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palday committed Sep 13, 2024
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2 changes: 1 addition & 1 deletion .nojekyll
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2 changes: 1 addition & 1 deletion AoGPlots.html
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>

<meta charset="utf-8">
<meta name="generator" content="quarto-1.5.56">
<meta name="generator" content="quarto-1.5.53">

<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">

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6 changes: 3 additions & 3 deletions about.html
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>

<meta charset="utf-8">
<meta name="generator" content="quarto-1.5.56">
<meta name="generator" content="quarto-1.5.53">

<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">

<meta name="author" content="Phillip Alday, Douglas Bates, and Reinhold Kliegl">
<meta name="dcterms.date" content="2024-06-27">
<meta name="dcterms.date" content="2024-06-28">

<title>About – SMLP2024: Advanced Frequentist Track</title>
<style>
Expand Down Expand Up @@ -336,7 +336,7 @@ <h1 class="title">About</h1>
<div>
<div class="quarto-title-meta-heading">Published</div>
<div class="quarto-title-meta-contents">
<p class="date">2024-06-27</p>
<p class="date">2024-06-28</p>
</div>
</div>

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130 changes: 65 additions & 65 deletions bootstrap.html
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>

<meta charset="utf-8">
<meta name="generator" content="quarto-1.5.56">
<meta name="generator" content="quarto-1.5.53">

<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">

<meta name="author" content="Phillip Alday, Douglas Bates, and Reinhold Kliegl">
<meta name="dcterms.date" content="2024-09-12">
<meta name="dcterms.date" content="2024-09-11">

<title>Parametric bootstrap for mixed-effects models – SMLP2024: Advanced Frequentist Track</title>
<style>
Expand Down Expand Up @@ -405,7 +405,7 @@ <h1 class="title">Parametric bootstrap for mixed-effects models</h1>
<div>
<div class="quarto-title-meta-heading">Published</div>
<div class="quarto-title-meta-contents">
<p class="date">2024-09-12</p>
<p class="date">2024-09-11</p>
</div>
</div>

Expand Down Expand Up @@ -591,53 +591,53 @@ <h1 data-number="2"><span class="header-section-number">2</span> A model of mode
</tr>
<tr class="even">
<td style="text-align: left;">(Intercept)</td>
<td style="text-align: right;">2181.6750</td>
<td style="text-align: right;">77.3029</td>
<td style="text-align: right;">2181.6729</td>
<td style="text-align: right;">77.3131</td>
<td style="text-align: right;">28.22</td>
<td style="text-align: right;">&lt;1e-99</td>
<td style="text-align: right;">301.8414</td>
<td style="text-align: right;">362.1701</td>
<td style="text-align: right;">301.6736</td>
<td style="text-align: right;">362.3182</td>
</tr>
<tr class="odd">
<td style="text-align: left;">spkr: old</td>
<td style="text-align: right;">67.7490</td>
<td style="text-align: right;">18.2824</td>
<td style="text-align: right;">18.2747</td>
<td style="text-align: right;">3.71</td>
<td style="text-align: right;">0.0002</td>
<td style="text-align: right;">43.0396</td>
<td style="text-align: right;">40.5288</td>
<td style="text-align: right;">42.5441</td>
<td style="text-align: right;">40.7073</td>
</tr>
<tr class="even">
<td style="text-align: left;">prec: maintain</td>
<td style="text-align: right;">-333.9206</td>
<td style="text-align: right;">47.1621</td>
<td style="text-align: right;">47.1388</td>
<td style="text-align: right;">-7.08</td>
<td style="text-align: right;">&lt;1e-11</td>
<td style="text-align: right;">62.1035</td>
<td style="text-align: right;">246.9365</td>
<td style="text-align: right;">61.9978</td>
<td style="text-align: right;">246.8078</td>
</tr>
<tr class="odd">
<td style="text-align: left;">load: yes</td>
<td style="text-align: right;">78.7681</td>
<td style="text-align: right;">19.5247</td>
<td style="text-align: right;">78.7702</td>
<td style="text-align: right;">19.5387</td>
<td style="text-align: right;">4.03</td>
<td style="text-align: right;">&lt;1e-04</td>
<td style="text-align: right;">65.1473</td>
<td style="text-align: right;">42.1755</td>
<td style="text-align: right;">64.9874</td>
<td style="text-align: right;">42.5139</td>
</tr>
<tr class="even">
<td style="text-align: left;">spkr: old &amp; prec: maintain</td>
<td style="text-align: right;">-21.9634</td>
<td style="text-align: right;">15.8062</td>
<td style="text-align: right;">-21.9655</td>
<td style="text-align: right;">15.8070</td>
<td style="text-align: right;">-1.39</td>
<td style="text-align: right;">0.1647</td>
<td style="text-align: right;">0.1646</td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
</tr>
<tr class="odd">
<td style="text-align: left;">spkr: old &amp; load: yes</td>
<td style="text-align: right;">18.3838</td>
<td style="text-align: right;">15.8062</td>
<td style="text-align: right;">15.8070</td>
<td style="text-align: right;">1.16</td>
<td style="text-align: right;">0.2448</td>
<td style="text-align: right;"></td>
Expand All @@ -646,24 +646,24 @@ <h1 data-number="2"><span class="header-section-number">2</span> A model of mode
<tr class="even">
<td style="text-align: left;">prec: maintain &amp; load: yes</td>
<td style="text-align: right;">4.5333</td>
<td style="text-align: right;">15.8062</td>
<td style="text-align: right;">15.8070</td>
<td style="text-align: right;">0.29</td>
<td style="text-align: right;">0.7743</td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
</tr>
<tr class="odd">
<td style="text-align: left;">spkr: old &amp; prec: maintain &amp; load: yes</td>
<td style="text-align: right;">23.6052</td>
<td style="text-align: right;">15.8062</td>
<td style="text-align: right;">23.6072</td>
<td style="text-align: right;">15.8070</td>
<td style="text-align: right;">1.49</td>
<td style="text-align: right;">0.1353</td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
</tr>
<tr class="even">
<td style="text-align: left;">Residual</td>
<td style="text-align: right;">668.5061</td>
<td style="text-align: right;">668.5371</td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
Expand Down Expand Up @@ -693,80 +693,80 @@ <h1 data-number="2"><span class="header-section-number">2</span> A model of mode
<tr class="even">
<td style="text-align: left;">subj</td>
<td style="text-align: left;">(Intercept)</td>
<td style="text-align: right;">91108.2428</td>
<td style="text-align: right;">301.8414</td>
<td style="text-align: right;">91006.9887</td>
<td style="text-align: right;">301.6736</td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
</tr>
<tr class="odd">
<td style="text-align: left;"></td>
<td style="text-align: left;">spkr: old</td>
<td style="text-align: right;">1852.4098</td>
<td style="text-align: right;">43.0396</td>
<td style="text-align: right;">+0.78</td>
<td style="text-align: right;">1810.0012</td>
<td style="text-align: right;">42.5441</td>
<td style="text-align: right;">+0.79</td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
</tr>
<tr class="even">
<td style="text-align: left;"></td>
<td style="text-align: left;">prec: maintain</td>
<td style="text-align: right;">3856.8408</td>
<td style="text-align: right;">62.1035</td>
<td style="text-align: right;">3843.7268</td>
<td style="text-align: right;">61.9978</td>
<td style="text-align: right;">-0.59</td>
<td style="text-align: right;">+0.02</td>
<td style="text-align: right;"></td>
</tr>
<tr class="odd">
<td style="text-align: left;"></td>
<td style="text-align: left;">load: yes</td>
<td style="text-align: right;">4244.1689</td>
<td style="text-align: right;">65.1473</td>
<td style="text-align: right;">4223.3647</td>
<td style="text-align: right;">64.9874</td>
<td style="text-align: right;">+0.36</td>
<td style="text-align: right;">+0.82</td>
<td style="text-align: right;">+0.53</td>
<td style="text-align: right;">+0.85</td>
<td style="text-align: right;">+0.54</td>
</tr>
<tr class="even">
<td style="text-align: left;">item</td>
<td style="text-align: left;">(Intercept)</td>
<td style="text-align: right;">131167.1572</td>
<td style="text-align: right;">362.1701</td>
<td style="text-align: right;">131274.4558</td>
<td style="text-align: right;">362.3182</td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
</tr>
<tr class="odd">
<td style="text-align: left;"></td>
<td style="text-align: left;">spkr: old</td>
<td style="text-align: right;">1642.5825</td>
<td style="text-align: right;">40.5288</td>
<td style="text-align: right;">1657.0830</td>
<td style="text-align: right;">40.7073</td>
<td style="text-align: right;">+0.44</td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
</tr>
<tr class="even">
<td style="text-align: left;"></td>
<td style="text-align: left;">prec: maintain</td>
<td style="text-align: right;">60977.6107</td>
<td style="text-align: right;">246.9365</td>
<td style="text-align: right;">60914.1141</td>
<td style="text-align: right;">246.8078</td>
<td style="text-align: right;">-0.69</td>
<td style="text-align: right;">+0.35</td>
<td style="text-align: right;"></td>
</tr>
<tr class="odd">
<td style="text-align: left;"></td>
<td style="text-align: left;">load: yes</td>
<td style="text-align: right;">1778.7763</td>
<td style="text-align: right;">42.1755</td>
<td style="text-align: right;">1807.4303</td>
<td style="text-align: right;">42.5139</td>
<td style="text-align: right;">+0.32</td>
<td style="text-align: right;">+0.23</td>
<td style="text-align: right;">-0.15</td>
<td style="text-align: right;">+0.15</td>
<td style="text-align: right;">-0.14</td>
</tr>
<tr class="even">
<td style="text-align: left;">Residual</td>
<td style="text-align: left;"></td>
<td style="text-align: right;">446900.4651</td>
<td style="text-align: right;">668.5061</td>
<td style="text-align: right;">446941.7901</td>
<td style="text-align: right;">668.5371</td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
<td style="text-align: right;"></td>
Expand Down Expand Up @@ -893,21 +893,21 @@ <h1 data-number="2"><span class="header-section-number">2</span> A model of mode
<tr class="even">
<td style="text-align: left;">item</td>
<td style="text-align: left;">(Intercept)</td>
<td style="text-align: right;">133026.916</td>
<td style="text-align: right;">133026.918</td>
<td style="text-align: right;">364.729</td>
<td style="text-align: right;"></td>
</tr>
<tr class="odd">
<td style="text-align: left;"></td>
<td style="text-align: left;">prec: maintain</td>
<td style="text-align: right;">63841.497</td>
<td style="text-align: right;">63841.496</td>
<td style="text-align: right;">252.669</td>
<td style="text-align: right;">-0.70</td>
</tr>
<tr class="even">
<td style="text-align: left;">subj</td>
<td style="text-align: left;">(Intercept)</td>
<td style="text-align: right;">88870.081</td>
<td style="text-align: right;">88870.080</td>
<td style="text-align: right;">298.111</td>
<td style="text-align: right;"></td>
</tr>
Expand Down Expand Up @@ -950,7 +950,7 @@ <h1 data-number="2"><span class="header-section-number">2</span> A model of mode
<td style="text-align: right;">28637</td>
<td style="text-align: right;">21</td>
<td style="text-align: right;">16</td>
<td style="text-align: left;">0.1655</td>
<td style="text-align: left;">0.1650</td>
</tr>
</tbody>
</table>
Expand Down Expand Up @@ -1032,11 +1032,11 @@ <h1 data-number="3"><span class="header-section-number">3</span> Bootstrap basic
β6 │ -11.3574 51.5299
β7 │ -27.1799 36.3332
β8 │ -9.28905 53.5917
ρ1 │ -0.912786 -0.471123
ρ1 │ -0.912778 -0.471128
σ │ 654.965 700.928
σ1 │ 265.276 456.967
σ2 │ 179.402 321.013
σ3 │ 232.096 359.745</code></pre>
σ2 │ 179.402 321.016
σ3 │ 232.096 359.744</code></pre>
</div>
</div>
<div id="28" class="cell" data-execution_count="1">
Expand Down Expand Up @@ -1231,22 +1231,22 @@ <h1 data-number="4"><span class="header-section-number">4</span> Singularity</h1
obj β1 β2 σ σ1 σ2 ρ1 ⋯
┌────────────────────────────────────────────────────────────────────
1 │ 1721.95 252.488 11.0328 22.4544 29.6185 6.33343 0.233383 ⋯
2 │ 1760.85 260.763 8.55352 27.3834 20.8073 4.32899 0.914653 ⋯
2 │ 1760.85 260.763 8.55352 27.3833 20.8066 4.32936 0.91467 ⋯
3 │ 1750.88 246.709 12.4613 25.9951 15.8702 6.33404 0.200358 ⋯
4 │ 1777.33 247.683 12.9824 27.7966 27.5413 4.9878 0.121411 ⋯
5 │ 1738.05 245.649 10.5792 25.3596 21.5208 4.26131 0.052677 ⋯
5 │ 1738.05 245.649 10.5792 25.3596 21.5208 4.26131 0.0526768 ⋯
6 │ 1751.25 255.669 10.1984 26.1432 22.5389 4.58209 0.225968 ⋯
7 │ 1727.51 248.986 7.62095 24.6451 19.0858 4.34881 0.212916 ⋯
8 │ 1754.18 246.075 11.0469 26.9407 19.8341 4.55961 -0.202146 ⋯
9 │ 1757.47 245.407 13.7475 25.8265 20.0014 7.7647 -0.266385 ⋯
10 │ 1752.8 253.911 11.4977 25.7077 20.6409 6.27298 0.171494 ⋯
11 │ 1707.8 248.887 10.1608 23.9684 10.5921 4.32046 1.0 ⋯
12 │ 1773.69 252.542 10.7379 26.8795 27.7956 6.20553 0.156472 ⋯
11 │ 1707.8 248.887 10.1608 23.9684 10.5922 4.32039 1.0 ⋯
12 │ 1773.69 252.542 10.7379 26.8794 27.7966 6.20556 0.156463 ⋯
13 │ 1761.27 254.712 11.0373 25.7998 23.2005 7.30831 0.368175 ⋯
14 │ 1737.0 260.299 10.5659 24.6504 29.0113 4.26877 -0.0785721 ⋯
15 │ 1760.12 258.949 10.1464 27.2088 8.03014 7.01905 0.72704 ⋯
14 │ 1737.0 260.299 10.5659 24.6504 29.0113 4.26877 -0.0785722 ⋯
15 │ 1760.12 258.949 10.1464 27.2088 8.02888 7.01928 0.727229 ⋯
16 │ 1723.7 249.204 11.7868 24.9861 18.6887 3.08433 0.633218 ⋯
17 │ 1734.14 262.586 8.96611 24.001 26.7969 5.376 0.297087 ⋯
17 │ 1734.14 262.586 8.96611 24.0011 26.7969 5.37598 0.29709 ⋯
⋮ │ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱</code></pre>
</div>
</div>
Expand All @@ -1261,7 +1261,7 @@ <h1 data-number="4"><span class="header-section-number">4</span> Singularity</h1
β2 │ 7.44545 13.3516
ρ1 │ -0.409926 1.0
σ │ 22.6345 28.5125
σ1 │ 10.6755 33.3567
σ1 │ 10.6764 33.3567
σ2 │ 3.07053 7.82205</code></pre>
</div>
</div>
Expand Down Expand Up @@ -1295,7 +1295,7 @@ <h1 data-number="4"><span class="header-section-number">4</span> Singularity</h1
<div id="54" class="cell" data-execution_count="1">
<div class="sourceCode cell-code" id="cb37"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a><span class="fu">count</span>(tblsleep.σ<span class="fl">1</span> <span class="op">.≈</span> <span class="fl">0</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display" data-execution_count="1">
<pre><code>6</code></pre>
<pre><code>7</code></pre>
</div>
</div>
<p>There is a general condition to check for singularity of an estimated covariance matrix or matrices in a bootstrap sample. The parameter optimized in the estimation is <code>θ</code>, the relative covariance parameter. Some of the elements of this parameter vector must be non-negative and, when one of these components is approximately zero, one of the covariance matrices will be singular.</p>
Expand All @@ -1304,7 +1304,7 @@ <h1 data-number="4"><span class="header-section-number">4</span> Singularity</h1
<div id="56" class="cell" data-execution_count="1">
<div class="sourceCode cell-code" id="cb39"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb39-1"><a href="#cb39-1" aria-hidden="true" tabindex="-1"></a><span class="fu">count</span>(<span class="fu">issingular</span>(sampsleep))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display" data-execution_count="1">
<pre><code>300</code></pre>
<pre><code>301</code></pre>
</div>
</div>
</section>
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