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<body>
<h1 class="title toc-ignore">Regularized MIMIC</h1>
<h4 class="author">Joshua Pritikin and Ross Jacobucci and Timothy R.
Brick</h4>
<h4 class="date">2024-10-18</h4>
<div id="regularized-mimic-model" class="section level1">
<h1>Regularized MIMIC model</h1>
<p>This example uses the immortal Holzinger Swineford data set.</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>(OpenMx)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(HS.ability.data)</span></code></pre></div>
<p>The OpenMx model looks like this:</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>HS.ability.data<span class="sc">$</span>ageym <span class="ot"><-</span> HS.ability.data<span class="sc">$</span>agey<span class="sc">*</span><span class="dv">12</span> <span class="sc">+</span> HS.ability.data<span class="sc">$</span>agem</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>HS.ability.data<span class="sc">$</span>male <span class="ot"><-</span> <span class="fu">as.numeric</span>(HS.ability.data<span class="sc">$</span>Gender <span class="sc">==</span> <span class="st">'Male'</span>)</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="co"># Specify variables</span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a>indicators <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">'visual'</span>,<span class="st">'cubes'</span>,<span class="st">'paper'</span>,<span class="st">'flags'</span>,<span class="st">'paperrev'</span>,<span class="st">'flagssub'</span>,</span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a> <span class="st">'general'</span>,<span class="st">'paragrap'</span>,<span class="st">'sentence'</span>,<span class="st">'wordc'</span>,<span class="st">'wordm'</span>)</span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a>covariates <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"male"</span>,<span class="st">"ageym"</span>,<span class="st">"grade"</span>)</span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a>latents <span class="ot">=</span> <span class="fu">c</span>(<span class="st">"g"</span>, covariates)</span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a><span class="co"># Build the model</span></span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a>mimicModel <span class="ot"><-</span> <span class="fu">mxModel</span>(</span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a> <span class="st">"MIMIC"</span>, <span class="at">type=</span><span class="st">"RAM"</span>,</span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a> <span class="at">manifestVars =</span> indicators, <span class="at">latentVars =</span> latents,</span>
<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a> <span class="co"># Set up exogenous predictors</span></span>
<span id="cb2-16"><a href="#cb2-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">mxPath</span>(<span class="st">"one"</span>, covariates, <span class="at">labels=</span><span class="fu">paste0</span>(<span class="st">'data.'</span>,covariates), <span class="at">free=</span><span class="cn">FALSE</span>),</span>
<span id="cb2-17"><a href="#cb2-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-18"><a href="#cb2-18" aria-hidden="true" tabindex="-1"></a> <span class="co"># Fix factor variance</span></span>
<span id="cb2-19"><a href="#cb2-19" aria-hidden="true" tabindex="-1"></a> <span class="fu">mxPath</span>(<span class="st">'g'</span>, <span class="at">arrows=</span><span class="dv">2</span>, <span class="at">free=</span><span class="cn">FALSE</span>, <span class="at">values=</span><span class="dv">1</span>),</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 class="co"># Error variances:</span></span>
<span id="cb2-22"><a href="#cb2-22" aria-hidden="true" tabindex="-1"></a> <span class="fu">mxPath</span>(<span class="at">from=</span><span class="fu">c</span>(indicators), <span class="at">arrows=</span><span class="dv">2</span>, <span class="at">free=</span><span class="cn">TRUE</span>, <span class="at">values=</span><span class="dv">10</span>),</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> <span class="co"># Means (saturated means model):</span></span>
<span id="cb2-25"><a href="#cb2-25" aria-hidden="true" tabindex="-1"></a> <span class="fu">mxPath</span>(<span class="at">from=</span><span class="st">"one"</span>, <span class="at">to=</span>indicators, <span class="at">values=</span><span class="fu">rep</span>(<span class="dv">5</span>, <span class="fu">length</span>(indicators))),</span>
<span id="cb2-26"><a href="#cb2-26" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-27"><a href="#cb2-27" aria-hidden="true" tabindex="-1"></a> <span class="co"># Loadings:</span></span>
<span id="cb2-28"><a href="#cb2-28" aria-hidden="true" tabindex="-1"></a> <span class="fu">mxPath</span>(<span class="at">from=</span><span class="st">"g"</span>, <span class="at">to=</span>indicators, <span class="at">values=</span>.<span class="dv">5</span>),</span>
<span id="cb2-29"><a href="#cb2-29" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-30"><a href="#cb2-30" aria-hidden="true" tabindex="-1"></a> <span class="co"># Covariate paths</span></span>
<span id="cb2-31"><a href="#cb2-31" aria-hidden="true" tabindex="-1"></a> <span class="fu">mxPath</span>(covariates, <span class="st">"g"</span>, <span class="at">labels=</span>covariates),</span>
<span id="cb2-32"><a href="#cb2-32" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-33"><a href="#cb2-33" aria-hidden="true" tabindex="-1"></a> <span class="co"># Data</span></span>
<span id="cb2-34"><a href="#cb2-34" aria-hidden="true" tabindex="-1"></a> <span class="fu">mxData</span>(<span class="at">observed =</span> HS.ability.data, <span class="at">type =</span> <span class="st">"raw"</span>))</span>
<span id="cb2-35"><a href="#cb2-35" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-36"><a href="#cb2-36" aria-hidden="true" tabindex="-1"></a><span class="co"># Get some good starting values for regularization. This</span></span>
<span id="cb2-37"><a href="#cb2-37" aria-hidden="true" tabindex="-1"></a><span class="co"># saves 2-3 minutes on my laptop.</span></span>
<span id="cb2-38"><a href="#cb2-38" aria-hidden="true" tabindex="-1"></a>mimicModel <span class="ot"><-</span> <span class="fu">mxRun</span>(mimicModel)</span></code></pre></div>
<pre><code>## Running MIMIC with 36 parameters</code></pre>
<p>Add the penalty:</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>mimicModel <span class="ot"><-</span> <span class="fu">mxModel</span>(</span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a> mimicModel,</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">mxMatrix</span>(<span class="st">'Full'</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="at">free=</span><span class="cn">TRUE</span>,<span class="at">values=</span><span class="dv">0</span>,<span class="at">labels=</span><span class="st">"lambda"</span>,<span class="at">name=</span><span class="st">"hparam"</span>),</span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a> <span class="co"># Set scale to ML estimates for adaptive lasso</span></span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">mxPenaltyLASSO</span>(<span class="at">what=</span>covariates, <span class="at">name=</span><span class="st">"LASSO"</span>,</span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a> <span class="at">scale =</span> <span class="fu">coef</span>(mimicModel)[covariates],</span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a> <span class="at">lambda =</span> <span class="dv">0</span>, <span class="at">lambda.max =</span><span class="dv">2</span>, <span class="at">lambda.step=</span>.<span class="dv">04</span>)</span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<p>Run the regularization. With only three covariates, the plot of
results is not very exciting. We learn that sex is not a good predictor
of this factor.</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>regMIMIC <span class="ot"><-</span> <span class="fu">mxPenaltySearch</span>(mimicModel)</span></code></pre></div>
<pre><code>## Running MIMIC with 37 parameters</code></pre>
<pre><code>## Warning: In model 'MIMIC' Optimizer returned a non-zero status code 6. The
## model does not satisfy the first-order optimality conditions to the required
## accuracy, and no improved point for the merit function could be found during
## the final linesearch (Mx status RED)</code></pre>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>detail <span class="ot"><-</span> regMIMIC<span class="sc">$</span>compute<span class="sc">$</span>steps<span class="sc">$</span>PS<span class="sc">$</span>output<span class="sc">$</span>detail</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(reshape2)</span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a>est <span class="ot"><-</span> detail[,<span class="fu">c</span>(covariates, <span class="st">'lambda'</span>)]</span>
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(<span class="fu">melt</span>(est, <span class="at">id.vars =</span> <span class="st">'lambda'</span>)) <span class="sc">+</span></span>
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_line</span>(<span class="fu">aes</span>(<span class="at">x=</span>lambda, <span class="at">y=</span>value, <span class="at">color=</span>variable)) <span class="sc">+</span></span>
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_vline</span>(<span class="fu">aes</span>(<span class="at">xintercept=</span><span class="fu">coef</span>(regMIMIC)[<span class="st">'lambda'</span>]),</span>
<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype=</span><span class="st">"dashed"</span>, <span class="at">alpha=</span>.<span class="dv">5</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>The regularized factor loadings can be found here,</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>detail[detail<span class="sc">$</span>EBIC <span class="sc">==</span> <span class="fu">min</span>(detail<span class="sc">$</span>EBIC), covariates]</span></code></pre></div>
<pre><code>## male ageym grade
## 36 3.47131e-07 -0.02792844 1.05808</code></pre>
<p>The regularization causes a lot of bias. One way to deal with this is
to fix zerod parameters to zero, discard the regularization penalty, and
re-fit model.</p>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>regMIMIC <span class="ot"><-</span> <span class="fu">mxPenaltyZap</span>(regMIMIC)</span></code></pre></div>
<pre><code>## Zapping 'male'</code></pre>
<pre><code>## Fixing 'lambda'</code></pre>
<pre><code>## Tip: Use
## model = mxRun(model)
## to re-estimate the model without any penalty terms.</code></pre>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>regMIMIC <span class="ot"><-</span> <span class="fu">mxRun</span>(regMIMIC)</span></code></pre></div>
<pre><code>## Running MIMIC with 35 parameters</code></pre>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(regMIMIC)</span></code></pre></div>
<pre><code>## Summary of MIMIC
##
## free parameters:
## name matrix row col Estimate Std.Error A
## 1 MIMIC.A[1,12] A visual g 2.61817105 0.364534563
## 2 MIMIC.A[2,12] A cubes g 0.93494431 0.256319516
## 3 MIMIC.A[3,12] A paper g 0.70084534 0.152041063
## 4 MIMIC.A[4,12] A flags g 1.57350766 0.491472833
## 5 MIMIC.A[5,12] A paperrev g 0.99009878 0.245139237
## 6 MIMIC.A[6,12] A flagssub g 3.33341890 0.640099599
## 7 MIMIC.A[7,12] A general g 9.23702148 0.536672435
## 8 MIMIC.A[8,12] A paragrap g 2.53491878 0.157363203
## 9 MIMIC.A[9,12] A sentence g 3.96091981 0.222177321
## 10 MIMIC.A[10,12] A wordc g 3.80400361 0.259672047
## 11 MIMIC.A[11,12] A wordm g 5.73048049 0.341017122
## 12 ageym A g ageym -0.02870563 0.006555489
## 13 grade A g grade 1.08144524 0.254231626
## 14 MIMIC.S[1,1] S visual visual 40.27126690 3.353608721
## 15 MIMIC.S[2,2] S cubes cubes 21.00803790 1.722367953
## 16 MIMIC.S[3,3] S paper paper 7.36559558 0.608809830
## 17 MIMIC.S[4,4] S flags flags 78.47401958 6.431633936
## 18 MIMIC.S[5,5] S paperrev paperrev 8.35237950 0.994140216 !
## 19 MIMIC.S[6,6] S flagssub flagssub 56.56099127 6.792986323 !
## 20 MIMIC.S[7,7] S general general 45.64524978 4.802395106
## 21 MIMIC.S[8,8] S paragrap paragrap 4.06598043 0.402084154
## 22 MIMIC.S[9,9] S sentence sentence 6.80451135 0.748411144
## 23 MIMIC.S[10,10] S wordc wordc 13.88560859 1.287061820
## 24 MIMIC.S[11,11] S wordm wordm 17.27853485 1.792470269
## 25 MIMIC.M[1,1] M 1 visual 21.29330086 6.209523404
## 26 MIMIC.M[1,2] M 1 cubes 21.38063178 2.205532617
## 27 MIMIC.M[1,3] M 1 paper 12.00174339 1.658232981
## 28 MIMIC.M[1,4] M 1 flags 13.00225084 3.769860864
## 29 MIMIC.M[1,5] M 1 paperrev 12.12979740 2.407687991
## 30 MIMIC.M[1,6] M 1 flagssub 24.45761673 8.142001966
## 31 MIMIC.M[1,7] M 1 general 11.26661411 22.007072505
## 32 MIMIC.M[1,8] M 1 paragrap 1.12600697 5.976502615
## 33 MIMIC.M[1,9] M 1 sentence 4.77315869 9.408036586
## 34 MIMIC.M[1,10] M 1 wordc 14.03600332 9.016417574
## 35 MIMIC.M[1,11] M 1 wordm -2.91414936 13.552291066
##
## Model Statistics:
## | Parameters | Degrees of Freedom | Fit (-2lnL units)
## Model: 35 2964 17843.68
## Saturated: 77 2922 NA
## Independence: 22 2977 NA
## Number of observations/statistics: 301/2999
##
## Information Criteria:
## | df Penalty | Parameters Penalty | Sample-Size Adjusted
## AIC: 11915.6773 17913.68 17923.19
## BIC: 927.8025 18043.43 17932.43
## To get additional fit indices, see help(mxRefModels)
## timestamp: 2024-10-18 13:30:26
## Wall clock time: 0.6433542 secs
## optimizer: SLSQP
## OpenMx version number: 2.21.13
## Need help? See help(mxSummary)</code></pre>
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