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<body>

<h1 id="probability-of-direction-pd">Probability of Direction (pd)</h1>
<ul>
<li><a href="#what-is-the-pd">What is the <em>pd?</em></a></li>
<li><a href="#relationship-with-the-p-value">Relationship with the <em>p</em>-value</a></li>
<li><a href="#methods-of-computation">Methods of computation</a></li>
<li><a href="#methods-comparison">Methods comparison</a>
<ul>
<li><a href="#correlation">Correlation</a></li>
<li><a href="#accuracy">Accuracy</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="what-is-the-pd">What is the <em>pd?</em></h1>
<p>The <strong>Probability of Direction (pd)</strong> is an index of <strong>effect existence</strong>, ranging from 50% to 100%, representing the certainty with which an effect goes in a particular direction (<em>i.e.</em>, is positive or negative).</p>
<p>Beyond its <strong>simplicity of interpretation, understanding and computation</strong>, this index also presents other interesting properties:</p>
<ul>
<li>It is <strong>independent from the model</strong>: It is solely based on the posterior distributions and does not require any additional information from the data or the model.</li>
<li>It is <strong>robust</strong> to the scale of both the response variable and the predictors.</li>
<li>It is strongly correlated with the frequentist <strong><em>p</em>-value</strong>, and can thus be used to draw parallels and give some reference to readers non-familiar with Bayesian statistics.</li>
</ul>
<p>However, this index is not relevant to assess the magnitude and importance of an effect (the meaning of “significance”), which is better achieved through other indices such as the <a href="https://easystats.github.io/bayestestR/articles/region_of_practical_equivalence.html">ROPE percentage</a>. In fact, indices of significance and existence are totally independent. You can have an effect with a <em>pd</em> of <strong>99.99%</strong>, for which the whole posterior distribution is concentrated in the <code>[0.0001, 0.002]</code> range. In this case, the effect is <strong>positive with a high certainty</strong>, but also <strong>not significant</strong> (<em>i.e.</em>, very small).</p>
<p>Indices of effect existence, such as the <em>pd</em>, are particularly useful in exploratory research or clinical studies, for which the focus is to make sure that the effect of interest is not in the opposite direction (for clinical studies, that a treatment is not harmful). However, once the effect’s direction is confirmed, the focus should shift toward its significance, including a precise estimation of its magnitude, relevance and importance.</p>
<h1 id="relationship-with-the-p-value">Relationship with the <em>p</em>-value</h1>
<p>In most cases, it seems that the <em>pd</em> has a direct correspondance with the frequentist <strong>one-sided <em>p</em>-value</strong> through the formula: [p_{one sided} = 1-p_d/100] Similarly, the <strong>two-sided <em>p</em>-value</strong> (the most commonly reported one) is equivalent through the formula: [p_{two sided} = 2*(1-p_d/100)] Thus, the two-sided <em>p</em>-value of respectively <strong>.1</strong>, <strong>.05</strong>, <strong>.01</strong> and <strong>.001</strong> would correspond approximately to a <em>pd</em> of <strong>95%</strong>, <strong>97.5%</strong>, <strong>99.5%</strong> and <strong>99.95%</strong> .</p>
<img 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" title="Correlation between the frequentist p-value and the probability of direction (pd)" alt="Correlation between the frequentist p-value and the probability of direction (pd)" style="display: block; margin: auto;" />

<blockquote>
<p><strong>But if it’s like the <em>p</em>-value, it must be bad because the <em>p</em>-value is bad [<em>insert reference to the reproducibility crisis</em>].</strong></p>
</blockquote>
<p>In fact, this aspect of the reproducibility crisis might have been misunderstood. Indeed, it is not that the <em>p</em>-value is an intrinsically bad or wrong index. Rather, it is its <strong>misuse</strong>, <strong>misunderstanding</strong> and <strong>misinterpretation</strong> that fuels the decay of the situation. For instance, the fact that the <strong>pd</strong> is highly correlated with the <em>p</em>-value suggests that the latter is more an index of effect <em>existence</em> than <em>significance</em> (<em>i.e.</em>, “worth of interest”). The Bayesian version, the <strong>pd</strong>, has an intuitive meaning and makes obvious the fact that <strong>all thresholds are arbitrary</strong>. Nevertheless, the <strong>mathematical and interpretative transparency</strong> of the <strong>pd</strong>, and its reconceptualisation as an index of effect existence, offers a valuable insight into the characterization of Bayesian results. Moreover, its concomittant proximity with the frequentist <em>p</em>-value makes it a perfect metric to ease the transition of psychological research into the adoption of the Bayesian framework.</p>
<h1 id="methods-of-computation">Methods of computation</h1>
<p>The most <strong>simple and direct</strong> way to compute the <strong>pd</strong> is to 1) look at the median’s sign, 2) select the portion of the posterior of the same sign and 3) compute the percentage that this portion represents. This “simple” method is the most straigtfoward, but its precision is directly tied to the number of posterior draws.</p>
<p>The second approach relies on <a href="https://easystats.github.io/bayestestR/reference/estimate_density.html"><strong>density estimation</strong></a>. It starts by estimating the density function (for which many methods are available), and then computing the <a href="https://easystats.github.io/bayestestR/reference/area_under_curve.html"><strong>area under the curve</strong></a> (AUC) of the density curve on the other side of 0. The density-based method could hypothetically be considered as more precise, but strongly depends on the method used to estimate the density function.</p>
<h1 id="methods-comparison">Methods comparison</h1>
<p>Let’s compare the 4 available methods, the <strong>direct</strong> method and 3 <strong>density-based</strong> methods differing by their density estimation algorithm (see <a href="https://easystats.github.io/bayestestR/reference/estimate_density.html"><code>estimate_density</code></a>).</p>
<h2 id="correlation">Correlation</h2>
<p>Let’s start by testing the proximity and similarity of the results obtained by different methods.</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>(bayestestR)</a>
<a class="sourceLine" id="cb1-2" title="2"><span class="kw">library</span>(logspline)</a>
<a class="sourceLine" id="cb1-3" title="3"><span class="kw">library</span>(KernSmooth)</a>
<a class="sourceLine" id="cb1-4" title="4"></a>
<a class="sourceLine" id="cb1-5" title="5"><span class="co"># Compute the correlations</span></a>
<a class="sourceLine" id="cb1-6" title="6">data &lt;-<span class="st"> </span><span class="kw">data.frame</span>()</a>
<a class="sourceLine" id="cb1-7" title="7"><span class="cf">for</span>(the_mean <span class="cf">in</span> <span class="kw">runif</span>(<span class="dv">25</span>, <span class="dv">0</span>, <span class="dv">4</span>)){</a>
<a class="sourceLine" id="cb1-8" title="8">  <span class="cf">for</span>(the_sd <span class="cf">in</span> <span class="kw">runif</span>(<span class="dv">25</span>, <span class="fl">0.5</span>, <span class="dv">4</span>)){</a>
<a class="sourceLine" id="cb1-9" title="9">    x &lt;-<span class="st"> </span><span class="kw">rnorm</span>(<span class="dv">100</span>, the_mean, <span class="kw">abs</span>(the_sd))</a>
<a class="sourceLine" id="cb1-10" title="10">    data &lt;-<span class="st"> </span><span class="kw">rbind</span>(data,</a>
<a class="sourceLine" id="cb1-11" title="11">      <span class="kw">data.frame</span>(<span class="st">&quot;direct&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x),</a>
<a class="sourceLine" id="cb1-12" title="12">                 <span class="st">&quot;kernel&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x, <span class="dt">method=</span><span class="st">&quot;kernel&quot;</span>),</a>
<a class="sourceLine" id="cb1-13" title="13">                 <span class="st">&quot;logspline&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x, <span class="dt">method=</span><span class="st">&quot;logspline&quot;</span>),</a>
<a class="sourceLine" id="cb1-14" title="14">                 <span class="st">&quot;KernSmooth&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x, <span class="dt">method=</span><span class="st">&quot;KernSmooth&quot;</span>)</a>
<a class="sourceLine" id="cb1-15" title="15">                 ))</a>
<a class="sourceLine" id="cb1-16" title="16">  }</a>
<a class="sourceLine" id="cb1-17" title="17">}</a>
<a class="sourceLine" id="cb1-18" title="18">data &lt;-<span class="st"> </span><span class="kw">as.data.frame</span>(<span class="kw">sapply</span>(data, as.numeric))</a>
<a class="sourceLine" id="cb1-19" title="19"></a>
<a class="sourceLine" id="cb1-20" title="20"><span class="co"># Visualize the correlations</span></a>
<a class="sourceLine" id="cb1-21" title="21"><span class="kw">library</span>(ggplot2)</a>
<a class="sourceLine" id="cb1-22" title="22"><span class="kw">library</span>(GGally)</a>
<a class="sourceLine" id="cb1-23" title="23"></a>
<a class="sourceLine" id="cb1-24" title="24">GGally<span class="op">::</span><span class="kw">ggpairs</span>(data) <span class="op">+</span></a>
<a class="sourceLine" id="cb1-25" title="25"><span class="st">  </span><span class="kw">theme_classic</span>()</a></code></pre></div>
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style="display: block; margin: auto;" />

<p>All methods give are highly correlated and give very similar results. That means that the method choice is not a drastic game changer and cannot be used to tweak the results too much.</p>
<h2 id="accuracy">Accuracy</h2>
<p>To test the accuracy of each methods, we will start by computing the <strong>direct <em>pd</em></strong> from a very dense distribution (with a large amount of observations). This will be our baseline, or “true” <em>pd</em>. Then, we will iteratively draw smaller samples from this parent distribution, and we will compute the <em>pd</em> with different methods. The closer this estimate is from the reference one, the better.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" title="1">data &lt;-<span class="st"> </span><span class="kw">data.frame</span>()</a>
<a class="sourceLine" id="cb2-2" title="2"><span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="dv">25</span>){</a>
<a class="sourceLine" id="cb2-3" title="3">  the_mean &lt;-<span class="st"> </span><span class="kw">runif</span>(<span class="dv">1</span>, <span class="dv">0</span>, <span class="dv">4</span>)</a>
<a class="sourceLine" id="cb2-4" title="4">  the_sd &lt;-<span class="st"> </span><span class="kw">abs</span>(<span class="kw">runif</span>(<span class="dv">1</span>, <span class="fl">0.5</span>, <span class="dv">4</span>))</a>
<a class="sourceLine" id="cb2-5" title="5">  parent_distribution &lt;-<span class="st"> </span><span class="kw">rnorm</span>(<span class="dv">100000</span>, the_mean, the_sd)</a>
<a class="sourceLine" id="cb2-6" title="6">  true_pd &lt;-<span class="st"> </span><span class="kw">pd</span>(parent_distribution)</a>
<a class="sourceLine" id="cb2-7" title="7">  </a>
<a class="sourceLine" id="cb2-8" title="8">  <span class="cf">for</span>(j <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="dv">25</span>){</a>
<a class="sourceLine" id="cb2-9" title="9">    sample_size &lt;-<span class="st"> </span><span class="kw">round</span>(<span class="kw">runif</span>(<span class="dv">1</span>, <span class="dv">25</span>, <span class="dv">5000</span>))</a>
<a class="sourceLine" id="cb2-10" title="10">    subsample &lt;-<span class="st"> </span><span class="kw">sample</span>(parent_distribution, sample_size)</a>
<a class="sourceLine" id="cb2-11" title="11">    data &lt;-<span class="st"> </span><span class="kw">rbind</span>(data,</a>
<a class="sourceLine" id="cb2-12" title="12">      <span class="kw">data.frame</span>(<span class="st">&quot;sample_size&quot;</span> =<span class="st"> </span>sample_size, </a>
<a class="sourceLine" id="cb2-13" title="13">                 <span class="st">&quot;true&quot;</span> =<span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-14" title="14">                 <span class="st">&quot;direct&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample) <span class="op">-</span><span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-15" title="15">                 <span class="st">&quot;kernel&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample, <span class="dt">method=</span><span class="st">&quot;kernel&quot;</span>)<span class="op">-</span><span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-16" title="16">                 <span class="st">&quot;logspline&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample, <span class="dt">method=</span><span class="st">&quot;logspline&quot;</span>) <span class="op">-</span><span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-17" title="17">                 <span class="st">&quot;KernSmooth&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample, <span class="dt">method=</span><span class="st">&quot;KernSmooth&quot;</span>) <span class="op">-</span><span class="st"> </span>true_pd</a>
<a class="sourceLine" id="cb2-18" title="18">                 ))</a>
<a class="sourceLine" id="cb2-19" title="19">  }</a>
<a class="sourceLine" id="cb2-20" title="20">}</a>
<a class="sourceLine" id="cb2-21" title="21">data &lt;-<span class="st"> </span><span class="kw">as.data.frame</span>(<span class="kw">sapply</span>(data, as.numeric))</a></code></pre></div>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb3-1" title="1"><span class="kw">library</span>(tidyr)</a>
<a class="sourceLine" id="cb3-2" title="2"><span class="kw">library</span>(dplyr)</a>
<a class="sourceLine" id="cb3-3" title="3"></a>
<a class="sourceLine" id="cb3-4" title="4">data <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb3-5" title="5"><span class="st">  </span>tidyr<span class="op">::</span><span class="kw">gather</span>(Method, Distance, <span class="op">-</span>sample_size, <span class="op">-</span>true) <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">ggplot</span>(<span class="kw">aes</span>(<span class="dt">x=</span>sample_size, <span class="dt">y =</span> Distance, <span class="dt">color =</span> Method, <span class="dt">fill=</span> Method)) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-7" title="7"><span class="st">  </span><span class="kw">geom_point</span>(<span class="dt">alpha=</span><span class="fl">0.3</span>, <span class="dt">stroke=</span><span class="dv">0</span>, <span class="dt">shape=</span><span class="dv">16</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-8" title="8"><span class="st">  </span><span class="kw">geom_smooth</span>(<span class="dt">alpha=</span><span class="fl">0.2</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-9" title="9"><span class="st">  </span><span class="kw">geom_hline</span>(<span class="dt">yintercept=</span><span class="dv">0</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-10" title="10"><span class="st">  </span><span class="kw">theme_classic</span>() <span class="op">+</span></a>
<a class="sourceLine" id="cb3-11" title="11"><span class="st">  </span><span class="kw">xlab</span>(<span class="st">&quot;</span><span class="ch">\n</span><span class="st">Distribution Size&quot;</span>)</a></code></pre></div>
<img 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" 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<p>The “Kernel” based density methods seems to consistently underestimate the <em>pd</em>. Interestingly, the “direct” method appears as being the more reliable, even in the case of small number of posterior draws.</p>

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