNzxuKUQda4XH8yW+8TiTLoJunph2xVorblbwI7D7TPO4t42Jxy4Z7fG6tkLq1clyuSyWML88zt8s1euY61asLHgMkzzOevMvHrvExDrmVyf5m1Wh75tPv67vZCjn4LER8BiPm1ydFMXvmSh53zx8kv+7+uS7bJ3/35M4HrsCj/G4yU7dLUXpvLon7YXHPoHHeNxEVKCl4vcs3zj7rGooqxPHY1ek6XHXzpMOGIXHomm8/s2uObzO/b08vvsyF3orMh77BB4rtsYdME6P17te6l0pjcc+kbTHPaTqcbNeva7VpkXbWZU4HrsCj9UMSSsSj1dFE7jRz7WqaVx7+ITHs1N/rC9v4HEHCXpcIj13yjUWJbCwm3q1O+qP9eUNPO7CZFpOMDEO5M3DTWlcik0/lzOk26t8r8XjLpL1uKheFxpfndwra9pLsXmWvz7Z7oPHMyM1d5rP+PFYTboej00cjy0idT82+yLxWA0eD00cjy0iPQ5sPhu07HFXigMPOEErPJ4pcTy2iAcet/7qwAPOrxUeD00cjy3isl6txyBh8FgbPI4Jl/1ceozxuHULJPA4Jlw+d9Ij+ILPU/A4KhyOA9EDj+2Ax3FRe6y/3ajA44jB42TA44jB42Qw7PE48NgOeJwMo6NhEjy2Ax4nAx5HDB4nAx5HDB4nAx5HDB4nAx5HDB4nAx5HDB4nAx5HDB4nAx5HDB4nAx5HDB4nAx5HzOwet4LHM4DHEYPHyYDHEYPHyeCFx13HhfHgcTL45HHrWcB4/PC4CR5bwF+PYTJ4nAx4HDF4nAx4HDF4nAx4HDF+elyBxybB44gZrVp9jezL42K9xXuZzsrZEyB/TaLDY40PwWtMrH9crUDS/BSP/QKPI2akavJaBZs1hHRWMABXEI2IGRlcee2g1b22T8k5fkE0Imasx9Jafmef5c3jI70V/sAVRCNiRgZXWlv38vjuy1zmI60Vd8EVRCNiTHhcffTJd3jsM0QjYozUq8VHD59Qr/YZohExw4O7KtrCzR6trFSbfi6fIRoRY+K5k9A3L4Z57uQzRCNijIwDKc09O9ofBwIzoRVqmImRTk1h9DGlBbPP8rr2k9qnADAnVLYAwgePAcIHjwHCB48BwgePAcIHjwHCB48BwscPj69OxBcfazMEGUQ17ZAZ1kvBExsn/+Z331XHEOdt4w/Yg2gocBINPbzw+Ookvxyr4ppvZwgyiWraIYNcHls5+cvjcqz69rzt/QE1iIYyWQfR0MQLj3ffr5C+QWUK1bRDBim/G2L85PP7fZHk9rwt/gE1iEY7bqKhiRceC4pb28pKWBXTDpnjzcOj2nFMsV4elZlxe972/oCWgxMNGafR6MUjj8/yK7KZIchswopphwweoUzTwsmLnLM5b3t/wD5EYx930ejFH4/z+91uhiCTKKcdMniEo/pxDFLmku15W/sDWg5MNPZxFo1+vPF4vetatNUss3bh60maPXlXOYdotKaMx32sa1Ug0fAwTMu0Q8Y4K279u+MYTNlRTY5otEK9uo9VvSVj63GHrY4JUZHbHcdg0m56VohGO/Rz9bASsxDsZggymbhy2iGzB7By8msXTzqIhgIn0dDDC4/Fg4KC7QxBJlFNO2SKTZIWTn7tYOQB0VAmzTiQTlZiLF1xSbYzBJnE8rRD26qV+ZOvypPtec8xbxLRUOEiGpp44TEATAKPAcIHjwHCB48BwgePAcIHjwHCB48BwgePAcIHjwHCB48BwgePAcIHjwHCB48BwgePAcIHjwHCB48BwgePAcIHjwHCB48BwgePAcIHjwHCB48BwgePAcIHjwHCB48BwgePAcIHjwHCB48BwgePAcIHjwHCB4+D4u39xWJx7Xnvfq9uPVD85PT692ZPCXwAj0PiYnE7//f0vWd9O6o9hijB45AQhenb+zf6dsTjxMDjgPj5aa1SfJrXsPPNV7f+Jq9rP7hYLPJS+u39YuN25fH5onwvuKgq5PmtoHib09wDAgaPQ+JisRW5KJp/fnojNza38zT/vJA8bz4/yD+5XXp8notdvC8pPihvA1X7uHwv7QEhg8dBURSlZetYVJzPrz0vPbwoC9drz0WNu/z0gRD0vOoUu9h0jlUen24VPtfoNgPfwePQyMtc0c/189OiplwKfVF8Unpc2J1v5Z9e1HwvXhfijfC4FF/eA0IGj8Pj56dlVTqX+Lzd40VeGD84X2ybweKXxPvS41e3ynJb3gMCBo8DYlN05tqKJ1AKj2vlcZ1c5QdVu7qsS+/vAaGCxwGxeeCUG1s6WPjY8Hhnt2j9Sq4W+xYeVw+gW/aAQMHjkBD91UVZXNaMz/fbx/kb8eMHpa3bR81ij/yf8rlT1UUt7QEhg8dBUY7LLAvQouf6+v8ta9B1j//jrbK9u31+vJX0vPrF0+t/eCqaxXndWtoDAgaPY0LUqyE98Dgm8DhV8Dgm8DhV8BggfPAYIHzwGCB88BggfPAYIHzwGCB88BggfP4//Rw0KsK54iIAAAAASUVORK5CYII=" /><!-- --></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>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:estimateMAP:value</td>
<td align="right">10.6</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typelinear:estimateMedian:value</td>
<td align="right">10.5</td>
<td align="right">0</td>
</tr>
<tr class="odd">
<td align="left">outcome_typelinear:estimateMean:value</td>
<td align="right">10.5</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typelinear:estimatebeta:value</td>
<td align="right">10.3</td>
<td align="right">0</td>
</tr>
<tr class="odd">
<td align="left">outcome_typebinary:estimateMAP:value</td>
<td align="right">5.1</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typebinary:estimateMedian:value</td>
<td align="right">4.9</td>
<td align="right">0</td>
</tr>
<tr class="odd">
<td align="left">outcome_typebinary:estimateMean:value</td>
<td align="right">4.8</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typebinary:estimatebeta:value</td>
<td align="right">4.5</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>beta</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 the frequentist <strong>beta</strong>.</li>
</ul>
<p>Overall, the <strong>median</strong> seems to be appears as an 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>
<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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