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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>
<li><a href="#can-the-pd-be-100">Can the pd be 100%?</a></li>
</ul></li>
</ul>
<p>This vignette can be referred to by citing the package:</p>
<ul>
<li>Makowski, D., Ben-Shachar, M. S., &amp; Lüdecke, D. (2019). <em>bayestestR: Describing Effects and their Uncertainty, Existence and Significance within the Bayesian Framework</em>. Journal of Open Source Software, 4(40), 1541. <a href="https://doi.org/10.21105/joss.01541">https://doi.org/10.21105/joss.01541</a></li>
<li>Makowski, D., Ben-Shachar, M. S., Chen, S. H. A., &amp; Lüdecke, D. (2019). <em>Indices of Effect Existence and Significance in the Bayesian Framework</em>. Retrieved from <a href="https://doi.org/10.31234/osf.io/2zexr">https://doi.org/10.31234/osf.io/2zexr</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 within the <code>[0.0001, 0.0002]</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 correspondence with the frequentist <strong>one-sided <em>p</em>-value</strong> through the formula: [p_{one-sided} = 1-p_d] 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)] 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. Instead, 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>. Additionally, 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 concomitant 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 straightforward, 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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" style="display: block; margin: auto;" />

<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>
<h2 id="can-the-pd-be-100">Can the pd be 100%?</h2>
<p><code>p = 0.000</code> is coined as one of the term to avoid when reporting results (Lilienfeld et al., 2015), even if often displayed by statistical software. The rationale is that for every probability distribution, there is no value with a probability of exactly 0. There is always some infinitesimal probability associated with each data point, and the <code>p = 0.000</code> returned by software is due to approximations related, among other, to finite memory hardware.</p>
<p>One could apply this rationale for the <em>pd</em>: since all data points have a non-null probability density, then the <em>pd</em> (a particular portion of the probability density) can <em>never</em> be 100%. While this is an entirely valid point, people using the <em>direct</em> method might argue that their <em>pd</em> is based on the posterior draws, rather than on the theoretical, hidden, true posterior distribution (which is only approximated by the posterior draws). These posterior draws represent a finite sample for which <code>pd = 100%</code> is a valid statement.</p>
<div id="refs" class="references">

<div id="ref-lilienfeld2015fifty">

<p>Lilienfeld, S. O., Sauvigné, K. C., Lynn, S. J., Cautin, R. L., Latzman, R. D., &amp; Waldman, I. D. (2015). Fifty psychological and psychiatric terms to avoid: A list of inaccurate, misleading, misused, ambiguous, and logically confused words and phrases. <em>Frontiers in Psychology</em>, <em>6</em>, 1100. <a href="https://doi.org/10.3389/fpsyg.2015.01100">https://doi.org/10.3389/fpsyg.2015.01100</a></p>
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