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6 changes: 3 additions & 3 deletions common-mistakes.html
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6 changes: 3 additions & 3 deletions coxph-model-building.html
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<span class="menu-text"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Models for Binary Outcomes (Logistic regression and variations)</span></span></a>
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<li class="sidebar-item">
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<a href="./logistic-regression.html" class="sidebar-item-text sidebar-link">
<span class="menu-text"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Models for Binary Outcomes (Logistic regression and variations)</span></span></a>
<span class="menu-text"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Models for Binary Outcomes</span></span></a>
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<title>Regression Models for Epidemiology - Appendix C — Introduction to Maximum Likelihood Inference</title>
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<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./logistic-regression.html" class="sidebar-item-text sidebar-link">
<span class="menu-text"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Models for Binary Outcomes (Logistic regression and variations)</span></span></a>
<span class="menu-text"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Models for Binary Outcomes</span></span></a>
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<span class="menu-text"><span class="chapter-number">4</span>&nbsp; <span class="chapter-title">Models for Count Outcomes (Poisson regression and variations)</span></span></a>
<span class="menu-text"><span class="chapter-number">4</span>&nbsp; <span class="chapter-title">Models for Count Outcomes</span></span></a>
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<div class="quarto-title-meta-heading">Published</div>
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<p>[We haven’t gone over this yet]</p>
<p>log(likelihood ratio) tests <span class="citation" data-cites="dobson2018introduction">(c.f. <a href="references.html#ref-dobson2018introduction" role="doc-biblioref">Dobson and Barnett 2018, sec. 5.7</a>)</span>:</p>
<p><span class="math display">\[2\left( \mathfrak{l -}\ell_{0} \right) \sim \chi^{2}(p - q)\]</span></p>
<p>See also https://online.stat.psu.edu/stat504/book/export/html/657</p>
</section><section id="prediction-intervals-for-mles" class="level3" data-number="C.2.7"><h3 data-number="C.2.7" class="anchored" data-anchor-id="prediction-intervals-for-mles">
<span class="header-section-number">C.2.7</span> Prediction intervals for MLEs</h3>
<p><span class="math display">\[\overline{X} \in \left\lbrack \widehat{\mu} \pm z_{1 - \alpha\text{/}2}\frac{\sigma}{m} \right\rbrack\]</span></p>
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<span id="cb12-343"><a href="#cb12-343" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-344"><a href="#cb12-344" aria-hidden="true" tabindex="-1"></a>$$2\left( \mathfrak{l -}\ell_{0} \right) \sim \chi^{2}(p - q)$$</span>
<span id="cb12-345"><a href="#cb12-345" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-346"><a href="#cb12-346" aria-hidden="true" tabindex="-1"></a><span class="fu">### Prediction intervals for MLEs</span></span>
<span id="cb12-346"><a href="#cb12-346" aria-hidden="true" tabindex="-1"></a>See also https://online.stat.psu.edu/stat504/book/export/html/657</span>
<span id="cb12-347"><a href="#cb12-347" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-348"><a href="#cb12-348" aria-hidden="true" tabindex="-1"></a>$$\overline{X} \in \left\lbrack \widehat{\mu} \pm z_{1 - \alpha\text{/}2}\frac{\sigma}{m} \right\rbrack$$</span>
<span id="cb12-348"><a href="#cb12-348" aria-hidden="true" tabindex="-1"></a><span class="fu">### Prediction intervals for MLEs</span></span>
<span id="cb12-349"><a href="#cb12-349" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-350"><a href="#cb12-350" aria-hidden="true" tabindex="-1"></a>Where $m$ is the sample size of the new data to be predicted (typically</span>
<span id="cb12-351"><a href="#cb12-351" aria-hidden="true" tabindex="-1"></a>1, except for binary outcomes, where it needs to be bigger for</span>
<span id="cb12-352"><a href="#cb12-352" aria-hidden="true" tabindex="-1"></a>prediction intervals to make sense)</span>
<span id="cb12-353"><a href="#cb12-353" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-354"><a href="#cb12-354" aria-hidden="true" tabindex="-1"></a><span class="ot">[^1]: </span>I might sometimes switch the order of $x,$ $\theta$; this is</span>
<span id="cb12-355"><a href="#cb12-355" aria-hidden="true" tabindex="-1"></a> unintentional and not meaningful.</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<span id="cb12-350"><a href="#cb12-350" aria-hidden="true" tabindex="-1"></a>$$\overline{X} \in \left\lbrack \widehat{\mu} \pm z_{1 - \alpha\text{/}2}\frac{\sigma}{m} \right\rbrack$$</span>
<span id="cb12-351"><a href="#cb12-351" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-352"><a href="#cb12-352" aria-hidden="true" tabindex="-1"></a>Where $m$ is the sample size of the new data to be predicted (typically</span>
<span id="cb12-353"><a href="#cb12-353" aria-hidden="true" tabindex="-1"></a>1, except for binary outcomes, where it needs to be bigger for</span>
<span id="cb12-354"><a href="#cb12-354" aria-hidden="true" tabindex="-1"></a>prediction intervals to make sense)</span>
<span id="cb12-355"><a href="#cb12-355" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-356"><a href="#cb12-356" aria-hidden="true" tabindex="-1"></a><span class="ot">[^1]: </span>I might sometimes switch the order of $x,$ $\theta$; this is</span>
<span id="cb12-357"><a href="#cb12-357" aria-hidden="true" tabindex="-1"></a> unintentional and not meaningful.</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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6 changes: 3 additions & 3 deletions intro-to-GLMs.html
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