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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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" 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>
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</div>
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