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<title>Probability of Direction (pd)</title>

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<h1 class="title toc-ignore">Probability of Direction (pd)</h1>


<div id="TOC">
<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>
</div>

<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" class="uri">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 />
<div id="what-is-the-pd" class="section level1">
<h1>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>
</div>
<div id="relationship-with-the-p-value" class="section level1">
<h1>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: <span class="math display">\[p_{one-sided} =
1-p_d\]</span> Similarly, the <strong>two-sided <em>p</em>-value</strong> (the most commonly reported one) is equivalent through the formula: <span class="math display">\[p_{two-sided} = 2*(1-p_d)\]</span> 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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<img 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" alt="Correlation between the frequentist p-value and the probability of direction (pd)" />
<p class="caption">
Correlation between the frequentist p-value and the probability of direction (pd)
</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>
</div>
<div id="methods-of-computation" class="section level1">
<h1>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>
</div>
<div id="methods-comparison" class="section level1">
<h1>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>
<div id="correlation" class="section level2">
<h2>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"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(bayestestR)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(logspline)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(KernSmooth)</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="co"># Compute the correlations</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a>data <span class="ot">&lt;-</span> <span class="fu">data.frame</span>()</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (the_mean <span class="cf">in</span> <span class="fu">runif</span>(<span class="dv">25</span>, <span class="dv">0</span>, <span class="dv">4</span>)) {</span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a>  <span class="cf">for</span> (the_sd <span class="cf">in</span> <span class="fu">runif</span>(<span class="dv">25</span>, <span class="fl">0.5</span>, <span class="dv">4</span>)) {</span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a>    x <span class="ot">&lt;-</span> <span class="fu">rnorm</span>(<span class="dv">100</span>, the_mean, <span class="fu">abs</span>(the_sd))</span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a>    data <span class="ot">&lt;-</span> <span class="fu">rbind</span>(</span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a>      data,</span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a>      <span class="fu">data.frame</span>(</span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a>        <span class="st">&quot;direct&quot;</span> <span class="ot">=</span> <span class="fu">pd</span>(x),</span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a>        <span class="st">&quot;kernel&quot;</span> <span class="ot">=</span> <span class="fu">pd</span>(x, <span class="at">method =</span> <span class="st">&quot;kernel&quot;</span>),</span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a>        <span class="st">&quot;logspline&quot;</span> <span class="ot">=</span> <span class="fu">pd</span>(x, <span class="at">method =</span> <span class="st">&quot;logspline&quot;</span>),</span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a>        <span class="st">&quot;KernSmooth&quot;</span> <span class="ot">=</span> <span class="fu">pd</span>(x, <span class="at">method =</span> <span class="st">&quot;KernSmooth&quot;</span>)</span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a>      )</span>
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a>    )</span>
<span id="cb1-19"><a href="#cb1-19" aria-hidden="true" tabindex="-1"></a>  }</span>
<span id="cb1-20"><a href="#cb1-20" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb1-21"><a href="#cb1-21" aria-hidden="true" tabindex="-1"></a>data <span class="ot">&lt;-</span> <span class="fu">as.data.frame</span>(<span class="fu">sapply</span>(data, as.numeric))</span>
<span id="cb1-22"><a href="#cb1-22" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-23"><a href="#cb1-23" aria-hidden="true" tabindex="-1"></a><span class="co"># Visualize the correlations</span></span>
<span id="cb1-24"><a href="#cb1-24" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
<span id="cb1-25"><a href="#cb1-25" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(GGally)</span>
<span id="cb1-26"><a href="#cb1-26" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-27"><a href="#cb1-27" aria-hidden="true" tabindex="-1"></a>GGally<span class="sc">::</span><span class="fu">ggpairs</span>(data) <span class="sc">+</span></span>
<span id="cb1-28"><a href="#cb1-28" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_classic</span>()</span></code></pre></div>
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" style="display: block; margin: auto;" /></p>
<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>
</div>
<div id="accuracy" class="section level2">
<h2>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"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>data <span class="ot">&lt;-</span> <span class="fu">data.frame</span>()</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">25</span>) {</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>  the_mean <span class="ot">&lt;-</span> <span class="fu">runif</span>(<span class="dv">1</span>, <span class="dv">0</span>, <span class="dv">4</span>)</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a>  the_sd <span class="ot">&lt;-</span> <span class="fu">abs</span>(<span class="fu">runif</span>(<span class="dv">1</span>, <span class="fl">0.5</span>, <span class="dv">4</span>))</span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a>  parent_distribution <span class="ot">&lt;-</span> <span class="fu">rnorm</span>(<span class="dv">100000</span>, the_mean, the_sd)</span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a>  true_pd <span class="ot">&lt;-</span> <span class="fu">pd</span>(parent_distribution)</span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a>  <span class="cf">for</span> (j <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">25</span>) {</span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a>    sample_size <span class="ot">&lt;-</span> <span class="fu">round</span>(<span class="fu">runif</span>(<span class="dv">1</span>, <span class="dv">25</span>, <span class="dv">5000</span>))</span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a>    subsample <span class="ot">&lt;-</span> <span class="fu">sample</span>(parent_distribution, sample_size)</span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a>    data <span class="ot">&lt;-</span> <span class="fu">rbind</span>(</span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a>      data,</span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a>      <span class="fu">data.frame</span>(</span>
<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a>        <span class="st">&quot;sample_size&quot;</span> <span class="ot">=</span> sample_size,</span>
<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a>        <span class="st">&quot;true&quot;</span> <span class="ot">=</span> true_pd,</span>
<span id="cb2-16"><a href="#cb2-16" aria-hidden="true" tabindex="-1"></a>        <span class="st">&quot;direct&quot;</span> <span class="ot">=</span> <span class="fu">pd</span>(subsample) <span class="sc">-</span> true_pd,</span>
<span id="cb2-17"><a href="#cb2-17" aria-hidden="true" tabindex="-1"></a>        <span class="st">&quot;kernel&quot;</span> <span class="ot">=</span> <span class="fu">pd</span>(subsample, <span class="at">method =</span> <span class="st">&quot;kernel&quot;</span>) <span class="sc">-</span> true_pd,</span>
<span id="cb2-18"><a href="#cb2-18" aria-hidden="true" tabindex="-1"></a>        <span class="st">&quot;logspline&quot;</span> <span class="ot">=</span> <span class="fu">pd</span>(subsample, <span class="at">method =</span> <span class="st">&quot;logspline&quot;</span>) <span class="sc">-</span> true_pd,</span>
<span id="cb2-19"><a href="#cb2-19" aria-hidden="true" tabindex="-1"></a>        <span class="st">&quot;KernSmooth&quot;</span> <span class="ot">=</span> <span class="fu">pd</span>(subsample, <span class="at">method =</span> <span class="st">&quot;KernSmooth&quot;</span>) <span class="sc">-</span> true_pd</span>
<span id="cb2-20"><a href="#cb2-20" aria-hidden="true" tabindex="-1"></a>      )</span>
<span id="cb2-21"><a href="#cb2-21" aria-hidden="true" tabindex="-1"></a>    )</span>
<span id="cb2-22"><a href="#cb2-22" aria-hidden="true" tabindex="-1"></a>  }</span>
<span id="cb2-23"><a href="#cb2-23" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb2-24"><a href="#cb2-24" aria-hidden="true" tabindex="-1"></a>data <span class="ot">&lt;-</span> <span class="fu">as.data.frame</span>(<span class="fu">sapply</span>(data, as.numeric))</span></code></pre></div>
<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><span class="fu">library</span>(tidyr)</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(dplyr)</span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a>data <span class="sc">%&gt;%</span></span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a>  tidyr<span class="sc">::</span><span class="fu">gather</span>(Method, Distance, <span class="sc">-</span>sample_size, <span class="sc">-</span>true) <span class="sc">%&gt;%</span></span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">ggplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> sample_size, <span class="at">y =</span> Distance, <span class="at">color =</span> Method, <span class="at">fill =</span> Method)) <span class="sc">+</span></span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="at">alpha =</span> <span class="fl">0.3</span>, <span class="at">stroke =</span> <span class="dv">0</span>, <span class="at">shape =</span> <span class="dv">16</span>) <span class="sc">+</span></span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_smooth</span>(<span class="at">alpha =</span> <span class="fl">0.2</span>) <span class="sc">+</span></span>
<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_hline</span>(<span class="at">yintercept =</span> <span class="dv">0</span>) <span class="sc">+</span></span>
<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_classic</span>() <span class="sc">+</span></span>
<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a>  <span class="fu">xlab</span>(<span class="st">&quot;</span><span class="sc">\n</span><span class="st">Distribution Size&quot;</span>)</span></code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<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>
</div>
<div id="can-the-pd-be-100" class="section level2">
<h2>Can the pd be 100%?</h2>
<p><code>p = 0.000</code> is coined as one of the term to avoid when reporting results <span class="citation">(Lilienfeld et al., 2015)</span>, 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 csl-bib-body hanging-indent" line-spacing="2">
<div id="ref-lilienfeld2015fifty" class="csl-entry">
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>
</div>
</div>
</div>
</div>



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