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model_building.html
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<div id="header">
<h1 class="title toc-ignore">jAMM: Model building</h1>
<h4 class="author">(Marcello Gallucci)</h4>
</div>
<p><span class="keywords"> <span class="keytitle"> keywords </span> Path
Diagram, Mediation, mediated moderation, moderated mediation,
conditional mediation </span></p>
<p>In this page we show how to set up some mediation models without
interactions. For models with interactions (conditional mediation,
moderated mediation, etc) see <a href="moderator_building.html">jAMM:
Building conditional models</a>.</p>
<div id="simple-mediation" class="section level1">
<h1>Simple mediation</h1>
<p>To set up a simple mediation model, simply define one dependent
variable, one independent variable and one mediator.</p>
<p><img src="models/m1.png" class="img-responsive" alt=""></p>
<p>jAMM will define the models for you, as shown in the model info
table.</p>
<p><img src="models/m1_2.png" class="img-responsive" alt=""></p>
</div>
<div id="categorical-independent-variables" class="section level1">
<h1>Categorical independent variables</h1>
<p>The same logic applies for categorical independent variables.</p>
<p><img src="models/m2.png" class="img-responsive" alt=""></p>
<p>However, for categorical independent variables, the path diagram
shows only one box for the IV, even though the estimation requires
dummies (contrast variables) to estimate the effects. This is signaled
in the notes.</p>
<p><img src="models/m2_2.png" class="img-responsive" alt=""></p>
<p>Thus, since <code>fact1</code> variable has 4 groups, in the results
we will find three mediated effects, one for the contrast variable
<code>fact11</code>, one for <code>fact12</code>, and one for
<code>fact11</code>.</p>
<p><img src="models/m2_3.png" class="img-responsive" alt=""></p>
</div>
<div id="multiple-independent-variables" class="section level1">
<h1>Multiple independent variables</h1>
<p>You can add as many independent variables as you need, the model is
updated, by default, accordingly with the simple rule that each IV is
mediatated by the mediator.</p>
<p><img src="models/m3.png" class="img-responsive" alt=""></p>
<p>Nonetheless, one may have in mind a different model (not necessarily
sensible in all applications). Assume we want the mediated effects of
<code>x1</code> and <code>x2</code> through <code>m1</code>, but we want
the effects on <code>y</code> (and only them) to be computed after
partializing <code>x3</code>. First, we go to
<code>Mediators models</code> and remove the effect of <code>x3</code>
from the list of predictors. In doing so, the jAMM removes
<code>x3</code> also from the <code>Full model</code>. We go there and
re-include <code>x3</code> in the list of predictors. So we obtain the
model we had in mind.</p>
<p><img src="models/m4.png" class="img-responsive" alt=""></p>
<p>Notice the green path. That path is not estimated, but jAMM suggests
to estimate it. That is because the model we just set up is not complete
in terms of <code>x3</code> mediation (recall that jAMM assumes you want
to estimate mediation models).</p>
<p><img src="models/m4.png" class="img-responsive" alt=""></p>
<p>If seeing the suggested paths disturb you, you can suppress them in
the <code>Mediation options</code> tab.</p>
</div>
<div id="multiple-mediators" class="section level1">
<h1>Multiple mediators</h1>
<div id="parallel-mediators" class="section level2">
<h2>Parallel mediators</h2>
<p>By defining two or more variables as mediators in the variables input
panel, we obtain a parallel mediators model by default.</p>
<p><img src="models/m5.png" class="img-responsive" alt=""></p>
<p>You can put as many mediators as you want</p>
<p><img src="models/m6.png" class="img-responsive" alt=""></p>
</div>
<div id="mediators-chains" class="section level2">
<h2>Mediators chains</h2>
<p>Several mediation models require building some sort of mediators
chain. For instance, we can have that variable <code>x</code> is
measured 4 times,and we want to see if <code>x1</code> affects
<code>x2</code>, <code>x2</code> affects <code>x3</code>, and
<code>x3</code> affects <code>x4</code>. To build such a model, first we
select <code>x1</code> as the independent variable (it is the only
exogenous variable in the model), <code>x2</code> and <code>x3</code> as
mediators and <code>x4</code> as dependent variable.</p>
<p><img src="models/m7_1.png" class="img-responsive" alt=""></p>
<p>While we do so, jAMM builds a parallel mediators model (the default),
but we ignore it and move on to change that. In fact, as compared with a
parallel mediators model, the model we have in mind requires also that
<code>x2</code> be a predictor of <code>x3</code>. We go to
<code>Mediators models</code> tab and add <code>x2</code> in the field
<em>Mediator=x3</em>. There we have it.</p>
<p><img src="models/m7.png" class="img-responsive" alt=""></p>
</div>
<div id="multi-layer-model" class="section level2">
<h2>Multi-layer model</h2>
<p>Assume you have <code>x1</code> as independent, that influences
<code>x2</code> and <code>x3</code>, that in turn affect <code>y</code>
through <code>m1</code>. We can think of this model as a multi-layer
model in terms of layers of mediators: first the <code>x2</code> and
<code>x3</code> layer, then <code>m1</code> layer. To set it up, first
we put all endogenous predictors in the mediators field and
<code>x1</code> and <code>y</code> in the independent and dependent
field, respectively.</p>
<p><img src="models/m8_1.png" class="img-responsive" alt=""></p>
<p>Again, we should change the automatically created parallel mediators
model. We should add the paths from <code>x2</code> and <code>x3</code>
to <code>m1</code>. To do so we go to <code>Mediators models</code> tab
and add <code>x2</code> and <code>x3</code> in the field
<em>Mediator=m1</em>.</p>
<p><img src="models/m8.png" class="img-responsive" alt=""></p>
<p>Suprised by the ugly picture? Well, the model is correct but the
picture can look better if one re-arranges the position of the terms.
First, remove the mediators (jAMM does not like re-arranging terms
already defined, so it is better to start anew). We want the last
mediator <code>m1</code> to be in the center of the diagram, so we
should put it as the second mediator of the list. Then we change the
<code>Mediators models</code> as we did before. Here is the input: a bit
better looking.
<img src="models/m8_2.png" class="img-responsive" alt=""></p>
<p>Here is the output.</p>
<p><img src="models/m8_3.png" class="img-responsive" alt=""></p>
</div>
</div>
<div id="multiple-iv-and-multiple-mediators" class="section level1">
<h1>Multiple IV and multiple mediators</h1>
<p>One can combine the multiple IVs and the multiple mediators models to
better suit the research aims. By defining multiple IV and multiple
mediators in the variale input tabs, one obtains, by default, a full
parallel mediators model.</p>
<p><img src="models/m9.png" class="img-responsive" alt=""></p>
<p>Obviously, one can then change the structure of the model, for
instance by making the mediators a chain of mediators, or by removing
some path from one IV to one mediator.</p>
<p><img src="models/m11.png" class="img-responsive" alt=""></p>
<p>Notice that the previos model is not equivalent to two independent
simple mediation models, because in the present model all the effects on
the dependent variable <code>y</code> are computed keeping constant both
independent variables. This feature is reminded by the notes of the path
diagram.</p>
<p><img src="models/m11_2.png" class="img-responsive" alt=""></p>
</div>
<div id="mis-specified-models" class="section level1">
<h1>Mis-specified models</h1>
<p>There are models that may make a lot of sense in general, but are not
mediation models. These models will not be estimated by jAMM, because
they cannot produce mediated effects (that are the effects jAMM
requires).</p>
<p>The first example is a model without mediators effect.</p>
<p><img src="models/m12.png" class="img-responsive" alt=""></p>
<p>In this model I removed the path from <code>m1</code> to
<code>y</code> in the <code>Full model</code> tab. That creates a model
in which the mediator has no role, and thus the path diagram shows a red
path indicating that that path is required. It also signals the problem
in the <code>Models info</code> table.</p>
<p><img src="models/m12_2.png" class="img-responsive" alt=""></p>
<p>Another possible error is to have each mediator to predict all the
other mediators. That would make the model recursive, and not a
mediation model.</p>
<p><img src="models/m13.png" class="img-responsive" alt=""></p>
<p>jAMM warns you of the problem with a purple path in the diagram, and
with some explanation in the <code>Models info</code> table.</p>
<p><img src="models/m13_2.png" class="img-responsive" alt=""></p>
</div>
<div id="list-of-docs" class="section level1">
<h1>List of docs</h1>
<ul>
<li>
<a href="estimation.html">jAMM: Model estimates</a>
</li>
<li>
<a href="glm.html">GLM mediation models</a>
</li>
<li>
<a href="model_building.html">jAMM: Model building</a>
</li>
<li>
<a href="moderator_building.html">jAMM: Building conditional models</a>
</li>
<li>
<a href="rosetta.html">Rosetta store: results across software</a>
</li>
</ul>
</div>
<div id="examples" class="section level1">
<h1>Examples</h1>
<ul>
<li>
<a href="glm_example1.html">jAMM: simple mediation</a>
</li>
<li>
<a href="glm_example2.html">jAMM: conditional mediation</a>
</li>
</ul>
<h1>
Comments?
</h1>
<p>
Got comments, issues or spotted a bug? Please open an issue on
<a href=" https://github.com/mcfanda/gamlj/issues "> GAMLj at
github“</a> or <a href="mailto:[email protected]">send me an email</a>
</p>
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