https://github.com/cran/bayestestR
Raw File
Tip revision: 6313ce21ea98857cf95d996de7978cfd52175e59 authored by Dominique Makowski on 08 April 2021, 04:40:02 UTC
version 0.9.0
Tip revision: 6313ce2
mediation.html
<!DOCTYPE html>

<html>

<head>

<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />

<meta name="viewport" content="width=device-width, initial-scale=1" />



<title>Summary of Mediation Analysis using Bayesian Regression Models</title>

<script src="data:application/javascript;base64,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"></script>

<style type="text/css">
  code{white-space: pre-wrap;}
  span.smallcaps{font-variant: small-caps;}
  span.underline{text-decoration: underline;}
  div.column{display: inline-block; vertical-align: top; width: 50%;}
  div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
  ul.task-list{list-style: none;}
    </style>


<style type="text/css">
  code {
    white-space: pre;
  }
  .sourceCode {
    overflow: visible;
  }
</style>
<style type="text/css" data-origin="pandoc">
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
  { counter-reset: source-line 0; }
pre.numberSource code > span
  { position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
  { content: counter(source-line);
    position: relative; left: -1em; text-align: right; vertical-align: baseline;
    border: none; display: inline-block;
    -webkit-touch-callout: none; -webkit-user-select: none;
    -khtml-user-select: none; -moz-user-select: none;
    -ms-user-select: none; user-select: none;
    padding: 0 4px; width: 4em;
    color: #aaaaaa;
  }
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa;  padding-left: 4px; }
div.sourceCode
  {   }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span.al { color: #ff0000; font-weight: bold; } /* Alert */
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
code span.at { color: #7d9029; } /* Attribute */
code span.bn { color: #40a070; } /* BaseN */
code span.bu { } /* BuiltIn */
code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */
code span.ch { color: #4070a0; } /* Char */
code span.cn { color: #880000; } /* Constant */
code span.co { color: #60a0b0; font-style: italic; } /* Comment */
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */
code span.do { color: #ba2121; font-style: italic; } /* Documentation */
code span.dt { color: #902000; } /* DataType */
code span.dv { color: #40a070; } /* DecVal */
code span.er { color: #ff0000; font-weight: bold; } /* Error */
code span.ex { } /* Extension */
code span.fl { color: #40a070; } /* Float */
code span.fu { color: #06287e; } /* Function */
code span.im { } /* Import */
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
code span.kw { color: #007020; font-weight: bold; } /* Keyword */
code span.op { color: #666666; } /* Operator */
code span.ot { color: #007020; } /* Other */
code span.pp { color: #bc7a00; } /* Preprocessor */
code span.sc { color: #4070a0; } /* SpecialChar */
code span.ss { color: #bb6688; } /* SpecialString */
code span.st { color: #4070a0; } /* String */
code span.va { color: #19177c; } /* Variable */
code span.vs { color: #4070a0; } /* VerbatimString */
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */

</style>
<script>
// apply pandoc div.sourceCode style to pre.sourceCode instead
(function() {
  var sheets = document.styleSheets;
  for (var i = 0; i < sheets.length; i++) {
    if (sheets[i].ownerNode.dataset["origin"] !== "pandoc") continue;
    try { var rules = sheets[i].cssRules; } catch (e) { continue; }
    for (var j = 0; j < rules.length; j++) {
      var rule = rules[j];
      // check if there is a div.sourceCode rule
      if (rule.type !== rule.STYLE_RULE || rule.selectorText !== "div.sourceCode") continue;
      var style = rule.style.cssText;
      // check if color or background-color is set
      if (rule.style.color === '' && rule.style.backgroundColor === '') continue;
      // replace div.sourceCode by a pre.sourceCode rule
      sheets[i].deleteRule(j);
      sheets[i].insertRule('pre.sourceCode{' + style + '}', j);
    }
  }
})();
</script>




<link rel="stylesheet" href="data:text/css,body%20%7B%0Abackground%2Dcolor%3A%20%23fff%3B%0Amargin%3A%201em%20auto%3B%0Amax%2Dwidth%3A%20700px%3B%0Aoverflow%3A%20visible%3B%0Apadding%2Dleft%3A%202em%3B%0Apadding%2Dright%3A%202em%3B%0Afont%2Dfamily%3A%20%22Open%20Sans%22%2C%20%22Helvetica%20Neue%22%2C%20Helvetica%2C%20Arial%2C%20sans%2Dserif%3B%0Afont%2Dsize%3A%2014px%3B%0Aline%2Dheight%3A%201%2E35%3B%0A%7D%0A%23TOC%20%7B%0Aclear%3A%20both%3B%0Amargin%3A%200%200%2010px%2010px%3B%0Apadding%3A%204px%3B%0Awidth%3A%20400px%3B%0Aborder%3A%201px%20solid%20%23CCCCCC%3B%0Aborder%2Dradius%3A%205px%3B%0Abackground%2Dcolor%3A%20%23f6f6f6%3B%0Afont%2Dsize%3A%2013px%3B%0Aline%2Dheight%3A%201%2E3%3B%0A%7D%0A%23TOC%20%2Etoctitle%20%7B%0Afont%2Dweight%3A%20bold%3B%0Afont%2Dsize%3A%2015px%3B%0Amargin%2Dleft%3A%205px%3B%0A%7D%0A%23TOC%20ul%20%7B%0Apadding%2Dleft%3A%2040px%3B%0Amargin%2Dleft%3A%20%2D1%2E5em%3B%0Amargin%2Dtop%3A%205px%3B%0Amargin%2Dbottom%3A%205px%3B%0A%7D%0A%23TOC%20ul%20ul%20%7B%0Amargin%2Dleft%3A%20%2D2em%3B%0A%7D%0A%23TOC%20li%20%7B%0Aline%2Dheight%3A%2016px%3B%0A%7D%0Atable%20%7B%0Amargin%3A%201em%20auto%3B%0Aborder%2Dwidth%3A%201px%3B%0Aborder%2Dcolor%3A%20%23DDDDDD%3B%0Aborder%2Dstyle%3A%20outset%3B%0Aborder%2Dcollapse%3A%20collapse%3B%0A%7D%0Atable%20th%20%7B%0Aborder%2Dwidth%3A%202px%3B%0Apadding%3A%205px%3B%0Aborder%2Dstyle%3A%20inset%3B%0A%7D%0Atable%20td%20%7B%0Aborder%2Dwidth%3A%201px%3B%0Aborder%2Dstyle%3A%20inset%3B%0Aline%2Dheight%3A%2018px%3B%0Apadding%3A%205px%205px%3B%0A%7D%0Atable%2C%20table%20th%2C%20table%20td%20%7B%0Aborder%2Dleft%2Dstyle%3A%20none%3B%0Aborder%2Dright%2Dstyle%3A%20none%3B%0A%7D%0Atable%20thead%2C%20table%20tr%2Eeven%20%7B%0Abackground%2Dcolor%3A%20%23f7f7f7%3B%0A%7D%0Ap%20%7B%0Amargin%3A%200%2E5em%200%3B%0A%7D%0Ablockquote%20%7B%0Abackground%2Dcolor%3A%20%23f6f6f6%3B%0Apadding%3A%200%2E25em%200%2E75em%3B%0A%7D%0Ahr%20%7B%0Aborder%2Dstyle%3A%20solid%3B%0Aborder%3A%20none%3B%0Aborder%2Dtop%3A%201px%20solid%20%23777%3B%0Amargin%3A%2028px%200%3B%0A%7D%0Adl%20%7B%0Amargin%2Dleft%3A%200%3B%0A%7D%0Adl%20dd%20%7B%0Amargin%2Dbottom%3A%2013px%3B%0Amargin%2Dleft%3A%2013px%3B%0A%7D%0Adl%20dt%20%7B%0Afont%2Dweight%3A%20bold%3B%0A%7D%0Aul%20%7B%0Amargin%2Dtop%3A%200%3B%0A%7D%0Aul%20li%20%7B%0Alist%2Dstyle%3A%20circle%20outside%3B%0A%7D%0Aul%20ul%20%7B%0Amargin%2Dbottom%3A%200%3B%0A%7D%0Apre%2C%20code%20%7B%0Abackground%2Dcolor%3A%20%23f7f7f7%3B%0Aborder%2Dradius%3A%203px%3B%0Acolor%3A%20%23333%3B%0Awhite%2Dspace%3A%20pre%2Dwrap%3B%20%0A%7D%0Apre%20%7B%0Aborder%2Dradius%3A%203px%3B%0Amargin%3A%205px%200px%2010px%200px%3B%0Apadding%3A%2010px%3B%0A%7D%0Apre%3Anot%28%5Bclass%5D%29%20%7B%0Abackground%2Dcolor%3A%20%23f7f7f7%3B%0A%7D%0Acode%20%7B%0Afont%2Dfamily%3A%20Consolas%2C%20Monaco%2C%20%27Courier%20New%27%2C%20monospace%3B%0Afont%2Dsize%3A%2085%25%3B%0A%7D%0Ap%20%3E%20code%2C%20li%20%3E%20code%20%7B%0Apadding%3A%202px%200px%3B%0A%7D%0Adiv%2Efigure%20%7B%0Atext%2Dalign%3A%20center%3B%0A%7D%0Aimg%20%7B%0Abackground%2Dcolor%3A%20%23FFFFFF%3B%0Apadding%3A%202px%3B%0Aborder%3A%201px%20solid%20%23DDDDDD%3B%0Aborder%2Dradius%3A%203px%3B%0Aborder%3A%201px%20solid%20%23CCCCCC%3B%0Amargin%3A%200%205px%3B%0A%7D%0Ah1%20%7B%0Amargin%2Dtop%3A%200%3B%0Afont%2Dsize%3A%2035px%3B%0Aline%2Dheight%3A%2040px%3B%0A%7D%0Ah2%20%7B%0Aborder%2Dbottom%3A%204px%20solid%20%23f7f7f7%3B%0Apadding%2Dtop%3A%2010px%3B%0Apadding%2Dbottom%3A%202px%3B%0Afont%2Dsize%3A%20145%25%3B%0A%7D%0Ah3%20%7B%0Aborder%2Dbottom%3A%202px%20solid%20%23f7f7f7%3B%0Apadding%2Dtop%3A%2010px%3B%0Afont%2Dsize%3A%20120%25%3B%0A%7D%0Ah4%20%7B%0Aborder%2Dbottom%3A%201px%20solid%20%23f7f7f7%3B%0Amargin%2Dleft%3A%208px%3B%0Afont%2Dsize%3A%20105%25%3B%0A%7D%0Ah5%2C%20h6%20%7B%0Aborder%2Dbottom%3A%201px%20solid%20%23ccc%3B%0Afont%2Dsize%3A%20105%25%3B%0A%7D%0Aa%20%7B%0Acolor%3A%20%230033dd%3B%0Atext%2Ddecoration%3A%20none%3B%0A%7D%0Aa%3Ahover%20%7B%0Acolor%3A%20%236666ff%3B%20%7D%0Aa%3Avisited%20%7B%0Acolor%3A%20%23800080%3B%20%7D%0Aa%3Avisited%3Ahover%20%7B%0Acolor%3A%20%23BB00BB%3B%20%7D%0Aa%5Bhref%5E%3D%22http%3A%22%5D%20%7B%0Atext%2Ddecoration%3A%20underline%3B%20%7D%0Aa%5Bhref%5E%3D%22https%3A%22%5D%20%7B%0Atext%2Ddecoration%3A%20underline%3B%20%7D%0A%0Acode%20%3E%20span%2Ekw%20%7B%20color%3A%20%23555%3B%20font%2Dweight%3A%20bold%3B%20%7D%20%0Acode%20%3E%20span%2Edt%20%7B%20color%3A%20%23902000%3B%20%7D%20%0Acode%20%3E%20span%2Edv%20%7B%20color%3A%20%2340a070%3B%20%7D%20%0Acode%20%3E%20span%2Ebn%20%7B%20color%3A%20%23d14%3B%20%7D%20%0Acode%20%3E%20span%2Efl%20%7B%20color%3A%20%23d14%3B%20%7D%20%0Acode%20%3E%20span%2Ech%20%7B%20color%3A%20%23d14%3B%20%7D%20%0Acode%20%3E%20span%2Est%20%7B%20color%3A%20%23d14%3B%20%7D%20%0Acode%20%3E%20span%2Eco%20%7B%20color%3A%20%23888888%3B%20font%2Dstyle%3A%20italic%3B%20%7D%20%0Acode%20%3E%20span%2Eot%20%7B%20color%3A%20%23007020%3B%20%7D%20%0Acode%20%3E%20span%2Eal%20%7B%20color%3A%20%23ff0000%3B%20font%2Dweight%3A%20bold%3B%20%7D%20%0Acode%20%3E%20span%2Efu%20%7B%20color%3A%20%23900%3B%20font%2Dweight%3A%20bold%3B%20%7D%20%0Acode%20%3E%20span%2Eer%20%7B%20color%3A%20%23a61717%3B%20background%2Dcolor%3A%20%23e3d2d2%3B%20%7D%20%0A" type="text/css" />




</head>

<body>




<h1 class="title toc-ignore">Summary of Mediation Analysis using Bayesian Regression Models</h1>


<div id="TOC">
<ul>
<li><a href="#mediation-analysis-in-brms-and-rstanarm">Mediation Analysis in brms and rstanarm</a></li>
<li><a href="#comparison-to-the-mediation-package">Comparison to the mediation package</a></li>
<li><a href="#comparison-to-sem-from-the-lavaan-package">Comparison to SEM from the lavaan package</a></li>
</ul>
</div>

<p>This vignettes demonstrates the <code>mediation()</code>-function. Before we start, we fit some models, including a mediation-object from the <em>mediation</em>-package and a structural equation modelling approach with the <em>lavaan</em>-package, both of which we use for comparison with <em>brms</em> and <em>rstanarm</em>.</p>
<div id="mediation-analysis-in-brms-and-rstanarm" class="section level2">
<h2>Mediation Analysis in brms and rstanarm</h2>
<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>(mediation)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(brms)</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(rstanarm)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="co"># load sample data</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(jobs)</span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">123</span>)</span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a><span class="co"># linear models, for mediation analysis</span></span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a>b1 <span class="ot">&lt;-</span> <span class="fu">lm</span>(job_seek <span class="sc">~</span> treat <span class="sc">+</span> econ_hard <span class="sc">+</span> sex <span class="sc">+</span> age, <span class="at">data =</span> jobs)</span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a>b2 <span class="ot">&lt;-</span> <span class="fu">lm</span>(depress2 <span class="sc">~</span> treat <span class="sc">+</span> job_seek <span class="sc">+</span> econ_hard <span class="sc">+</span> sex <span class="sc">+</span> age, <span class="at">data =</span> jobs)</span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a><span class="co"># mediation analysis, for comparison with brms</span></span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a>m1 <span class="ot">&lt;-</span> <span class="fu">mediate</span>(b1, b2, <span class="at">sims =</span> <span class="dv">1000</span>, <span class="at">treat =</span> <span class="st">&quot;treat&quot;</span>, <span class="at">mediator =</span> <span class="st">&quot;job_seek&quot;</span>)</span></code></pre></div>
<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><span class="co"># Fit Bayesian mediation model in brms</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>f1 <span class="ot">&lt;-</span> <span class="fu">bf</span>(job_seek <span class="sc">~</span> treat <span class="sc">+</span> econ_hard <span class="sc">+</span> sex <span class="sc">+</span> age)</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>f2 <span class="ot">&lt;-</span> <span class="fu">bf</span>(depress2 <span class="sc">~</span> treat <span class="sc">+</span> job_seek <span class="sc">+</span> econ_hard <span class="sc">+</span> sex <span class="sc">+</span> age)</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a>m2 <span class="ot">&lt;-</span> <span class="fu">brm</span>(f1 <span class="sc">+</span> f2 <span class="sc">+</span> <span class="fu">set_rescor</span>(<span class="cn">FALSE</span>), <span class="at">data =</span> jobs, <span class="at">cores =</span> <span class="dv">4</span>)</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="co"># Fit Bayesian mediation model in rstanarm</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>m3 <span class="ot">&lt;-</span> <span class="fu">stan_mvmer</span>(</span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">list</span>(job_seek <span class="sc">~</span> treat <span class="sc">+</span> econ_hard <span class="sc">+</span> sex <span class="sc">+</span> age <span class="sc">+</span> (<span class="dv">1</span> <span class="sc">|</span> occp),</span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a>       depress2 <span class="sc">~</span> treat <span class="sc">+</span> job_seek <span class="sc">+</span> econ_hard <span class="sc">+</span> sex <span class="sc">+</span> age <span class="sc">+</span> (<span class="dv">1</span> <span class="sc">|</span> occp)),</span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a>  <span class="at">data =</span> jobs,</span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a>  <span class="at">cores =</span> <span class="dv">4</span>,</span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a>  <span class="at">refresh =</span> <span class="dv">0</span></span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<p><code>mediation()</code> is a summary function, especially for mediation analysis, i.e. for multivariate response models with casual mediation effects.</p>
<p>In the models <code>m2</code> and <code>m3</code>, <code>treat</code> is the treatment effect and <code>job_seek</code> is the mediator effect. For the <em>brms</em> model (<code>m2</code>), <code>f1</code> describes the mediator model and <code>f2</code> describes the outcome model. This is similar for the <em>rstanarm</em> model.</p>
<p><code>mediation()</code> returns a data frame with information on the <em>direct effect</em> (median value of posterior samples from treatment of the outcome model), <em>mediator effect</em> (median value of posterior samples from mediator of the outcome model), <em>indirect effect</em> (median value of the multiplication of the posterior samples from mediator of the outcome model and the posterior samples from treatment of the mediation model) and the <em>total effect</em> (median value of sums of posterior samples used for the direct and indirect effect). The <em>proportion mediated</em> is the indirect effect divided by the total effect.</p>
<p>The simplest call just needs the model-object.</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># for brms</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="fu">mediation</span>(m2)</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; # Causal Mediation Analysis for Stan Model</span></span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Treatment: treat</span></span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Mediator : job_seek</span></span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Response : depress2</span></span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Effect                 | Estimate |          95% ETI</span></span>
<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; ----------------------------------------------------</span></span>
<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Direct Effect (ADE)    |   -0.040 | [-0.124,  0.046]</span></span>
<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Indirect Effect (ACME) |   -0.015 | [-0.041,  0.008]</span></span>
<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Mediator Effect        |   -0.240 | [-0.294, -0.185]</span></span>
<span id="cb4-14"><a href="#cb4-14" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Total Effect           |   -0.055 | [-0.145,  0.034]</span></span>
<span id="cb4-15"><a href="#cb4-15" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb4-16"><a href="#cb4-16" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Proportion mediated: 28.14% [-181.46%, 237.75%]</span></span>
<span id="cb4-17"><a href="#cb4-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-18"><a href="#cb4-18" aria-hidden="true" tabindex="-1"></a><span class="co"># for rstanarm</span></span>
<span id="cb4-19"><a href="#cb4-19" aria-hidden="true" tabindex="-1"></a><span class="fu">mediation</span>(m3)</span>
<span id="cb4-20"><a href="#cb4-20" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; # Causal Mediation Analysis for Stan Model</span></span>
<span id="cb4-21"><a href="#cb4-21" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb4-22"><a href="#cb4-22" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Treatment: treat</span></span>
<span id="cb4-23"><a href="#cb4-23" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Mediator : job_seek</span></span>
<span id="cb4-24"><a href="#cb4-24" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Response : depress2</span></span>
<span id="cb4-25"><a href="#cb4-25" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb4-26"><a href="#cb4-26" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Effect                 | Estimate |          95% ETI</span></span>
<span id="cb4-27"><a href="#cb4-27" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; ----------------------------------------------------</span></span>
<span id="cb4-28"><a href="#cb4-28" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Direct Effect (ADE)    |   -0.040 | [-0.129,  0.048]</span></span>
<span id="cb4-29"><a href="#cb4-29" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Indirect Effect (ACME) |   -0.018 | [-0.042,  0.006]</span></span>
<span id="cb4-30"><a href="#cb4-30" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Mediator Effect        |   -0.241 | [-0.296, -0.187]</span></span>
<span id="cb4-31"><a href="#cb4-31" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Total Effect           |   -0.057 | [-0.151,  0.033]</span></span>
<span id="cb4-32"><a href="#cb4-32" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb4-33"><a href="#cb4-33" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Proportion mediated: 30.59% [-221.09%, 282.26%]</span></span></code></pre></div>
<p>Typically, <code>mediation()</code> finds the treatment and mediator variables automatically. If this does not work, use the <code>treatment</code> and <code>mediator</code> arguments to specify the related variable names. For all values, the 89% credible intervals are calculated by default. Use <code>ci</code> to calculate a different interval.</p>
</div>
<div id="comparison-to-the-mediation-package" class="section level2">
<h2>Comparison to the mediation package</h2>
<p>Here is a comparison with the <em>mediation</em> package. Note that the <code>summary()</code>-output of the <em>mediation</em> package shows the indirect effect first, followed by the direct effect.</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(m1)</span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Causal Mediation Analysis </span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Quasi-Bayesian Confidence Intervals</span></span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;                Estimate 95% CI Lower 95% CI Upper p-value</span></span>
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; ACME            -0.0157      -0.0387         0.01    0.19</span></span>
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; ADE             -0.0438      -0.1315         0.04    0.35</span></span>
<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Total Effect    -0.0595      -0.1530         0.02    0.21</span></span>
<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Prop. Mediated   0.2137      -2.0277         2.70    0.32</span></span>
<span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Sample Size Used: 899 </span></span>
<span id="cb5-14"><a href="#cb5-14" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-15"><a href="#cb5-15" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-16"><a href="#cb5-16" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Simulations: 1000</span></span>
<span id="cb5-17"><a href="#cb5-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-18"><a href="#cb5-18" aria-hidden="true" tabindex="-1"></a><span class="fu">mediation</span>(m2, <span class="at">ci =</span> .<span class="dv">95</span>)</span>
<span id="cb5-19"><a href="#cb5-19" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; # Causal Mediation Analysis for Stan Model</span></span>
<span id="cb5-20"><a href="#cb5-20" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-21"><a href="#cb5-21" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Treatment: treat</span></span>
<span id="cb5-22"><a href="#cb5-22" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Mediator : job_seek</span></span>
<span id="cb5-23"><a href="#cb5-23" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Response : depress2</span></span>
<span id="cb5-24"><a href="#cb5-24" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-25"><a href="#cb5-25" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Effect                 | Estimate |          95% ETI</span></span>
<span id="cb5-26"><a href="#cb5-26" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; ----------------------------------------------------</span></span>
<span id="cb5-27"><a href="#cb5-27" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Direct Effect (ADE)    |   -0.040 | [-0.124,  0.046]</span></span>
<span id="cb5-28"><a href="#cb5-28" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Indirect Effect (ACME) |   -0.015 | [-0.041,  0.008]</span></span>
<span id="cb5-29"><a href="#cb5-29" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Mediator Effect        |   -0.240 | [-0.294, -0.185]</span></span>
<span id="cb5-30"><a href="#cb5-30" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Total Effect           |   -0.055 | [-0.145,  0.034]</span></span>
<span id="cb5-31"><a href="#cb5-31" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-32"><a href="#cb5-32" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Proportion mediated: 28.14% [-181.46%, 237.75%]</span></span>
<span id="cb5-33"><a href="#cb5-33" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-34"><a href="#cb5-34" aria-hidden="true" tabindex="-1"></a><span class="fu">mediation</span>(m3, <span class="at">ci =</span> .<span class="dv">95</span>)</span>
<span id="cb5-35"><a href="#cb5-35" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; # Causal Mediation Analysis for Stan Model</span></span>
<span id="cb5-36"><a href="#cb5-36" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-37"><a href="#cb5-37" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Treatment: treat</span></span>
<span id="cb5-38"><a href="#cb5-38" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Mediator : job_seek</span></span>
<span id="cb5-39"><a href="#cb5-39" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Response : depress2</span></span>
<span id="cb5-40"><a href="#cb5-40" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-41"><a href="#cb5-41" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Effect                 | Estimate |          95% ETI</span></span>
<span id="cb5-42"><a href="#cb5-42" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; ----------------------------------------------------</span></span>
<span id="cb5-43"><a href="#cb5-43" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Direct Effect (ADE)    |   -0.040 | [-0.129,  0.048]</span></span>
<span id="cb5-44"><a href="#cb5-44" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Indirect Effect (ACME) |   -0.018 | [-0.042,  0.006]</span></span>
<span id="cb5-45"><a href="#cb5-45" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Mediator Effect        |   -0.241 | [-0.296, -0.187]</span></span>
<span id="cb5-46"><a href="#cb5-46" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Total Effect           |   -0.057 | [-0.151,  0.033]</span></span>
<span id="cb5-47"><a href="#cb5-47" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb5-48"><a href="#cb5-48" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Proportion mediated: 30.59% [-221.09%, 282.26%]</span></span></code></pre></div>
<p>If you want to calculate mean instead of median values from the posterior samples, use the <code>centrality</code>-argument. Furthermore, there is a <code>print()</code>-method, which allows to print more digits.</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>m <span class="ot">&lt;-</span> <span class="fu">mediation</span>(m2, <span class="at">centrality =</span> <span class="st">&quot;mean&quot;</span>, <span class="at">ci =</span> .<span class="dv">95</span>)</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(m, <span class="at">digits =</span> <span class="dv">4</span>)</span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; # Causal Mediation Analysis for Stan Model</span></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Treatment: treat</span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Mediator : job_seek</span></span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Response : depress2</span></span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Effect                 | Estimate |            95% ETI</span></span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; ------------------------------------------------------</span></span>
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Direct Effect (ADE)    |  -0.0395 | [-0.1237,  0.0456]</span></span>
<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Indirect Effect (ACME) |  -0.0158 | [-0.0405,  0.0083]</span></span>
<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Mediator Effect        |  -0.2401 | [-0.2944, -0.1846]</span></span>
<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Total Effect           |  -0.0553 | [-0.1454,  0.0341]</span></span>
<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb6-16"><a href="#cb6-16" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Proportion mediated: 28.60% [-181.01%, 238.20%]</span></span></code></pre></div>
<p>As you can see, the results are similar to what the <em>mediation</em> package produces for non-Bayesian models.</p>
</div>
<div id="comparison-to-sem-from-the-lavaan-package" class="section level2">
<h2>Comparison to SEM from the lavaan package</h2>
<p>Finally, we also compare the results to a SEM model, using <em>lavaan</em>. This example should demonstrate how to “translate” the same model in different packages or modeling approached.</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(lavaan)</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(jobs)</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">1234</span>)</span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>model <span class="ot">&lt;-</span> <span class="st">&#39; # direct effects</span></span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a><span class="st">             depress2 ~ c1*treat + c2*econ_hard + c3*sex + c4*age + b*job_seek</span></span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a><span class="st">             </span></span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a><span class="st">           # mediation</span></span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a><span class="st">             job_seek ~ a1*treat + a2*econ_hard + a3*sex + a4*age</span></span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a><span class="st">             </span></span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a><span class="st">           # indirect effects (a*b)</span></span>
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a><span class="st">             indirect_treat := a1*b</span></span>
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a><span class="st">             indirect_econ_hard := a2*b</span></span>
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a><span class="st">             indirect_sex := a3*b</span></span>
<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a><span class="st">             indirect_age := a4*b</span></span>
<span id="cb7-16"><a href="#cb7-16" aria-hidden="true" tabindex="-1"></a><span class="st">             </span></span>
<span id="cb7-17"><a href="#cb7-17" aria-hidden="true" tabindex="-1"></a><span class="st">           # total effects</span></span>
<span id="cb7-18"><a href="#cb7-18" aria-hidden="true" tabindex="-1"></a><span class="st">             total_treat := c1 + (a1*b)</span></span>
<span id="cb7-19"><a href="#cb7-19" aria-hidden="true" tabindex="-1"></a><span class="st">             total_econ_hard := c2 + (a2*b)</span></span>
<span id="cb7-20"><a href="#cb7-20" aria-hidden="true" tabindex="-1"></a><span class="st">             total_sex := c3 + (a3*b)</span></span>
<span id="cb7-21"><a href="#cb7-21" aria-hidden="true" tabindex="-1"></a><span class="st">             total_age := c4 + (a4*b)</span></span>
<span id="cb7-22"><a href="#cb7-22" aria-hidden="true" tabindex="-1"></a><span class="st">         &#39;</span></span>
<span id="cb7-23"><a href="#cb7-23" aria-hidden="true" tabindex="-1"></a>m4 <span class="ot">&lt;-</span> <span class="fu">sem</span>(model, <span class="at">data =</span> jobs)</span>
<span id="cb7-24"><a href="#cb7-24" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(m4)</span>
<span id="cb7-25"><a href="#cb7-25" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; lavaan 0.6-8 ended normally after 25 iterations</span></span>
<span id="cb7-26"><a href="#cb7-26" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb7-27"><a href="#cb7-27" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Estimator                                         ML</span></span>
<span id="cb7-28"><a href="#cb7-28" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Optimization method                           NLMINB</span></span>
<span id="cb7-29"><a href="#cb7-29" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Number of model parameters                        11</span></span>
<span id="cb7-30"><a href="#cb7-30" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;                                                       </span></span>
<span id="cb7-31"><a href="#cb7-31" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Number of observations                           899</span></span>
<span id="cb7-32"><a href="#cb7-32" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;                                                       </span></span>
<span id="cb7-33"><a href="#cb7-33" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Model Test User Model:</span></span>
<span id="cb7-34"><a href="#cb7-34" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;                                                       </span></span>
<span id="cb7-35"><a href="#cb7-35" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Test statistic                                 0.000</span></span>
<span id="cb7-36"><a href="#cb7-36" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Degrees of freedom                                 0</span></span>
<span id="cb7-37"><a href="#cb7-37" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb7-38"><a href="#cb7-38" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Parameter Estimates:</span></span>
<span id="cb7-39"><a href="#cb7-39" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb7-40"><a href="#cb7-40" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Standard errors                             Standard</span></span>
<span id="cb7-41"><a href="#cb7-41" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Information                                 Expected</span></span>
<span id="cb7-42"><a href="#cb7-42" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Information saturated (h1) model          Structured</span></span>
<span id="cb7-43"><a href="#cb7-43" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb7-44"><a href="#cb7-44" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Regressions:</span></span>
<span id="cb7-45"><a href="#cb7-45" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;                    Estimate  Std.Err  z-value  P(&gt;|z|)</span></span>
<span id="cb7-46"><a href="#cb7-46" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   depress2 ~                                          </span></span>
<span id="cb7-47"><a href="#cb7-47" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     treat     (c1)   -0.040    0.043   -0.929    0.353</span></span>
<span id="cb7-48"><a href="#cb7-48" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     econ_hard (c2)    0.149    0.021    7.156    0.000</span></span>
<span id="cb7-49"><a href="#cb7-49" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     sex       (c3)    0.107    0.041    2.604    0.009</span></span>
<span id="cb7-50"><a href="#cb7-50" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     age       (c4)    0.001    0.002    0.332    0.740</span></span>
<span id="cb7-51"><a href="#cb7-51" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     job_seek   (b)   -0.240    0.028   -8.524    0.000</span></span>
<span id="cb7-52"><a href="#cb7-52" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   job_seek ~                                          </span></span>
<span id="cb7-53"><a href="#cb7-53" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     treat     (a1)    0.066    0.051    1.278    0.201</span></span>
<span id="cb7-54"><a href="#cb7-54" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     econ_hard (a2)    0.053    0.025    2.167    0.030</span></span>
<span id="cb7-55"><a href="#cb7-55" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     sex       (a3)   -0.008    0.049   -0.157    0.875</span></span>
<span id="cb7-56"><a href="#cb7-56" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     age       (a4)    0.005    0.002    1.983    0.047</span></span>
<span id="cb7-57"><a href="#cb7-57" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb7-58"><a href="#cb7-58" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Variances:</span></span>
<span id="cb7-59"><a href="#cb7-59" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;                    Estimate  Std.Err  z-value  P(&gt;|z|)</span></span>
<span id="cb7-60"><a href="#cb7-60" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;    .depress2          0.373    0.018   21.201    0.000</span></span>
<span id="cb7-61"><a href="#cb7-61" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;    .job_seek          0.524    0.025   21.201    0.000</span></span>
<span id="cb7-62"><a href="#cb7-62" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb7-63"><a href="#cb7-63" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Defined Parameters:</span></span>
<span id="cb7-64"><a href="#cb7-64" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;                    Estimate  Std.Err  z-value  P(&gt;|z|)</span></span>
<span id="cb7-65"><a href="#cb7-65" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     indirect_treat   -0.016    0.012   -1.264    0.206</span></span>
<span id="cb7-66"><a href="#cb7-66" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     indirct_cn_hrd   -0.013    0.006   -2.100    0.036</span></span>
<span id="cb7-67"><a href="#cb7-67" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     indirect_sex      0.002    0.012    0.157    0.875</span></span>
<span id="cb7-68"><a href="#cb7-68" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     indirect_age     -0.001    0.001   -1.932    0.053</span></span>
<span id="cb7-69"><a href="#cb7-69" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     total_treat      -0.056    0.045   -1.244    0.214</span></span>
<span id="cb7-70"><a href="#cb7-70" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     total_econ_hrd    0.136    0.022    6.309    0.000</span></span>
<span id="cb7-71"><a href="#cb7-71" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     total_sex         0.109    0.043    2.548    0.011</span></span>
<span id="cb7-72"><a href="#cb7-72" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;     total_age        -0.000    0.002   -0.223    0.824</span></span>
<span id="cb7-73"><a href="#cb7-73" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-74"><a href="#cb7-74" aria-hidden="true" tabindex="-1"></a><span class="co"># just to have the numbers right at hand and you don&#39;t need to scroll up</span></span>
<span id="cb7-75"><a href="#cb7-75" aria-hidden="true" tabindex="-1"></a><span class="fu">mediation</span>(m2, <span class="at">ci =</span> .<span class="dv">95</span>)</span>
<span id="cb7-76"><a href="#cb7-76" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; # Causal Mediation Analysis for Stan Model</span></span>
<span id="cb7-77"><a href="#cb7-77" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb7-78"><a href="#cb7-78" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Treatment: treat</span></span>
<span id="cb7-79"><a href="#cb7-79" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Mediator : job_seek</span></span>
<span id="cb7-80"><a href="#cb7-80" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt;   Response : depress2</span></span>
<span id="cb7-81"><a href="#cb7-81" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb7-82"><a href="#cb7-82" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Effect                 | Estimate |          95% ETI</span></span>
<span id="cb7-83"><a href="#cb7-83" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; ----------------------------------------------------</span></span>
<span id="cb7-84"><a href="#cb7-84" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Direct Effect (ADE)    |   -0.040 | [-0.124,  0.046]</span></span>
<span id="cb7-85"><a href="#cb7-85" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Indirect Effect (ACME) |   -0.015 | [-0.041,  0.008]</span></span>
<span id="cb7-86"><a href="#cb7-86" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Mediator Effect        |   -0.240 | [-0.294, -0.185]</span></span>
<span id="cb7-87"><a href="#cb7-87" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Total Effect           |   -0.055 | [-0.145,  0.034]</span></span>
<span id="cb7-88"><a href="#cb7-88" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; </span></span>
<span id="cb7-89"><a href="#cb7-89" aria-hidden="true" tabindex="-1"></a><span class="co">#&gt; Proportion mediated: 28.14% [-181.46%, 237.75%]</span></span></code></pre></div>
<p>The summary output from <em>lavaan</em> is longer, but we can find the related numbers quite easily:</p>
<ul>
<li>the <em>direct effect</em> of treatment is <code>treat (c1)</code>, which is <code>-0.040</code></li>
<li>the <em>indirect effect</em> of treatment is <code>indirect_treat</code>, which is <code>-0.016</code></li>
<li>the <em>mediator effect</em> of job_seek is <code>job_seek (b)</code>, which is <code>-0.240</code></li>
<li>the <em>total effect</em> is <code>total_treat</code>, which is <code>-0.056</code></li>
</ul>
</div>



<!-- code folding -->


<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
  (function () {
    var script = document.createElement("script");
    script.type = "text/javascript";
    script.src  = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
    document.getElementsByTagName("head")[0].appendChild(script);
  })();
</script>

</body>
</html>
back to top