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ACI Quizzes.html
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<!DOCTYPE html>
<html lang="en"><head>
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<meta name="author" content="Felix Wortmann Callejón">
<title>Advanced Causal Inference</title>
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</head>
<body class="quarto-light">
<div class="reveal">
<div class="slides">
<section id="title-slide" class="quarto-title-block center">
<h1 class="title">Advanced Causal Inference</h1>
<div class="quarto-title-authors">
<div class="quarto-title-author">
<div class="quarto-title-author-name">
Felix Wortmann Callejón
</div>
</div>
</div>
</section>
<section>
<section id="introduction-to-declaredesign" class="title-slide slide level1 center">
<h1>Introduction to <code>DeclareDesign</code></h1>
</section>
<section id="q2.1-false-positives-and-ns" class="slide level2">
<h2>Q2.1: <strong>False positives and</strong> <span class="math inline">\(N\)</span>s</h2>
<ul>
<li>Sometimes people worry that with larger samples you are more likely to get a false positive. Is that true?</li>
<li>Assess by generating a simple experimental design from scratch in which we can vary the <code>N</code> and <em>in which there is no true effect</em> of some treatment.</li>
</ul>
</section>
<section id="q2.1-false-positives-and-ns-1" class="slide level2">
<h2>Q2.1: <strong>False positives and</strong> <span class="math inline">\(N\)</span>s</h2>
<p>Then:</p>
<ul>
<li>Plot the distribution of <span class="math inline">\(p\)</span> values from the <code>simulations_df</code>. What shape is it and why?</li>
<li>Plot the power as <span class="math inline">\(N\)</span> increases, using the <code>diagnosands_df</code></li>
<li>Plot the estimates against <span class="math inline">\(p\)</span> values for different values of <span class="math inline">\(N\)</span>; what do you see?</li>
<li>Discuss</li>
</ul>
</section>
<section id="q2.1-answer" class="slide level2">
<h2>Q2.1 Answer</h2>
<p>I proceed by copying the code for a simple experimental design from the lecture slides. Crucially, I set <span class="math inline">\(\tau\)</span> represented by <code>b = 0</code>.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1"></a>b <span class="ot"><-</span> <span class="dv">0</span></span>
<span id="cb1-2"><a href="#cb1-2"></a>N <span class="ot"><-</span> <span class="dv">100</span></span>
<span id="cb1-3"><a href="#cb1-3"></a></span>
<span id="cb1-4"><a href="#cb1-4"></a>design <span class="ot"><-</span> <span class="fu">declare_model</span>(<span class="at">N =</span> N, <span class="at">U =</span> <span class="fu">rnorm</span>(N), <span class="fu">potential_outcomes</span>(Y <span class="sc">~</span> b <span class="sc">*</span> Z <span class="sc">+</span> U)) <span class="sc">+</span> </span>
<span id="cb1-5"><a href="#cb1-5"></a> <span class="fu">declare_assignment</span>(<span class="at">Z =</span> <span class="fu">simple_ra</span>(N), <span class="at">Y =</span> <span class="fu">reveal_outcomes</span>(Y <span class="sc">~</span> Z)) <span class="sc">+</span> </span>
<span id="cb1-6"><a href="#cb1-6"></a> <span class="fu">declare_inquiry</span>(<span class="at">ate =</span> <span class="fu">mean</span>(Y_Z_1 <span class="sc">-</span> Y_Z_0)) <span class="sc">+</span> </span>
<span id="cb1-7"><a href="#cb1-7"></a> <span class="fu">declare_estimator</span>(Y <span class="sc">~</span> Z, <span class="at">inquiry =</span> <span class="st">"ate"</span>, <span class="at">.method =</span> lm_robust)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="q2.1-answer-1" class="slide level2">
<h2>Q2.1 Answer</h2>
<p>Then, I simulate the design <span class="math inline">\(10^4\)</span> times</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1"></a>n_sims <span class="ot"><-</span> <span class="dv">10</span><span class="sc">^</span><span class="dv">4</span></span>
<span id="cb2-2"><a href="#cb2-2"></a>sims <span class="ot"><-</span> <span class="fu">simulate_design</span>(design, <span class="at">sims =</span> n_sims)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="q2.1-answer-2" class="slide level2">
<h2>Q2.1 Answer</h2>
<p>And plot the density for the <code>p.value</code>s</p>
<div class="cell">
<details>
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1"></a><span class="fu">ggplot</span>(sims, <span class="fu">aes</span>(p.value)) <span class="sc">+</span></span>
<span id="cb3-2"><a href="#cb3-2"></a> <span class="fu">scale_x_continuous</span>(<span class="st">"p-value"</span>, <span class="at">label =</span> scales<span class="sc">::</span><span class="fu">label_percent</span>(<span class="dv">1</span>)) <span class="sc">+</span></span>
<span id="cb3-3"><a href="#cb3-3"></a> <span class="fu">scale_y_continuous</span>(<span class="st">"Probability density"</span>) <span class="sc">+</span></span>
<span id="cb3-4"><a href="#cb3-4"></a> <span class="fu">geom_density</span>(<span class="at">fill =</span> <span class="st">"blue"</span>, <span class="at">color =</span> <span class="st">"blue"</span>, <span class="at">alpha =</span> <span class="fl">0.2</span>) <span class="sc">+</span></span>
<span id="cb3-5"><a href="#cb3-5"></a> <span class="fu">theme_light</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
</div>
<img data-src="ACI-Quizzes_files/figure-revealjs/plot_pval_density-1.png" width="960" class="r-stretch"></section>
<section id="q2.1-answer-3" class="slide level2">
<h2>Q2.1 Answer</h2>
<p>Next, I diagnose the design for a series of values of <span class="math inline">\(N\)</span></p>
<div class="cell">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1"></a>diagnose <span class="ot"><-</span> <span class="fu">redesign</span>(design, <span class="at">N =</span> <span class="fu">c</span>(<span class="dv">100</span>, <span class="dv">150</span>, <span class="dv">200</span>, <span class="dv">250</span>, <span class="dv">300</span>, <span class="dv">350</span>, <span class="dv">400</span>, <span class="dv">450</span>, <span class="dv">500</span>,</span>
<span id="cb4-2"><a href="#cb4-2"></a> <span class="dv">1000</span>, <span class="dv">1500</span>, <span class="dv">2000</span>, <span class="dv">2500</span>, <span class="dv">3000</span>, <span class="dv">3500</span>, <span class="dv">4000</span>, <span class="dv">4500</span>, <span class="dv">5000</span>)) <span class="sc">|></span></span>
<span id="cb4-3"><a href="#cb4-3"></a> <span class="fu">diagnose_design</span>() </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="q2.1-answer-4" class="slide level2">
<h2>Q2.1 Answer</h2>
<p>And plot power as a function of <span class="math inline">\(N\)</span></p>
<div class="cell">
<details>
<summary>Code</summary>
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode numberSource r number-lines code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1"></a><span class="fu">ggplot</span>(diagnose<span class="sc">$</span>diagnosands_df, <span class="fu">aes</span>(N, power)) <span class="sc">+</span></span>
<span id="cb5-2"><a href="#cb5-2"></a> <span class="fu">scale_x_log10</span>(<span class="st">"N"</span>, <span class="at">labels =</span> scales<span class="sc">::</span><span class="fu">label_comma</span>(<span class="dv">1</span>)) <span class="sc">+</span></span>
<span id="cb5-3"><a href="#cb5-3"></a> <span class="fu">scale_y_continuous</span>(<span class="st">"Power"</span>, <span class="at">limits =</span> <span class="fu">c</span>(<span class="dv">0</span>,<span class="dv">1</span>), <span class="at">labels =</span> scales<span class="sc">::</span><span class="fu">label_percent</span>(<span class="dv">1</span>)) <span class="sc">+</span></span>
<span id="cb5-4"><a href="#cb5-4"></a> <span class="fu">geom_point</span>() <span class="sc">+</span></span>
<span id="cb5-5"><a href="#cb5-5"></a> <span class="fu">geom_line</span>() <span class="sc">+</span></span>
<span id="cb5-6"><a href="#cb5-6"></a> <span class="fu">theme_light</span>() </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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