swh:1:snp:2c68a6c5a8af2f06ac2c0225927f25b54fd1f9d0
Tip revision: 3da49db3cf0eea4d2c5eba241ddb5470cd7dd929 authored by Dominique Makowski on 26 January 2021, 16:40:03 UTC
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Tip revision: 3da49db
indicesEstimationComparison.html
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<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., & 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"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(dplyr)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidyr)</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(see)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(parameters)</span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a>df <span class="ot"><-</span> <span class="fu">read.csv</span>(<span class="st">"https://raw.github.com/easystats/circus/master/data/bayesSim_study1.csv"</span>)</span></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"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>df <span class="sc">%>%</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(error, true_effect, outcome_type, Coefficient, Median, Mean, MAP) <span class="sc">%>%</span></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">gather</span>(estimate, value, <span class="sc">-</span>error, <span class="sc">-</span>true_effect, <span class="sc">-</span>outcome_type) <span class="sc">%>%</span></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">temp =</span> <span class="fu">as.factor</span>(<span class="fu">cut</span>(error, <span class="dv">10</span>, <span class="at">labels =</span> <span class="cn">FALSE</span>))) <span class="sc">%>%</span> </span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(temp) <span class="sc">%>%</span> </span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">error_group =</span> <span class="fu">round</span>(<span class="fu">mean</span>(error), <span class="dv">1</span>)) <span class="sc">%>%</span> </span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">ungroup</span>() <span class="sc">%>%</span> </span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(value <span class="sc"><</span> <span class="dv">6</span>) <span class="sc">%>%</span> </span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> error_group, <span class="at">y =</span> value, <span class="at">fill =</span> estimate, <span class="at">group =</span> <span class="fu">interaction</span>(estimate, error_group))) <span class="sc">+</span></span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a> <span class="co"># geom_hline(yintercept = 0) +</span></span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a> <span class="co"># geom_point(alpha=0.05, size=2, stroke = 0, shape=16) +</span></span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a> <span class="co"># geom_smooth(method="loess") +</span></span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_boxplot</span>(<span class="at">outlier.shape=</span><span class="cn">NA</span>) <span class="sc">+</span></span>
<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme_modern</span>() <span class="sc">+</span></span>
<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_fill_manual</span>(<span class="at">values =</span> <span class="fu">c</span>(<span class="st">"Coefficient"</span> <span class="ot">=</span> <span class="st">"#607D8B"</span>, <span class="st">"MAP"</span> <span class="ot">=</span> <span class="st">"#795548"</span>, <span class="st">"Mean"</span> <span class="ot">=</span> <span class="st">"#FF9800"</span>, <span class="st">"Median"</span> <span class="ot">=</span> <span class="st">"#FFEB3B"</span>),</span>
<span id="cb2-16"><a href="#cb2-16" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"Index"</span>) <span class="sc">+</span></span>
<span id="cb2-17"><a href="#cb2-17" aria-hidden="true" tabindex="-1"></a> <span class="fu">ylab</span>(<span class="st">"Point-estimate"</span>) <span class="sc">+</span></span>
<span id="cb2-18"><a href="#cb2-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">xlab</span>(<span class="st">"Noise"</span>) <span class="sc">+</span></span>
<span id="cb2-19"><a href="#cb2-19" aria-hidden="true" tabindex="-1"></a> <span class="fu">facet_wrap</span>(<span class="sc">~</span> outcome_type <span class="sc">*</span> true_effect, <span class="at">scales=</span><span class="st">"free"</span>) </span></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"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>df <span class="sc">%>%</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(sample_size, true_effect, outcome_type, Coefficient, Median, Mean, MAP) <span class="sc">%>%</span></span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">gather</span>(estimate, value, <span class="sc">-</span>sample_size, <span class="sc">-</span>true_effect, <span class="sc">-</span>outcome_type) <span class="sc">%>%</span></span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">temp =</span> <span class="fu">as.factor</span>(<span class="fu">cut</span>(sample_size, <span class="dv">10</span>, <span class="at">labels =</span> <span class="cn">FALSE</span>))) <span class="sc">%>%</span> </span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(temp) <span class="sc">%>%</span> </span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">size_group =</span> <span class="fu">round</span>(<span class="fu">mean</span>(sample_size))) <span class="sc">%>%</span> </span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">ungroup</span>() <span class="sc">%>%</span> </span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(value <span class="sc"><</span> <span class="dv">6</span>) <span class="sc">%>%</span> </span>
<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> size_group, <span class="at">y =</span> value, <span class="at">fill =</span> estimate, <span class="at">group =</span> <span class="fu">interaction</span>(estimate, size_group))) <span class="sc">+</span></span>
<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a> <span class="co"># geom_hline(yintercept = 0) +</span></span>
<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a> <span class="co"># geom_point(alpha=0.05, size=2, stroke = 0, shape=16) +</span></span>
<span id="cb3-12"><a href="#cb3-12" aria-hidden="true" tabindex="-1"></a> <span class="co"># geom_smooth(method="loess") +</span></span>
<span id="cb3-13"><a href="#cb3-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_boxplot</span>(<span class="at">outlier.shape=</span><span class="cn">NA</span>) <span class="sc">+</span></span>
<span id="cb3-14"><a href="#cb3-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme_modern</span>() <span class="sc">+</span></span>
<span id="cb3-15"><a href="#cb3-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_fill_manual</span>(<span class="at">values =</span> <span class="fu">c</span>(<span class="st">"Coefficient"</span> <span class="ot">=</span> <span class="st">"#607D8B"</span>, <span class="st">"MAP"</span> <span class="ot">=</span> <span class="st">"#795548"</span>, <span class="st">"Mean"</span> <span class="ot">=</span> <span class="st">"#FF9800"</span>, <span class="st">"Median"</span> <span class="ot">=</span> <span class="st">"#FFEB3B"</span>),</span>
<span id="cb3-16"><a href="#cb3-16" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"Index"</span>) <span class="sc">+</span></span>
<span id="cb3-17"><a href="#cb3-17" aria-hidden="true" tabindex="-1"></a> <span class="fu">ylab</span>(<span class="st">"Point-estimate"</span>) <span class="sc">+</span></span>
<span id="cb3-18"><a href="#cb3-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">xlab</span>(<span class="st">"Sample size"</span>) <span class="sc">+</span></span>
<span id="cb3-19"><a href="#cb3-19" aria-hidden="true" tabindex="-1"></a> <span class="fu">facet_wrap</span>(<span class="sc">~</span> outcome_type <span class="sc">*</span> true_effect, <span class="at">scales=</span><span class="st">"free"</span>)</span></code></pre></div>
<p><img 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odiiwfa9A0IYrNSqSSseCx0PldLVhfLzosLdMRYVvnm0VHy9VS0i1Gk1/jKbnfyma/qK7Z4qE3fgCBKCCZhw+Nsib+RUR9zU/m2uqyyfGW9ENkJF6LbPT84SptjscUDbXrt6xNEjkASextIbmAF5fNARkddLHv6C21VKZFq8yqzEZd4P5Nd4iu93VnrWW7xQJteB0Gs0TeJvfdLFB6n1wfX9Jdnk8nN5P+/O1ytwnd+WLUi32zjyfJ5IGOjLs+5OH736ySLI8FqiyqzvRrp/bKL46P1F5EibSnFFg+z6bWvTRBr9E2i1uNZenH/SeValqofbdWXVsit7R+Pf4XE2sWyw+ybDdN81usT3G6LHhOEXu9AHmeL7tXswSo9q/vfioIlLM5zLfSLZbOdEFGSKocZzp2qz//Vi0hVa29cTRA6Q42rl6dK/p8ybDbJl97J7vv07EZu3+9TTbPFvM6Ln28qP3+WGHpbFSx/Dlid59Iulh3mmMcg0yvZaG71IlL1WpvnIogSvee5qj3WVtebLW8Atbzv07I/Tt3Nb+ZW/JwVUIvmXvp4S3889jzX8mLZ7G0S/aguqhzkcEf+yS++3XM7x50IYoO+SdTMV68bls1GzZSV6Q+XH697vCy5+jktcDMdmm/xeOR5rtXFsuk7JDq9sqpyiNMPlvVJb/fcznkgBLFZcc8kavrjdY+zXeXka3Hfp3WP8x3pbK3r9QLqma3zXDekbzvTxNrFsqfp2XWiFFVO5U9uLEZYwtud9yjFFg+w6VUQxAZ9k2gxrs5kS5Sc5YsE6R7nU86px+sFWni8nObigieAXmyb55qp2SqtP14sFs39cf6gTX8MABK0OO60tn+cW1m/f7xWAI8BxqL5PJBXD1QPq81Xq1NDNuark2F48fOyQObxxkQWHgOIU39+dbrzmo2utePHyb6s5vHG8eO8QPrlpP748fnhlT+xfwwgSgTXHwMEDx4D+I8Nj43vmwoAVsFjAP8Z4v7HADAuQ9z/GADGhXkugOGwMl+tTuM+q109CAA6YsXjk8uPn924ql3sDADm2Fn39mZ60ifz1QC9sL7urTolG48BerH3UYnl9cf5saBZvvN6kj8+yQ4UmQ+Eyx4nQ2vumwrQj3qPl/6m35/98J+zPvMkfXh+aGyevn985U+HV+0sRw8QELUe/016bPf8H/8pNfbs8n9mFySf5FdAVa5r3YbSfPXk8mOmuQB6Uuvx1ZN09YArv1HiJg9z23KPzRfWivH48be795L/bG8FBJxEvcczZezJzVTcWbaM7UK6P46EMJuOjwSbRM18deLxsx89VidOpuKqL9le7HL/2HgorHt8fji58mcLd3kal6wXeL7/kw93fr1YPP9w962Hi8Vf9neTRy/v/mD/2n/b3sBoCDaJ+v741YPbybD6SyWuWlo+PWmjmK82N0/zOOnWz658mVUfMMvW8/ZfP7n2+fP9W6+fJN9+/HCRfHt599rntjcvIoJNot7jxdnVZFiddsBny/Vsi3G1OeXzQNQxp9CPOy1bzy3VXp7uPEyHd6//8MvdnYcv7163vXUxEWwSDR4/+9F//evHStx8iisdTIt6nJ4HojwO/DwQvfXsKm4933/rd098bz3eEWwSDR6/evAvyS5yIu5yUkvNdAn3x1dTj3tX6jgbvUCC+paO5q5b3rioCDaJBo+TfeGsA15qpvZjRT1WJ1cnHp9Nxrw7jAW01qO+JU3n6e697+763gt4R7BJ1M9XZ+tWJ+L+b3Gs+OTyY1mPs8V1jY9h+YLWehbf7u/uJDtln+zu/Gr3nt+txzvCT4L1MgH8B48B/MeWx+PeOhUAJMBjAP/BYwD/wWMA/8FjgOFgvhrAf7hPG4D/4DGAt9hb95b7tAFIsfdNiZp1b8XgPm0A4tR7rK17KwfzXADi1Hqsr3srR3nd2xT2jwH6UOuxtu7t2XIf9iRb3ef88GeHE7Orhsv3aev7DwCABo/X1r1VC4Gki+GdXM1WBTk/LBbC7Up5XZ/oyBdpBPu8/sTnpfU02qx7m+k2u/w4nZdSJ2Clz5idiRW7xy/vXn/95O2vbG8GLBbffbgbjse1/fFq3dtsfa5c25kaT58fpoPrvh7HeEcYtUDjtzt0yPZ5eXdnPwKPV+vezoplb5P95PRGT0IeZysHxUXqcah3NfCKl7/9Y0Dj6nqPi3Vvi5vApF3yMzmP09W5IpuvforHzhDS/nG9x8W6t4WwM+XbTG5cHSP0x+4Qh8fFurfZzPTJpY+zrnhyE4/NYf/YHULyePu6t/nxY9UXn6lFahOh8dgY5qvdISCPC0a/3un88MqfItw/5vixO+CxObH3xwBDgscA0Bbd42c3YrgvDEBolM4DUSdmBn+fNoDQqDovM/T7pgKERtV1EqzPBSCDjXkuqf6YuTNXIAnbWJmvFto/pvW4AknYxs5xJ5n5alqPK5CEJeyte+t4nWACSVhi7/sS29e9neXnV5uBxyFDEpao97h23dtZr3HwWtJnE8O1+hrqBKuQhCVqPa5f91bK42L1vt7QelyBJCxR63H1urfqwsV/X46rjRbBXbsvTDpXLXEKCK3HFUjCEvUeV657e/lxssece2y2CO7adYv5Kpz9/xG0HlcgCUt0Wvc2WzIzX0fAcBHcsscSF0nQelyBJCxR3x9XrHubdZ5r89UGi+DicciQhCXqPa5Y9/ZM89hsEVw8DhmSsESDx5vr3mr9seEiuHgcMiRhiQaPN9e9zXaCzzKPDRfBXfN4dR/znpNdtB5XIAlLNHi8ue5t+sNyvtpwEVzO5woZkrBEt3VvtePHZovg4nHIkIRtfF5nj9bjCiRhGzyG/pCEbfAY+kMSsYDHIUMSsYDHIUMSsYDHIVORxFg7bDAqI3lM6xmSFz//Yvnj/ODgp58VvyCJWBjXYxrREFwcv7P0eJ5IPF+JjMexYNNjmpQISRe89PjNo6Pk6+l7y19t9Xiv4jnwECse0zsLMj84mi89fnHnfvJ1WnTPLZMgCO/B4wBYefzBZ+sP8Tga8DgACnGzXePVDjIexwIeBwAeRw8eBwDj6ujB4wBgnit68DgA5t2POzV6TDDegccBMO9+HggehwUeB0Dq8ZtHqhuetjwvs4PHpOUBeBwy/TwmLX9wyWNaijRDekxaLuGgxzQQMUbwuDktshwJdz3G6v6M5zGdtl3wOGRc8RjZhwaPQ8Yrj0m6B3gcMh56TJ9thHceE2gHgvNY4DM+zP7B3GN9JajF4vTdr+vrxGMrROZxq7bR5g3wD2OPS2cAJlrjsXNE7XGHmobr/cfC1OPyGfkXx+N67PSb6gxxety9ULwel6+Qm777qT2PnX6HbYLHeNxM6Yr15OG4+8eNoUMOHuNxM/oKMmqUjcfugcd43Izu8TRxGI/dA4/xuBltXJ0+wGP3wGM8bkab55oeZNyvrdNm6BGDx3jcTPm4k1P9sX8xDAQe4/EWyueB4LGD4DEebyNfCSpbFmrhn8dOxyIEHuOxaJ2+hu45eIzHonX6Grrn4DEei9bpa+iLxqedB4/xWLROX0NfND7tPHiMx6J1hhS624Fq4DEei9YZUuhGgVb+zeAtA4/xWLTOkELv4/HILQOP8Vi0zpBCryvUCB63LITHRuCxVCHxDwSBdoPHeCxaZ0ihj+xxn+aDx3gsWmdIoQ/usVzzwWM8Fq0zpNDxeMhCeGwEHksVwmORQnhsBB5LFcJjkUJ4bAQeSxXCY5FCeGwEHksVwmORQnhsBB5LFcJjkUJ4bAQeSxXCY5FCeGwEHksVsubx+o0vL47VuqXF6od4jMeidYYUumMeawseZsuKF+AxHsvVuaex8D10tzzWFyAubriVgcd4LFfn3vuKvb2PFHsbVq/KNXyrLoTHpRtfTt/TfonHeCxXZ8njbxR7e98r8LhzoRL6jS9Pf5HsHh8Vv8RjPJarE48H9Fi7Yd7FsVpE/PRo+cuaPZxy5U68f3jcB2c83mtAq2xVFI8X5RtfZk8VO8k1SZQrd+L9w+M+uONxB9k/qtjT1l6w4dtghSx5XLqhfPrUnfyGebVJNH1Y1n1K4vHCYTzzOCuUe/xNVkhigO6xx9o8V/ZUcfCpOYn192/1BmZl3s89rvmwrDv20P1fVK4Jj43AY6lCljzWjjtlUm8dV7fyOKc5rca9oFayN9RUrkji1drUhMfVdY7rcZfQt+Xpgcf6eSCpzw3zXB08FktrSxJtIpV+teY3oGXbcIoAPZZrh+UInfRYv/Hl6ep28gtXPNYKfW8cqWAD6v8GuAYety5U+cG8etx/NCc/nMNjPJarMxCPG0PvMJrreeBNLgk8xuMudcbg8fomCb5az+aDx3gsVyce4zEeD4u5x+uXveoP8BiP275/eCyDscfa4Q7tAR7jcev3D49lMPVYO/1AvwYWj/G49fuHxzKYeqydDlg6N3C46yRalWnVDtvXVDzfw+Oe/zY8xuMtGHu8fnp+6Vz95vVA+jTjMSrqVmjcV+sKHuNxM9rlcqVr58w8FhtXy71aTl6osibxfxvjajw2YBSPpWNoETr7x9uTqGnG+qcXHgftcadxNR674rHmaLPHOuWNbSV7VSEjj7u8WoeRER4PMM+Fx+N53NTWl/+iZh9aSdOz0ICv1uGDLA+iVJFrcNwpKo/rFd3SHZV9aFFRy0Jt7Ovyar077TZlnIPzQGL0uPew0vf940aP9TcgJ9Bxdemy1ynnZeKxRx73fgNcg+skxve4+hN+iOEcHuOxXJ1Be9zGvo2n91ZPam9Uwzcj8BiP5ep00ePu+tX3kHtrXy2s69MAHuOxXJ2jTFOUymyPQc4sPMZj23jmsTYyrW7q3XpRPMZjPG5Xp+h0rda6B5cGj/EYj3PEjuyl5da/4XEzeIzHcnUaDZlbtXU8biYqj3XwWLxOoyEzHkficUbucc3UZfcpjx41LR9XbBEe47FUoS544HH2L1x5YiXSqjJ1A0Q3seBxm4/TjW/VhfC4GW88Xn1zxuOtFTnFKB6XzRWLAY+bGc7jNiPdVoXK/1A8NmIMjxeDxYDHzfRZD6STfZ5Hisct6wwp9MA9Ft1YTyLF45Z1hhQ6Hg9ZCI+NwGOpQl54nIPHeGxUZ0ihe+xxXt22fV88blORU+CxVCGPPC5/c+L9w+M+4LFUITwWKYTHRuCxVCE8FimEx0bgsVQhPBYphMdG4LFUoaFerQ94jMeidYYU+nAeV/7JVubraw5rD/C4ZSE8bllnSKH38biy2n403BAAj1sWwuOWdYYU+hZHqxnM46Yb9OBxy0J43LLOkEJ3K9CmG+bhcctC/sVeBo/7F7JK0w1s8bhlIf9iL4PHjYUWjU+7QNMN5fG4ZSE8blmnr6EvGp92ATwWKITHLet0PnRvYVwtUAiPW9bpYOiBwDyXQCH/GxAeew7HnQQK+d+A8Nh3OA+kfyH/GxAee880OxXzzaP3Vg9y8BiPt6GfyZuM5t79ur5OB0OPATzG4y2URnCJ1s553OLJwMFjM4/1oj5g6nF5RuXi2HWPYwSPtzWO2D0uH+GYvvvpqB43loEcPO7lsUcYe6yfcZA8HHf/GNqAx7E0GFOP9TMA1Sh7JI+hA3gcSwOS8XiaOIzH7oHHsTQgkXF1+gCP3QOPY2lABh5PDw4OjrR5LvWM4n5tncRgBTyOpQFJHXeiP3YRPI6lAYmdB4LHDhKcx1CD+XmZ2mm9Czx2ET88XjQ+DW3w7joJ6AAex4KDHoMYeBwLeBwyXnkMPXDJY5AGj2MBj0NmBI+bIemRwOOQGdLjLpD00OBxyLjiMQwNHocMHscCHocMHscCHocMHscCHocMHscCHodMP4/BH/A4ZAw9Bu/A45DB41gY12P9Ec1naPA4FvA4ZPA4FvA4ZPA4Fqx4DCOBx7GAxyGDx7EwksdgBTyOBTwOma0eQyDgcciwhxMLeBwyJBELeBwyJBELeBwyJBELeOw98+zGHikXx+p+ecVdt0giFvDYd7QbbWW3sy0giVjAY8/Rb3yZ35B6CUnEAh57jnYj6sX0Pe2XJBELeOw52Uh62Q+f/kLdZL74JUnEAh57TrZrnO8gXxyrm9eeHi1/SRKxgMeeo3mcP1XsJJNELOCx5+jj6uypdJdZQRKxgMf+MlX7wvo8V8rq4BNJxIJ50uunH6RNatkJ0HrGRDvulEnNuDo+jJPWTj+YqgcHjOZsoAWR+sw8V3yYJq11A28evbd6QOsZmWk2MMpDWB8YkUQ0mCat7ZbhsaOQRCwYe6xNkzKudhOSiAXTpEuHLbVJrwkMS/t0YVAM5RkAGY9Pk375xZ0jqY0CgE6IjKsrjmECwHgYeLx5+kHFuYEAMB4ix53Kpx8AwKjInAfC/jGATcyn3DZOPzgS2ygA6IRDU+cAYIhNj988ynvx0iqPEqyq1A5tSzA/yLgvvt0vfv5F/gLZFotveg0EUcZWEsZY9PjNo+Stmap3v7TKowRFldp+vBwXx/LbfXGczhQWWzzQpm9AEJuV2tY2txsAAAOvSURBVEnCHIserw5dDTDTvaxSX05SjvSIm+x2J5/5qr5ii4fa9A0IooS1JMyxvn+sPuam8u/QssqBTlHJJudFt3t+cJQ2x2KLRz67hiCW2E7CBOseq0NWpVUeRarNq6xY9kak+rRC6e3OWs9yiwfa9DoIYg2rSZhg2+Pks29jlUcBiiqHOdXs4vhosbk6ZW/SllJs8bhnyRHEOjaTMMKyx/PVJOMw+2bDRLBen+B2W2w9BKHXi8ddmK8NhlarPIqRVDnMkOhUff6vXkSqWnujOYLQYVzdhen6Ps0wxzwGmaLIRnOrF5Gq19rsCkGUYJ6rA9N8BZEBLrMoqhzkkEH+yS++3XNLRzsIooytJIyxevz4KP+ptMqjBEWVQxzCL5ZPEN7uuZ2zDwhis2LOA2nNNDurTr09+iqPIhRVTuVPqStGWMLbnfcoxRYPsOlVEMQGlpIwx/ZxJwDoDx4D+A8eA/gPHgP4Dx4D+A8eA/gPHgP4Dx4D+A8eA/gPHgP4Dx4D+A8eA/gPHgP4Dx4D+A8eA/gPHgP4Dx4D+A8eA/gPHgP4Dx4D+A8eA/gPHgP4Dx4D+A8eA/gPHgP4Dx4D+A8eA/gPHgP4Dx4D+A8eA/gPHgP4Dx47zfnhZDK5/HhruWc3btf85uTKl7KbBC6Cxy4zm9xMvp5c+nhbwXqPIQrw2GWyzvT88Oq2gngcOXjsMK8erA2KT5IRdvLw2Y2fJWPt27PJJOmlzw/Vg5u5x2eT9OeMWT4gTz4K1I8J5RIQEHjsMrNJIbLqml89uJoYm9h5kjyvJE92n28nz9xMPT5LxFY/p6gn0o+BfP84/VkrASGBx06jutJ07zgbOJ9dfpx6OEs718uPsxF3+uztTNCzfFJstpwcyz0+KRQ+azFtBr6Bx66T9LnZPNerB2qknAo9U8+kHiu7k0fJs7M139X3SfZD5nEqvl4CQgKP3efVg3QonUh8Vu3xJOmMb59Nit3g7I+yn1OPn91I+229BAQEHjvMsutMtM2OQNV4vNYfr5OofDvfr07H0pslIBTw2GGWB5wSY1MHlY8lj1d2Z3u/mquqrPI4PwBdUQICAY9dJpuvVn1xOjI+29w/Tn7Ifn07tbU41JyVSL6kx53yKWqtBIQEHjtNel5m2oGqmesr/5OOoNc9/tsb6f5ucfy4kPQs/8OTK39+kO0WJ2NrrQQEBB77TDauBsBjn8FjyMBjn8FjyMBjAP/BYwD/wWMA/8FjAP/BYwD/wWMA/8FjAP/5fzY0G0FwUVQVAAAAAElFTkSuQmCC" /><!-- --></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"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>df <span class="sc">%>%</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(sample_size, error, true_effect, outcome_type, Coefficient, Median, Mean, MAP) <span class="sc">%>%</span></span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a> tidyr<span class="sc">::</span><span class="fu">pivot_longer</span>(<span class="fu">c</span>(<span class="sc">-</span>sample_size, <span class="sc">-</span>error, <span class="sc">-</span>true_effect, <span class="sc">-</span>outcome_type), <span class="at">names_to=</span><span class="st">"estimate"</span>) <span class="sc">%>%</span></span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">glm</span>(true_effect <span class="sc">~</span> outcome_type <span class="sc">/</span> estimate <span class="sc">/</span> value, <span class="at">data=</span>., <span class="at">family=</span><span class="st">"binomial"</span>) <span class="sc">%>%</span></span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a> parameters<span class="sc">::</span><span class="fu">parameters</span>(<span class="at">df_method=</span><span class="st">"wald"</span>) <span class="sc">%>%</span></span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(Parameter, Coefficient, p) <span class="sc">%>%</span></span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(stringr<span class="sc">::</span><span class="fu">str_detect</span>(Parameter, <span class="st">'outcome_type'</span>),</span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a> stringr<span class="sc">::</span><span class="fu">str_detect</span>(Parameter, <span class="st">':value'</span>)) <span class="sc">%>%</span></span>
<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">arrange</span>(<span class="fu">desc</span>(Coefficient)) <span class="sc">%>%</span> </span>
<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a> knitr<span class="sc">::</span><span class="fu">kable</span>(<span class="at">digits=</span><span class="dv">2</span>) </span></code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">Parameter</th>
<th align="right">Coefficient</th>
<th align="right">p</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">outcome_typelinear:estimateMean:value</td>
<td align="right">10.85</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typelinear:estimateMedian:value</td>
<td align="right">10.84</td>
<td align="right">0</td>
</tr>
<tr class="odd">
<td align="left">outcome_typelinear:estimateMAP:value</td>
<td align="right">10.72</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typelinear:estimateCoefficient:value</td>
<td align="right">10.54</td>
<td align="right">0</td>
</tr>
<tr class="odd">
<td align="left">outcome_typebinary:estimateMAP:value</td>
<td align="right">4.39</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typebinary:estimateMedian:value</td>
<td align="right">4.28</td>
<td align="right">0</td>
</tr>
<tr class="odd">
<td align="left">outcome_typebinary:estimateMean:value</td>
<td align="right">4.21</td>
<td align="right">0</td>
</tr>
<tr class="even">
<td align="left">outcome_typebinary:estimateCoefficient:value</td>
<td align="right">3.87</td>
<td align="right">0</td>
</tr>
</tbody>
</table>
<!-- REMOVE THIS TABLE ONCE NEW PARAMETERS IS ON CRAN SO IT CAN BE GENERATED ON THE RUN-->
<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"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>df <span class="ot"><-</span> <span class="fu">read.csv</span>(<span class="st">"https://raw.github.com/easystats/circus/master/data/bayesSim_study2.csv"</span>)</span></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"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>df <span class="sc">%>%</span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(iterations, true_effect, outcome_type, beta, Median, Mean, MAP) <span class="sc">%>%</span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">gather</span>(estimate, value, <span class="sc">-</span>iterations, <span class="sc">-</span>true_effect, <span class="sc">-</span>outcome_type) <span class="sc">%>%</span></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">temp =</span> <span class="fu">as.factor</span>(<span class="fu">cut</span>(iterations, <span class="dv">5</span>, <span class="at">labels =</span> <span class="cn">FALSE</span>))) <span class="sc">%>%</span> </span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(temp) <span class="sc">%>%</span> </span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">iterations_group =</span> <span class="fu">round</span>(<span class="fu">mean</span>(iterations), <span class="dv">1</span>)) <span class="sc">%>%</span> </span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">ungroup</span>() <span class="sc">%>%</span> </span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(value <span class="sc"><</span> <span class="dv">6</span>) <span class="sc">%>%</span></span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> iterations_group, <span class="at">y =</span> value, <span class="at">fill =</span> estimate, <span class="at">group =</span> <span class="fu">interaction</span>(estimate, iterations_group))) <span class="sc">+</span></span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_boxplot</span>(<span class="at">outlier.shape=</span><span class="cn">NA</span>) <span class="sc">+</span></span>
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme_classic</span>() <span class="sc">+</span></span>
<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_fill_manual</span>(<span class="at">values =</span> <span class="fu">c</span>(<span class="st">"beta"</span> <span class="ot">=</span> <span class="st">"#607D8B"</span>, <span class="st">"MAP"</span> <span class="ot">=</span> <span class="st">"#795548"</span>, <span class="st">"Mean"</span> <span class="ot">=</span> <span class="st">"#FF9800"</span>, <span class="st">"Median"</span> <span class="ot">=</span> <span class="st">"#FFEB3B"</span>),</span>
<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"Index"</span>) <span class="sc">+</span></span>
<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">ylab</span>(<span class="st">"Point-estimate of the true value 0</span><span class="sc">\n</span><span class="st">"</span>) <span class="sc">+</span></span>
<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">xlab</span>(<span class="st">"</span><span class="sc">\n</span><span class="st">Number of Iterations"</span>) <span class="sc">+</span></span>
<span id="cb6-16"><a href="#cb6-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">facet_wrap</span>(<span class="sc">~</span> outcome_type <span class="sc">*</span> true_effect, <span class="at">scales=</span><span class="st">"free"</span>) </span></code></pre></div>
<p><img src="data:image/png;base64,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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"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>df <span class="sc">%>%</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">warmup =</span> warmup <span class="sc">/</span> iterations) <span class="sc">%>%</span> </span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(warmup, true_effect, outcome_type, beta, Median, Mean, MAP) <span class="sc">%>%</span></span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">gather</span>(estimate, value, <span class="sc">-</span>warmup, <span class="sc">-</span>true_effect, <span class="sc">-</span>outcome_type) <span class="sc">%>%</span></span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">temp =</span> <span class="fu">as.factor</span>(<span class="fu">cut</span>(warmup, <span class="dv">3</span>, <span class="at">labels =</span> <span class="cn">FALSE</span>))) <span class="sc">%>%</span> </span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(temp) <span class="sc">%>%</span> </span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">warmup_group =</span> <span class="fu">round</span>(<span class="fu">mean</span>(warmup), <span class="dv">1</span>)) <span class="sc">%>%</span> </span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">ungroup</span>() <span class="sc">%>%</span> </span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(value <span class="sc"><</span> <span class="dv">6</span>) <span class="sc">%>%</span> </span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> warmup_group, <span class="at">y =</span> value, <span class="at">fill =</span> estimate, <span class="at">group =</span> <span class="fu">interaction</span>(estimate, warmup_group))) <span class="sc">+</span></span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_boxplot</span>(<span class="at">outlier.shape=</span><span class="cn">NA</span>) <span class="sc">+</span></span>
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme_classic</span>() <span class="sc">+</span></span>
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">scale_fill_manual</span>(<span class="at">values =</span> <span class="fu">c</span>(<span class="st">"beta"</span> <span class="ot">=</span> <span class="st">"#607D8B"</span>, <span class="st">"MAP"</span> <span class="ot">=</span> <span class="st">"#795548"</span>, <span class="st">"Mean"</span> <span class="ot">=</span> <span class="st">"#FF9800"</span>, <span class="st">"Median"</span> <span class="ot">=</span> <span class="st">"#FFEB3B"</span>),</span>
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"Index"</span>) <span class="sc">+</span></span>
<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">ylab</span>(<span class="st">"Point-estimate of the true value 0</span><span class="sc">\n</span><span class="st">"</span>) <span class="sc">+</span></span>
<span id="cb7-16"><a href="#cb7-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">xlab</span>(<span class="st">"</span><span class="sc">\n</span><span class="st">Number of Iterations"</span>) <span class="sc">+</span></span>
<span id="cb7-17"><a href="#cb7-17" aria-hidden="true" tabindex="-1"></a> <span class="fu">facet_wrap</span>(<span class="sc">~</span> outcome_type <span class="sc">*</span> true_effect, <span class="at">scales=</span><span class="st">"free"</span>) </span></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>
</body>
</html>
