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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>. Frontiers in Psychology 2019;10:2767. <a href="https://doi.org/10.3389/fpsyg.2019.02767">10.3389/fpsyg.2019.02767</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>
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" alt="Correlation between the frequentist p-value and the probability of direction (pd)" />

<p class="caption">

<p>Correlation between the frequentist p-value and the probability of direction (pd)</p>
</p>

</div>

<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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" 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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>
<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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