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            <h2><font color="#ffffff">Search Algorithms: MIMBuild</font></h2>
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<p><font color="#000000"><b><br>
</b><b>Introduction </b></font></p>
<p>MIM Build stands for Multiple Indicator Model Build. It is one of
    the three algorithms in Tetrad designed to build <font color="#000000"><b><a
            href="../../definitions/measurement_structural_graph.html">pure
        measurement/structural models</a></b></font> (the others are the <font
            color="#000000"><b><a href="../../search/cluster.html">Build Pure Clusters algorithm</a></b></font>
    and the <font color="#000000"><b><a href="../../search/purify.html">Purify algorithm</a></b></font>).</p>
<p> MIM Build should be used to learn causal relationships among latent
    variables in a <font color="#000000"> when the measurement model is
        given in advance but the structural model is unknown.</font></p>
<p>The MIM Build algorithm also assumes that the underlying (unknown)
    data generating process is a linear graph. If the user strongly
    suspects that the latents or indicators may be non-linearly related<font
            color="#000000">, MIM Build should not be used. We are also assuming
        that latents here do not have other hidden common causes.</font></p>
<p><font color="#000000">A</font><font color="#000000">ll observed
    variables are assumed to be continuous, and therefore the current
    implementation of the algorithm accepts only continuous data sets as
    input. For general information about model building algorithms, consult
    the <font color="#000000"><b><a href="../../search/../search.html">Search
        Algorithms</a></b></font> page.</font></p>
<p><font color="#000000"><b><a name="Introduction" id="Introduction"></a><br>
    Entering MIM Build parameters</b></font></p>
<p>Create a new <font color="#000000">Search nodes</font> as
    described in the <font color="#000000"><a href="search_box.html">Search
        Algorithms</a></font> page, but in order to follow this tutorial,
    use the following graph to generate a simulated continuous data set:</p>
<blockquote>
    <p><font color="#000000"><img src="../../images/mimbuild1.png"
                                  width="769" height="470"></font></p>
</blockquote>
<p>When the MIM Build algorithm is chosen from the Search box, a window
    appears for specifying search parameters.<br>
</p>
<p>The parameters that are used by MIM Build can be specified in this
    window. The parameters are as follows:</p>
<ul>
    <li><strong>depErrorsAlpha value</strong>: if you choose the PC search in the
        combo box "Choice of algorithm", MIM Build uses statistical hypothesis
        tests in order to generate models automatically. The depErrorsAlpha value
        parameter represents the level by which such tests are used to accept
        or reject constraints that compose the final output. The default value
        is 0.05, but the user may want to experiment with different depErrorsAlpha
        values in order to test the sensitivity of her data within this
        algorithm.
    </li>
    <li><strong>number of clusters</strong>: MIM Build needs a pure
        measurement model specified in advance. The measurement model is
        defined by a set of clusters of variables, where each cluster
        represents a set of pure indicators of a single latent. In this box,
        the user specifies how many latents there are in the measurement model
        based in prior knowledge. In our example, let's use three clusters.
    </li>
    <li><strong>edit cluster assignments</strong>: once the number of
        latents is specified, the user should now determine which variables in
        the data set should be clustered together. When this button is clicked,
        the following dialog box appears:
        <p><font color="#000000"><img src="../../images/mimbuild3.png"
                                      width="1011" height="289"></font></p>
        <p>In this example, we want to enter the measurement model that we
            know is the correct one by assumption. In other words, variables X1, X2
            and X3 should be clustered together, since they are pure indicators of
            a same latent. Variables X4, X5 and X6 form another cluster, and the
            same holds for X7, X8 and X9. In order to perform cluster assignment,
            since click the respective combo box and choose the cluster that shows
            up in the list. For example, click the X4 combo box and choose Cluster
            1. Do the same for X5 and X6. For variables X7, X8 and X9, choose
            Cluster 2. The final outcome should be as follows:</p>
        <p><font color="#000000"><img src="../../images/mimbuild4.png"
                                      width="1011" height="289"></font></p>
    </li>
    <li><strong>algorithm</strong>: MIM Build is actually a family of
        algorithms for the problem of learning structural models. Currently, we
        offer two alternatives, both corresponding to the case where we have no
        latent variables: the <a href="../../search/ges.html"><strong>GES</strong></a> and <a
                href="../../search/pc.html"><strong>PC</strong></a> search algorithms. The PC
        version can be slower and less robust than GES, but might be useful to
        indicate if the assumption of no extra hidden common causes among the
        latents holds (the appearance of double directed edges is an indication
        of that possibility).
    </li>
    <li><strong>view background knowledge</strong>: this button gives
        access to a <font color="#000000"><b><a
                href="../../search/../search.html#BackgroundKnowledge">background knowledge editor</a></b></font>
        that is analogous to the one used in most search algorithms, but with
        one difference: instead of entering background knowledge about observed
        variables (in MIM Build case, all background knowledge about observed
        variables boils down to the specification of a measurement model), the
        user here enters prior knowledge about causal relations of latent
        variables. Latents are denoted by the label _L<em>x</em>, where <em>x</em>
        is the number of the respective cluster. In our example, the latent
        parent of X7, X8 and X9 is referred as _L2. <em>Note: use of
            background knowledge is not implemented for GES yet.</em></li>
</ul>
<p>Execute the search as explained in the <font color="#000000"><b><a
        href="../../search/../search.html">Search Algorithms</a></b></font> page.</p>
<p><font color="#000000"><b><a name="Interpretation" id="Interpretation"></a><br>
</b><b>Interpreting the output</b></font></p>
<p><font color="#000000">MIM Build returns a CPDAG over latent
    variables that is completely analogous to the one produced by a <b><a
            href="../../search/pc.html">PC Search</a></b></font><font color="#000000">, or <b><a
        href="../../search/ges.html">GES Search</a></b></font><font color="#000000">. The
    same interpretation used in such algorithms can be applied to MIM Build
    output. <br>
</font></p>
<p>&nbsp;</p>
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