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VeenDuco · Jan 22, 2020 · 3e212cc · 3e212cc
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diff --git a/_bookdown.yml b/_bookdown.yml
@@ -1,3 +1,4 @@
 #book_filename: "my-book.Rmd"
 #edit: https://github.com/rstudio/bookdown-demo/edit/master/%s
 output_dir: "docs"
+book_filename: "Dissertation_Duco_Veen"
diff --git a/_bookdown_files/Dissertation_Duco_Veen_files/figure-html/binomInf-1.png b/_bookdown_files/Dissertation_Duco_Veen_files/figure-html/binomInf-1.png
diff --git a/_bookdown_files/Dissertation_Duco_Veen_files/figure-html/binomUninformative-1.png b/_bookdown_files/Dissertation_Duco_Veen_files/figure-html/binomUninformative-1.png
diff --git a/_bookdown_files/Dissertation_Duco_Veen_files/figure-html/ch06fig1-1.png b/_bookdown_files/Dissertation_Duco_Veen_files/figure-html/ch06fig1-1.png
diff --git a/_bookdown_files/Dissertation_Duco_Veen_files/figure-latex/binomInf-1.pdf b/_bookdown_files/Dissertation_Duco_Veen_files/figure-latex/binomInf-1.pdf
diff --git a/_bookdown_files/Dissertation_Duco_Veen_files/figure-latex/binomUninformative-1.pdf b/_bookdown_files/Dissertation_Duco_Veen_files/figure-latex/binomUninformative-1.pdf
diff --git a/_bookdown_files/Dissertation_Duco_Veen_files/figure-latex/ch06fig1-1.pdf b/_bookdown_files/Dissertation_Duco_Veen_files/figure-latex/ch06fig1-1.pdf
diff --git a/docs/Burns.html b/docs/Burns.html
@@ -936,7 +936,7 @@ <h3>References</h3>
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diff --git a/docs/DAC1.html b/docs/DAC1.html
@@ -934,7 +934,7 @@ <h3>References</h3>
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diff --git a/docs/Dissertation_Duco_Veen.pdf b/docs/Dissertation_Duco_Veen.pdf
diff --git a/docs/Dissertation_Duco_Veen.tex b/docs/Dissertation_Duco_Veen.tex
diff --git a/docs/Dissertation_Duco_Veen_files/figure-html/binomInf-1.png b/docs/Dissertation_Duco_Veen_files/figure-html/binomInf-1.png
diff --git a/docs/Dissertation_Duco_Veen_files/figure-html/binomUninformative-1.png b/docs/Dissertation_Duco_Veen_files/figure-html/binomUninformative-1.png
diff --git a/docs/Dissertation_Duco_Veen_files/figure-html/ch06fig1-1.png b/docs/Dissertation_Duco_Veen_files/figure-html/ch06fig1-1.png
diff --git a/docs/Hierarchical.html b/docs/Hierarchical.html
@@ -2084,7 +2084,7 @@ <h3>References</h3>
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diff --git a/docs/curriculum-vitae.html b/docs/curriculum-vitae.html
@@ -390,7 +390,7 @@ <h2>Awards</h2>
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diff --git a/docs/dankwoord.html b/docs/dankwoord.html
@@ -335,7 +335,7 @@ <h1>Dankwoord</h1>
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diff --git a/docs/elicitlgm.html b/docs/elicitlgm.html
@@ -290,7 +290,7 @@ <h3><span class="header-section-number">6.2.1</span> Motivating Example</h3>
 <p>The motivating example for this paper is the development of Posttraumatic Stress Symptoms (PTSS) in children after a burn event. In a prospective study on child and parent adjustment after pediatric burns, data on these symptoms were collected in three Dutch and four Belgian burn centers. Children aged 8-18 years old were eligible to participate in the study if they had been hospitalized for more than 24 hours and if the percentage total body surface area (TBSA) burned was at least 1%. In <span class="citation">Egberts et al. (<a href="#ref-egberts_mother_2018" role="doc-biblioref">2018</a>)</span>, a more detailed description of the overall study and sample can be found here. This sample consists of 100 children that reported on their symptoms of traumatic stress within the first month after the burn event (T1), and subsequently at 3 (T2) months post-burn. For the purpose of the current study, we also included the measures obtained 12 months (T3) post-burn. Children filled out the Children’s Responses to Trauma Inventory (CRTI, revised version; <span class="citation">Alisic, Eland, &amp; Kleber (<a href="#ref-alisic_childrens_2006" role="doc-biblioref">2006</a>)</span>). This measure assesses four symptom clusters of posttraumatic stress, including intrusion (e.g., repetitive, intrusive recollections of the trauma), avoidance (e.g., avoiding conversations of the event), arousal (e.g., difficulty concentrating), and other child-specific responses (e.g., feelings of guilt). Further details on this measure can be found in <span class="citation">Alisic, Eland, Huijbregts, &amp; Kleber (<a href="#ref-alisic_manual_2011" role="doc-biblioref">2011</a>)</span>.</p>
 <p>As the current study includes three measurements of PTSS at different time points a straightforward model to analyse the development of PTSS symptoms is an LGM. Figure <a href="elicitlgm.html#fig:ch06fig1">6.1</a> provides a visual representation of an LGM for this motivating example. The model is parameterized such that the latent intercept provides an estimate for PTSS in the first month after the burn event. The latent slope describes the change in PTSS one year post-burn. Parameterizing the slope by year instead of per month is done to ease the reasoning in the elicitation procedure. Furthermore, the scale of the PTSS scores has been standardized for the data of the prospective study and for the elicitation study. The scores can fall between 0-100. A zero score means that none of the symptoms of any of the clusters of posttraumatic stress are present. A score of 100 means that all symptoms from all clusters are present to their maximum extent. A standardized cut-off value of 42 was used to indicate clinical relevance of symptoms and corresponds to the cut-off value provided in the CRTI manual.</p>
 <div class="figure" style="text-align: center"><span id="fig:ch06fig1"></span>
-<img src="_main_files/figure-html/ch06fig1-1.png" alt="Visual representation of a Latent Growth Curve Model with three observed time points for PTSS. " width="50%" />
+<img src="Dissertation_Duco_Veen_files/figure-html/ch06fig1-1.png" alt="Visual representation of a Latent Growth Curve Model with three observed time points for PTSS. " width="50%" />
 <p class="caption">
 Figure 6.1: Visual representation of a Latent Growth Curve Model with three observed time points for PTSS.
 </p>
@@ -724,7 +724,7 @@ <h3>References</h3>
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diff --git a/docs/fivestep.html b/docs/fivestep.html
@@ -958,7 +958,7 @@ <h3>References</h3>
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diff --git a/docs/index.html b/docs/index.html
@@ -279,14 +279,14 @@ <h2><span class="header-section-number">1.1</span> Bayesian Statistics</h2>
 <p>To make this more intuitive I very briefly describe learning via Bayesian statistics. I use the example describing how we could learn about the unknown proportion of a sequence of ‘Bernoulli trials’ that result in either 0 or 1, or in case of a coin, tails (<span class="math inline">\(T\)</span>) for 0 or head (<span class="math inline">\(H\)</span>) for 1. We say that <span class="math inline">\(\theta\)</span> is the proportion of coin flips resulting in heads facing upwards. It turns out that we can use the Beta distribution in a very convenient way to update our beliefs, or state of knowledge, concerning <span class="math inline">\(\theta\)</span>. That is, we can express which values are consistent with both our <em>prior</em> state of knowledge and the newly <em>observed data</em> <span class="citation">(Jaynes, <a href="#ref-jaynes_bayesian_1996" role="doc-biblioref">1996</a>)</span>. The distribution of probability indicates which values are most consistent with both sources. For mathematical details see for instance <span class="citation">Gelman et al. (<a href="#ref-gelman_bayesian_2013" role="doc-biblioref">2013</a> Chapter 2)</span>. The intuition is as follows: the Beta distribution has two parameters, <span class="math inline">\(\alpha\)</span> and <span class="math inline">\(\beta\)</span>, which can be interpreted as follows in our example; there have ‘Bernoulli trials’, and <span class="math inline">\(\alpha - 1\)</span> of them have been a success whilst <span class="math inline">\(\beta - 1\)</span> of them have been a failure. In other words we have observed heads <span class="math inline">\(\alpha - 1\)</span> times and tails <span class="math inline">\(\beta - 1\)</span> times.</p>
 <p>Now let us start with a prior state of ignorance, we have neither observed head nor tails before. We then specify a <span class="math inline">\(Beta(\alpha = 1, \beta = 1)\)</span> <em>prior</em> distribution. It turns out that this neatly coincides with an initial state of ignorance. Every proportion in the interval from 0 up to 1 is assigned equal probability to be the value for <span class="math inline">\(\theta\)</span> based on no initial evidence, see Figure <a href="index.html#fig:binomUninformative">1.1</a> panel A. Now we observe heads four times and tails once (<span class="math inline">\(THHHH\)</span>) in the first five trials and we learn from this data such that we update to a <em>posterior</em> distribution represented by a <span class="math inline">\(Beta(\alpha = 5, \beta = 2)\)</span>, which can be seen in Figure <a href="index.html#fig:binomUninformative">1.1</a> panel B. Before we observe more trials and new data we have an updated state of belief. The <em>posterior</em> distribution can become our new <em>prior</em> distribution, which we, in turn, update with new information to obtain a new posterior distribution. This is what happens in panels C and D of Figure <a href="index.html#fig:binomUninformative">1.1</a> where we in turn observe <span class="math inline">\(HTHHT\)</span> and <span class="math inline">\(THTTH\)</span> to come to a <span class="math inline">\(Beta(\alpha = 8, \beta = 4)\)</span> as a posterior in panel C and a <span class="math inline">\(Beta(\alpha = 10, \beta = 7)\)</span> as posterior in panel D. After 15 trials, and without initial prior knowledge, slightly more heads were observed than tails, thus values just above a proportion of .5 are assigned the largest probability. However, given the few trials that we observed, a wide range of possible values for the proportion of coin flips resulting in heads facing upwards are still assigned probability. Note too, that nowhere do I state which value for <span class="math inline">\(\theta\)</span> I used to simulate these results, for in practice this is unknown and the best we can do is what we just did, use the knowledge available to us to assign probabilities to values for <span class="math inline">\(\theta\)</span>.</p>
 <div class="figure" style="text-align: center"><span id="fig:binomUninformative"></span>
-<img src="_main_files/figure-html/binomUninformative-1.png" alt="Example of Bayesian updating. Panel A shows a $Beta(\alpha = 1, \beta = 1)$ distribution representing a prior state of knowledge equal to ignorance. Panels B, C and D show how the state of knowledge updated after new data is observed, each time the previous panel is the prior belief for the next panel, combined with the information from five new observations." width="672" />
+<img src="Dissertation_Duco_Veen_files/figure-html/binomUninformative-1.png" alt="Example of Bayesian updating. Panel A shows a $Beta(\alpha = 1, \beta = 1)$ distribution representing a prior state of knowledge equal to ignorance. Panels B, C and D show how the state of knowledge updated after new data is observed, each time the previous panel is the prior belief for the next panel, combined with the information from five new observations." width="672" />
 <p class="caption">
 Figure 1.1: Example of Bayesian updating. Panel A shows a <span class="math inline">\(Beta(\alpha = 1, \beta = 1)\)</span> distribution representing a prior state of knowledge equal to ignorance. Panels B, C and D show how the state of knowledge updated after new data is observed, each time the previous panel is the prior belief for the next panel, combined with the information from five new observations.
 </p>
 </div>
 <p>Now, let us suppose that we did not have an initial state of ignorance. The <em>prior</em> need not be ignorance as we noticed when the previous posterior became our new prior each time. Would of belief differ if we had more initial information? Figure <a href="index.html#fig:binomInf">1.2</a> shows learning from the same data as in the example presented in Figure <a href="index.html#fig:binomUninformative">1.1</a> with our initial state of knowledge expressed by a <span class="math inline">\(Beta(\alpha = 51, \beta = 51)\)</span> distribution. In other words, before the new trials we had initial information equivalent to 100 previous coin flips that were distributed equally between head and tails. The new data is very much in line with our previous data and we only slightly adjust our beliefs, assigning even more probability to values near .5.</p>
 <div class="figure" style="text-align: center"><span id="fig:binomInf"></span>
-<img src="_main_files/figure-html/binomInf-1.png" alt="Example of Bayesian updating. Panel A shows a $Beta(\alpha = 51, \beta = 51)$ distribution. This is updated using the same data as in Figure 1.1, only the initial prior contains more information." width="672" />
+<img src="Dissertation_Duco_Veen_files/figure-html/binomInf-1.png" alt="Example of Bayesian updating. Panel A shows a $Beta(\alpha = 51, \beta = 51)$ distribution. This is updated using the same data as in Figure 1.1, only the initial prior contains more information." width="672" />
 <p class="caption">
 Figure 1.2: Example of Bayesian updating. Panel A shows a <span class="math inline">\(Beta(\alpha = 51, \beta = 51)\)</span> distribution. This is updated using the same data as in Figure 1.1, only the initial prior contains more information.
 </p>
@@ -442,7 +442,7 @@ <h3>References</h3>
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diff --git a/docs/nederlandse-samenvatting.html b/docs/nederlandse-samenvatting.html
@@ -343,7 +343,7 @@ <h3>References</h3>
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diff --git a/docs/ref.html b/docs/ref.html
@@ -892,7 +892,7 @@ <h1>References</h1>
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diff --git a/docs/thesisdiscussion.html b/docs/thesisdiscussion.html
@@ -416,7 +416,7 @@ <h3>References</h3>
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diff --git a/index.Rmd b/index.Rmd
@@ -1,7 +1,7 @@
 ---
 author            : "Duco Veen"
 date              : "Department of Methodology & Statistics, Utrecht University"
-title             : "Alternative Information: Bayesian Statistics, Expert Elicitation and Information Theory in the Social Sciences"
+subtitle             : "Alternative Information: Bayesian Statistics, Expert Elicitation and Information Theory in the Social Sciences"
 # header-includes:
 site: bookdown::bookdown_site
 output: