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Expand Down Expand Up @@ -716,8 +716,8 @@ <h2 data-number="A.4" class="anchored" data-anchor-id="the-dataframes-package"><
<p>The <a href="https://github.com/JuliaData">JuliaData</a> organization manages the development of several packages related to data science and data management, including <a href="https://github.com/JuliaData/DataFrames.jl">DataFrames.jl</a>, a comprehensive system for working with column-oriented data tables in Julia. <span class="citation" data-cites="Kaminski2023">Kamiński (<a href="references.html#ref-Kaminski2023" role="doc-biblioref">2023</a>)</span>, written by the primary author of that package, provides an in-depth introduction to data science facilities, in particular the <code>DataFrames</code> package, in Julia.</p>
<p>This package is particularly well-suited to more advanced data manipulation such as the <code>split-apply-combine</code> strategy <span class="citation" data-cites="Wickham2011">(<a href="references.html#ref-Wickham2011" role="doc-biblioref">Wickham, 2011</a>)</span> and “joins” of data tables.</p>
<p><span class="citation" data-cites="JSSv107i04">Bouchet-Valat &amp; Kamiński (<a href="references.html#ref-JSSv107i04" role="doc-biblioref">2023</a>)</span> compares the performance of DataFrames.jl to other data frame implementations in R and Python.</p>
<p><em>This page was rendered from git revision <a href="https://github.com/JuliaMixedModels/EmbraceUncertainty/tree/05a171b
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<meta name="author" content="Phillip Alday">
<meta name="author" content="Reinhold Kliegl">
<meta name="author" content="Douglas Bates">
<meta name="dcterms.date" content="2024-07-02">
<meta name="dcterms.date" content="2024-08-13">

<title>Embrace Uncertainty</title>
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Expand Down Expand Up @@ -252,7 +252,7 @@ <h1 class="title">Embrace Uncertainty</h1>
<div>
<div class="quarto-title-meta-heading">Published</div>
<div class="quarto-title-meta-contents">
<p class="date">July 2, 2024</p>
<p class="date">August 13, 2024</p>
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</div>

Expand All @@ -270,8 +270,8 @@ <h1 class="unnumbered">Preface</h1>
<p>The practical aspects of fitting such models to experimental or observational data and in evaluating such models are introduced through the <a href="https://julialang.org">Julia programming language</a> and its <a href="https://github.com/JuliaStats/MixedModels.jl">MixedModels</a> package.</p>
<p>This book is intended for researchers in applications areas, such as Psychology or Linguistics, and for researchers in Statistical methods. Some of the technical discussions, especially in the appendices, may be rather daunting for applications-area researchers, who should feel free to skim those sections. The purpose of those technical discussions is to establish a firm mathematical and theoretical basis for the computational methods.</p>
<p>This book has been produced with Quarto. To learn more about Quarto books visit <a href="https://quarto.org/docs/books">https://quarto.org/docs/books</a>.</p>
<p><em>This page was rendered from git revision <a href="https://github.com/JuliaMixedModels/EmbraceUncertainty/tree/05a171b
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Expand Down Expand Up @@ -1281,21 +1281,21 @@ <h2 data-number="1.5" class="anchored" data-anchor-id="sec-furtherassess"><span
<span id="cb44-4"><a href="#cb44-4" aria-hidden="true" tabindex="-1"></a><span class="fu">first</span>(dsm01pars, <span class="fl">7</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<pre><code>┌ Warning: NLopt was roundoff limited
└ @ MixedModels ~/.julia/packages/MixedModels/peUlR/src/optsummary.jl:160
└ @ MixedModels ~/.julia/packages/MixedModels/hs2Ke/src/optsummary.jl:160
┌ Warning: NLopt was roundoff limited
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┌ Warning: NLopt was roundoff limited
└ @ MixedModels ~/.julia/packages/MixedModels/peUlR/src/optsummary.jl:160
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┌ Warning: NLopt was roundoff limited
└ @ MixedModels ~/.julia/packages/MixedModels/peUlR/src/optsummary.jl:160
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┌ Warning: NLopt was roundoff limited
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┌ Warning: NLopt was roundoff limited
└ @ MixedModels ~/.julia/packages/MixedModels/peUlR/src/optsummary.jl:160
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┌ Warning: NLopt was roundoff limited
└ @ MixedModels ~/.julia/packages/MixedModels/peUlR/src/optsummary.jl:160</code></pre>
└ @ MixedModels ~/.julia/packages/MixedModels/hs2Ke/src/optsummary.jl:160</code></pre>
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<div id="dsm01samp" class="cell-output cell-output-display" data-execution_count="1">
<div><div style="float: left;"><span>7×5 DataFrame</span></div><div style="clear: both;"></div></div><div class="data-frame" style="overflow-x: scroll;">
Expand Down Expand Up @@ -2146,8 +2146,8 @@ <h2 data-number="1.8" class="anchored" data-anchor-id="sec-ChIntroSummary"><span
<p>The maximum likelihood estimates of the parameters are obtained by minimizing the deviance. For linear mixed models we can minimize the profiled deviance, which is a function of <span class="math inline">\({\boldsymbol{\theta}}\)</span> only, thereby considerably simplifying the optimization problem.</p>
<p>To assess the precision of the parameter estimates we use a parametric bootstrap sample, when feasible. Re-fitting a simple model, such as those shown in this chapter, to a randomly generated response vector is quite fast and it is reasonable to work with bootstrap samples of tens of thousands of replicates. With larger data sets and more complex models, large bootstrap samples of parameter estimates could take much longer.</p>
<p>Prediction intervals from the conditional distribution of the random effects, given the observed data, allow us to assess the precision of the random effects.</p>
<p><em>This page was rendered from git revision <a href="https://github.com/JuliaMixedModels/EmbraceUncertainty/tree/05a171b
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Expand Down Expand Up @@ -599,7 +599,7 @@ <h2 data-number="B.5" class="anchored" data-anchor-id="numerical-example"><span
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<pre><code>2-element Vector{Float64}:
267.04479999999995
11.298073333333344</code></pre>
11.298073333333345</code></pre>
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<p>Alternatively, we could carry out the two solutions of the triangular systems explicitly by first solving for <span class="math inline">\(\mathbf{r}_{Xy}\)</span></p>
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<pre><code>2-element Vector{Float64}:
1005.244207376381
102.61984718485854</code></pre>
102.61984718485859</code></pre>
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<p>then solving in-place to obtain <span class="math inline">\(\widehat{{\boldsymbol{\beta}}}\)</span></p>
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<pre><code>2-element Vector{Float64}:
267.0447999999998
11.298073333333361</code></pre>
11.298073333333367</code></pre>
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<p>The residual vector, <span class="math inline">\({\mathbf{y}}-{\mathbf{X}}\widehat{{\boldsymbol{\beta}}}\)</span>, is</p>
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Expand Down Expand Up @@ -331,8 +331,8 @@ <h1 class="title">References</h1>
<em>Journal of Statistical Software</em>, <em>40</em>(1), 1–29. <a href="https://doi.org/10.18637/jss.v040.i01">https://doi.org/10.18637/jss.v040.i01</a>
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