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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
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<title>Modern Sweden Sensitivity</title>
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<div style="width:100%;height:200px;background-image:url('library/header/swed.jpg');background-size:cover;"></div>
<div class="container-fluid main-container"><div class="row"><div class="col-md-4"><a href="index.html"><i class="glyphicon glyphicon-th-list"></i> Back to index</a></div></div></div>
<div class="container-fluid main-container">
<div id="th-century-sweden-sensitivity-analyses" class="section level1 tab-content">
<h1>20th century Sweden sensitivity analyses</h1>
<div id="loading-details" class="section level3 accordion">
<h3>Loading details</h3>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">source</span>(<span class="st">"0__helpers.R"</span>)
opts_chunk$<span class="kw">set</span>(<span class="dt">warning=</span><span class="ot">TRUE</span>, <span class="dt">cache=</span>F,<span class="dt">cache.lazy=</span>F,<span class="dt">tidy=</span><span class="ot">FALSE</span>,<span class="dt">autodep=</span><span class="ot">TRUE</span>,<span class="dt">dev=</span><span class="kw">c</span>(<span class="st">'png'</span>,<span class="st">'pdf'</span>),<span class="dt">fig.width=</span><span class="dv">20</span>,<span class="dt">fig.height=</span><span class="fl">12.5</span>,<span class="dt">out.width=</span><span class="st">'1440px'</span>,<span class="dt">out.height=</span><span class="st">'900px'</span>,<span class="dt">cache.extra=</span><span class="kw">file.info</span>(<span class="st">'swed1.rdata'</span>)[, <span class="st">'mtime'</span>])
make_path =<span class="st"> </span>function(file) {
<span class="kw">get_coefficient_path</span>(file, <span class="st">"swed"</span>)
}
<span class="co"># options for each chunk calling knit_child</span>
opts_chunk$<span class="kw">set</span>(<span class="dt">warning=</span><span class="ot">FALSE</span>, <span class="dt">message =</span> <span class="ot">FALSE</span>, <span class="dt">echo =</span> <span class="ot">FALSE</span>)</code></pre></div>
</div>
<div id="analysis-description" class="section level2">
<h2>Analysis description</h2>
<div id="data-subset" class="section level3">
<h3>Data subset</h3>
<p>The <code>swed_subset_children.1</code> dataset is based on the full dataset of all participants where paternal age is known and birth years are from 1947 to 1959. The subset contains 88707 randomly drawn participants from 56679 families.</p>
</div>
<div id="model-description" class="section level3">
<h3>Model description</h3>
<p>All of the following models are the same as our main model m3, except for the noted changes to test robustness.</p>
</div>
</div>
<div id="s1-mediation-via-age" class="section level2 tab-content">
<h2><em>s1</em>: Mediation via age</h2>
<p>Here, we tested whether the effect on reproductive success is mediated by age (mortality). Unfortunately for the cohort we use for computing an effect on number of children, we have both left and right censoring (because the death register was only established in 1962, so some people may have died before then, and because many people born in 1958 are still alive). So we can only include people who died after their 11th-15th birthday, and have to enter an unknown age for those who have not died before their 51st-63rd birthday.</p>
<div id="model-summary" class="section level3 tab-content">
<h3>Model summary</h3>
<div id="full-summary" class="section level4">
<h4>Full summary</h4>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model_summary =<span class="st"> </span><span class="kw">summary</span>(model, <span class="dt">use_cache =</span> <span class="ot">FALSE</span>, <span class="dt">priors =</span> <span class="ot">TRUE</span>)</code></pre></div>
<pre><code>## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See http://mc-stan.org/misc/
## warnings.html#divergent-transitions-after-warmup</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">print</span>(model_summary)</code></pre></div>
<pre><code>## Family: poisson(log)
## Formula: children ~ paternalage + age + birth_cohort + male + maternalage.factor + paternalage.mean + paternal_loss + maternal_loss + older_siblings + nr.siblings + last_born + (1 | idParents)
## Data: model_data (Number of observations: 127284)
## Samples: 6 chains, each with iter = 1000; warmup = 500; thin = 1;
## total post-warmup samples = 3000
## WAIC: Not computed
##
## Priors:
## b ~ normal(0,5)
## sd ~ student_t(3, 0, 5)
##
## Group-Level Effects:
## ~idParents (Number of levels: 80000)
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sd(Intercept) 0.01 0.01 0 0.02 517 1
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample
## Intercept 0.41 0.02 0.36 0.45 3000
## paternalage -0.05 0.01 -0.08 -0.02 1281
## age5063 0.19 0.02 0.15 0.23 3000
## age025 -2.94 0.14 -3.22 -2.67 3000
## ageunknown 0.34 0.02 0.31 0.37 3000
## birth_cohort1950M1955 -0.01 0.01 -0.02 0.00 3000
## birth_cohort1955M1960 0.00 0.01 -0.01 0.01 3000
## male1 -0.06 0.00 -0.07 -0.05 3000
## maternalage.factor1420 0.07 0.01 0.06 0.09 3000
## maternalage.factor3561 -0.01 0.01 -0.02 0.01 3000
## paternalage.mean 0.00 0.01 -0.02 0.03 1290
## paternal_loss01 0.07 0.22 -0.38 0.47 3000
## paternal_loss15 -0.01 0.06 -0.13 0.10 3000
## paternal_loss510 -0.05 0.03 -0.11 0.01 3000
## paternal_loss1015 -0.02 0.02 -0.06 0.01 3000
## paternal_loss1520 0.00 0.01 -0.02 0.03 3000
## paternal_loss2025 0.00 0.01 -0.03 0.02 3000
## paternal_loss2530 -0.02 0.01 -0.03 0.00 3000
## paternal_loss3035 -0.01 0.01 -0.02 0.01 3000
## paternal_loss3540 -0.01 0.01 -0.02 0.01 3000
## paternal_loss4045 -0.01 0.01 -0.03 0.00 3000
## paternal_lossunclear -0.06 0.01 -0.07 -0.05 3000
## maternal_loss01 -0.19 0.21 -0.61 0.19 3000
## maternal_loss15 -0.03 0.09 -0.22 0.15 3000
## maternal_loss510 0.03 0.04 -0.06 0.11 3000
## maternal_loss1015 -0.01 0.03 -0.07 0.04 3000
## maternal_loss1520 -0.01 0.02 -0.04 0.03 3000
## maternal_loss2025 0.02 0.02 -0.01 0.05 3000
## maternal_loss2530 0.00 0.01 -0.03 0.03 3000
## maternal_loss3035 0.00 0.01 -0.02 0.02 3000
## maternal_loss3540 0.00 0.01 -0.02 0.02 3000
## maternal_loss4045 0.00 0.01 -0.02 0.02 3000
## maternal_lossunclear -0.02 0.01 -0.03 -0.01 3000
## older_siblings1 0.02 0.01 0.00 0.03 1523
## older_siblings2 0.03 0.01 0.00 0.05 1369
## older_siblings3 0.03 0.02 0.00 0.07 1265
## older_siblings4 0.01 0.02 -0.03 0.06 1427
## older_siblings5P -0.06 0.03 -0.12 0.00 1258
## nr.siblings 0.04 0.00 0.03 0.04 1357
## last_born1 0.01 0.00 0.00 0.02 3000
## Rhat
## Intercept 1
## paternalage 1
## age5063 1
## age025 1
## ageunknown 1
## birth_cohort1950M1955 1
## birth_cohort1955M1960 1
## male1 1
## maternalage.factor1420 1
## maternalage.factor3561 1
## paternalage.mean 1
## paternal_loss01 1
## paternal_loss15 1
## paternal_loss510 1
## paternal_loss1015 1
## paternal_loss1520 1
## paternal_loss2025 1
## paternal_loss2530 1
## paternal_loss3035 1
## paternal_loss3540 1
## paternal_loss4045 1
## paternal_lossunclear 1
## maternal_loss01 1
## maternal_loss15 1
## maternal_loss510 1
## maternal_loss1015 1
## maternal_loss1520 1
## maternal_loss2025 1
## maternal_loss2530 1
## maternal_loss3035 1
## maternal_loss3540 1
## maternal_loss4045 1
## maternal_lossunclear 1
## older_siblings1 1
## older_siblings2 1
## older_siblings3 1
## older_siblings4 1
## older_siblings5P 1
## nr.siblings 1
## last_born1 1
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).</code></pre>
</div>
<div id="table-of-fixed-effects" class="section level4">
<h4>Table of fixed effects</h4>
<p>Estimates are <code>exp(b)</code>. When they are referring to the hurdle (hu) component, or a dichotomous outcome, they are odds ratios, when they are referring to a Poisson component, they are hazard ratios. In both cases, they are presented with 95% credibility intervals. To see the effects on the response scale (probability or number of children), consult the marginal effect plots.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">fixed_eff =<span class="st"> </span><span class="kw">data.frame</span>(model_summary$fixed, <span class="dt">check.names =</span> F)
fixed_eff$Est.Error =<span class="st"> </span>fixed_eff$Eff.Sample =<span class="st"> </span>fixed_eff$Rhat =<span class="st"> </span><span class="ot">NULL</span>
fixed_eff$<span class="st">`</span><span class="dt">Odds/hazard ratio</span><span class="st">`</span> =<span class="st"> </span><span class="kw">exp</span>(fixed_eff$Estimate)
fixed_eff$<span class="st">`</span><span class="dt">OR/HR low 95%</span><span class="st">`</span> =<span class="st"> </span><span class="kw">exp</span>(fixed_eff$<span class="st">`</span><span class="dt">l-95% CI</span><span class="st">`</span>)
fixed_eff$<span class="st">`</span><span class="dt">OR/HR high 95%</span><span class="st">`</span> =<span class="st"> </span><span class="kw">exp</span>(fixed_eff$<span class="st">`</span><span class="dt">u-95% CI</span><span class="st">`</span>)
fixed_eff =<span class="st"> </span>fixed_eff %>%<span class="st"> </span><span class="kw">select</span>(<span class="st">`</span><span class="dt">Odds/hazard ratio</span><span class="st">`</span>, <span class="st">`</span><span class="dt">OR/HR low 95%</span><span class="st">`</span>, <span class="st">`</span><span class="dt">OR/HR high 95%</span><span class="st">`</span>)
pander::<span class="kw">pander</span>(fixed_eff)</code></pre></div>
<table>
<colgroup>
<col width="35%" />
<col width="24%" />
<col width="19%" />
<col width="19%" />
</colgroup>
<thead>
<tr class="header">
<th align="center"> </th>
<th align="center">Odds/hazard ratio</th>
<th align="center">OR/HR low 95%</th>
<th align="center">OR/HR high 95%</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center"><strong>Intercept</strong></td>
<td align="center">1.5</td>
<td align="center">1.439</td>
<td align="center">1.562</td>
</tr>
<tr class="even">
<td align="center"><strong>paternalage</strong></td>
<td align="center">0.9516</td>
<td align="center">0.926</td>
<td align="center">0.9772</td>
</tr>
<tr class="odd">
<td align="center"><strong>age5063</strong></td>
<td align="center">1.212</td>
<td align="center">1.164</td>
<td align="center">1.263</td>
</tr>
<tr class="even">
<td align="center"><strong>age025</strong></td>
<td align="center">0.05311</td>
<td align="center">0.04001</td>
<td align="center">0.06917</td>
</tr>
<tr class="odd">
<td align="center"><strong>ageunknown</strong></td>
<td align="center">1.409</td>
<td align="center">1.367</td>
<td align="center">1.454</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1950M1955</strong></td>
<td align="center">0.9936</td>
<td align="center">0.9829</td>
<td align="center">1.004</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1955M1960</strong></td>
<td align="center">0.9969</td>
<td align="center">0.9858</td>
<td align="center">1.008</td>
</tr>
<tr class="even">
<td align="center"><strong>male1</strong></td>
<td align="center">0.9444</td>
<td align="center">0.9369</td>
<td align="center">0.952</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternalage.factor1420</strong></td>
<td align="center">1.074</td>
<td align="center">1.058</td>
<td align="center">1.09</td>
</tr>
<tr class="even">
<td align="center"><strong>maternalage.factor3561</strong></td>
<td align="center">0.9922</td>
<td align="center">0.9775</td>
<td align="center">1.007</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternalage.mean</strong></td>
<td align="center">1.003</td>
<td align="center">0.9757</td>
<td align="center">1.03</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss01</strong></td>
<td align="center">1.075</td>
<td align="center">0.6867</td>
<td align="center">1.603</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss15</strong></td>
<td align="center">0.9884</td>
<td align="center">0.8753</td>
<td align="center">1.111</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss510</strong></td>
<td align="center">0.9528</td>
<td align="center">0.8998</td>
<td align="center">1.009</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss1015</strong></td>
<td align="center">0.979</td>
<td align="center">0.9454</td>
<td align="center">1.014</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss1520</strong></td>
<td align="center">1.003</td>
<td align="center">0.9761</td>
<td align="center">1.031</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss2025</strong></td>
<td align="center">0.9959</td>
<td align="center">0.9753</td>
<td align="center">1.017</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss2530</strong></td>
<td align="center">0.9848</td>
<td align="center">0.9672</td>
<td align="center">1.003</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss3035</strong></td>
<td align="center">0.9933</td>
<td align="center">0.9766</td>
<td align="center">1.009</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss3540</strong></td>
<td align="center">0.9933</td>
<td align="center">0.9787</td>
<td align="center">1.008</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss4045</strong></td>
<td align="center">0.9883</td>
<td align="center">0.9735</td>
<td align="center">1.003</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_lossunclear</strong></td>
<td align="center">0.9443</td>
<td align="center">0.9337</td>
<td align="center">0.9552</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss01</strong></td>
<td align="center">0.829</td>
<td align="center">0.5418</td>
<td align="center">1.208</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss15</strong></td>
<td align="center">0.9694</td>
<td align="center">0.8032</td>
<td align="center">1.164</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss510</strong></td>
<td align="center">1.029</td>
<td align="center">0.9465</td>
<td align="center">1.114</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss1015</strong></td>
<td align="center">0.9861</td>
<td align="center">0.9352</td>
<td align="center">1.042</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss1520</strong></td>
<td align="center">0.9948</td>
<td align="center">0.9573</td>
<td align="center">1.032</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss2025</strong></td>
<td align="center">1.023</td>
<td align="center">0.99</td>
<td align="center">1.056</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss2530</strong></td>
<td align="center">1</td>
<td align="center">0.9727</td>
<td align="center">1.029</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss3035</strong></td>
<td align="center">1</td>
<td align="center">0.9763</td>
<td align="center">1.025</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss3540</strong></td>
<td align="center">1.003</td>
<td align="center">0.9842</td>
<td align="center">1.023</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss4045</strong></td>
<td align="center">0.9963</td>
<td align="center">0.9778</td>
<td align="center">1.016</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_lossunclear</strong></td>
<td align="center">0.9789</td>
<td align="center">0.9687</td>
<td align="center">0.9887</td>
</tr>
<tr class="even">
<td align="center"><strong>older_siblings1</strong></td>
<td align="center">1.017</td>
<td align="center">1.003</td>
<td align="center">1.03</td>
</tr>
<tr class="odd">
<td align="center"><strong>older_siblings2</strong></td>
<td align="center">1.026</td>
<td align="center">1.003</td>
<td align="center">1.049</td>
</tr>
<tr class="even">
<td align="center"><strong>older_siblings3</strong></td>
<td align="center">1.034</td>
<td align="center">1.001</td>
<td align="center">1.07</td>
</tr>
<tr class="odd">
<td align="center"><strong>older_siblings4</strong></td>
<td align="center">1.011</td>
<td align="center">0.968</td>
<td align="center">1.058</td>
</tr>
<tr class="even">
<td align="center"><strong>older_siblings5P</strong></td>
<td align="center">0.9442</td>
<td align="center">0.8909</td>
<td align="center">0.9997</td>
</tr>
<tr class="odd">
<td align="center"><strong>nr.siblings</strong></td>
<td align="center">1.04</td>
<td align="center">1.035</td>
<td align="center">1.046</td>
</tr>
<tr class="even">
<td align="center"><strong>last_born1</strong></td>
<td align="center">1.01</td>
<td align="center">1.001</td>
<td align="center">1.019</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="paternal-age-effect" class="section level3">
<h3>Paternal age effect</h3>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">pander::<span class="kw">pander</span>(<span class="kw">paternal_age_10y_effect</span>(model))</code></pre></div>
<table style="width:89%;">
<colgroup>
<col width="27%" />
<col width="25%" />
<col width="18%" />
<col width="18%" />
</colgroup>
<thead>
<tr class="header">
<th align="center">effect</th>
<th align="center">median_estimate</th>
<th align="center">ci_95</th>
<th align="center">ci_80</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center">estimate father 25y</td>
<td align="center">1.39</td>
<td align="center">[1.34;1.44]</td>
<td align="center">[1.36;1.42]</td>
</tr>
<tr class="even">
<td align="center">estimate father 35y</td>
<td align="center">1.32</td>
<td align="center">[1.28;1.37]</td>
<td align="center">[1.29;1.35]</td>
</tr>
<tr class="odd">
<td align="center">percentage change</td>
<td align="center">-4.87</td>
<td align="center">[-7.4;-2.28]</td>
<td align="center">[-6.48;-3.13]</td>
</tr>
<tr class="even">
<td align="center">OR/IRR</td>
<td align="center">0.95</td>
<td align="center">[0.93;0.98]</td>
<td align="center">[0.94;0.97]</td>
</tr>
</tbody>
</table>
</div>
<div id="marginal-effect-plots" class="section level3">
<h3>Marginal effect plots</h3>
<p>In these marginal effect plots, we set all predictors except the one shown on the X axis to their mean and in the case of factors to their reference level. We then plot the estimated association between the X axis predictor and the outcome on the response scale (e.g. probability of survival/marriage or number of children).</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot.brmsMarginalEffects_shades</span>(
<span class="dt">x =</span> <span class="kw">marginal_effects</span>(model, <span class="dt">re_formula =</span> <span class="ot">NA</span>, <span class="dt">probs =</span> <span class="kw">c</span>(<span class="fl">0.025</span>,<span class="fl">0.975</span>)),
<span class="dt">y =</span> <span class="kw">marginal_effects</span>(model, <span class="dt">re_formula =</span> <span class="ot">NA</span>, <span class="dt">probs =</span> <span class="kw">c</span>(<span class="fl">0.1</span>,<span class="fl">0.9</span>)),
<span class="dt">ask =</span> <span class="ot">FALSE</span>)</code></pre></div>
<p><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-1.png" width="1440px" height="900px" /><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-2.png" width="1440px" height="900px" /><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-3.png" width="1440px" height="900px" /><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-4.png" width="1440px" height="900px" /><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-5.png" width="1440px" height="900px" /><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-6.png" width="1440px" height="900px" /><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-7.png" width="1440px" height="900px" /><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-8.png" width="1440px" height="900px" /><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-9.png" width="1440px" height="900px" /><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-10.png" width="1440px" height="900px" /><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-7-11.png" width="1440px" height="900px" /></p>
</div>
<div id="coefficient-plot" class="section level3">
<h3>Coefficient plot</h3>
<p>Here, we plotted the 95% posterior densities for the unexponentiated model coefficients (<code>b_</code>). The darkly shaded area represents the 50% credibility interval, the dark line represent the posterior mean estimate.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">mcmc_areas</span>(<span class="kw">as.matrix</span>(model$fit), <span class="dt">regex_pars =</span> <span class="st">"b_[^I]"</span>, <span class="dt">point_est =</span> <span class="st">"mean"</span>, <span class="dt">prob =</span> <span class="fl">0.50</span>, <span class="dt">prob_outer =</span> <span class="fl">0.95</span>) +<span class="st"> </span><span class="kw">ggtitle</span>(<span class="st">"Posterior densities with means and 50% intervals"</span>) +<span class="st"> </span>analysis_theme +<span class="st"> </span><span class="kw">theme</span>(<span class="dt">axis.text =</span> <span class="kw">element_text</span>(<span class="dt">size =</span> <span class="dv">12</span>), <span class="dt">panel.grid =</span> <span class="kw">element_blank</span>()) +<span class="st"> </span><span class="kw">xlab</span>(<span class="st">"Coefficient size"</span>)</code></pre></div>
<p><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-8-1.png" width="1440px" height="900px" /></p>
</div>
<div id="diagnostics" class="section level3 tab-content">
<h3>Diagnostics</h3>
<p>These plots were made to diagnose misfit and nonconvergence.</p>
<div id="posterior-predictive-checks" class="section level4">
<h4>Posterior predictive checks</h4>
<p>In posterior predictive checks, we test whether we can approximately reproduce the real data distribution from our model.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">brms::<span class="kw">pp_check</span>(model, <span class="dt">re_formula =</span> <span class="ot">NA</span>, <span class="dt">type =</span> <span class="st">"dens_overlay"</span>)</code></pre></div>
<p><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-9-1.png" width="1440px" height="900px" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">brms::<span class="kw">pp_check</span>(model, <span class="dt">re_formula =</span> <span class="ot">NA</span>, <span class="dt">type =</span> <span class="st">"hist"</span>)</code></pre></div>
<p><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-9-2.png" width="1440px" height="900px" /></p>
</div>
<div id="rhat" class="section level4">
<h4>Rhat</h4>
<p>Did the 6 chains converge?</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">stanplot</span>(model, <span class="dt">pars =</span> <span class="st">"^b_[^I]"</span>, <span class="dt">type =</span> <span class="st">'rhat'</span>)</code></pre></div>
<p><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-10-1.png" width="1440px" height="900px" /></p>
</div>
<div id="effective-sample-size-over-average-sample-size" class="section level4">
<h4>Effective sample size over average sample size</h4>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">stanplot</span>(model, <span class="dt">pars =</span> <span class="st">"^b"</span>, <span class="dt">type =</span> <span class="st">'neff_hist'</span>)</code></pre></div>
<p><img src="6_swed_sensitivity_files/figure-html/unnamed-chunk-11-1.png" width="1440px" height="900px" /></p>
</div>
<div id="trace-plots" class="section level4">
<h4>Trace plots</h4>
<p>Trace plots are only shown in the case of nonconvergence.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">if(<span class="kw">any</span>( <span class="kw">summary</span>(model)$fixed[,<span class="st">"Rhat"</span>] ><span class="st"> </span><span class="fl">1.1</span>)) { <span class="co"># only do traceplots if not converged</span>
<span class="kw">plot</span>(model, <span class="dt">N =</span> <span class="dv">3</span>, <span class="dt">ask =</span> <span class="ot">FALSE</span>)
}</code></pre></div>
</div>
<div id="filecluster-script-name" class="section level4">
<h4>File/cluster script name</h4>
<p>This model was stored in the file: coefs/swed/s1_control_age.rds.</p>
<p>Click the following link to see the script used to generate this model:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opts_chunk$<span class="kw">set</span>(<span class="dt">echo =</span> <span class="ot">FALSE</span>)
clusterscript =<span class="st"> </span><span class="kw">str_replace</span>(<span class="kw">basename</span>(model_filename), <span class="st">"</span><span class="ch">\\</span><span class="st">.rds"</span>,<span class="st">".html"</span>)
<span class="kw">cat</span>(<span class="st">"[Cluster script]("</span> , clusterscript, <span class="st">")"</span>, <span class="dt">sep =</span> <span class="st">""</span>)</code></pre></div>
<p><a href="s1_control_age.html">Cluster script</a></p>
</div>
</div>
</div>
<div id="s2-mediation-via-reproductive-timing" class="section level2 tab-content">
<h2><em>s2</em>: Mediation via reproductive timing</h2>
<p>Here, we tested whether the paternal age effect on reproductive succes is mediated by reproductive timing (as indexed by anchors’ ages at first and last birth). Because age at first and last birth are by definition only available for anchors who had at least one child, this analysis has to be restricted to such anchors. Hence, paternal age effects on mortality until age 1 and 15 cannot, in principle, be mediated by reproductive timing of the anchors.</p>
<div id="model-summary-1" class="section level3 tab-content">
<h3>Model summary</h3>
<div id="full-summary-1" class="section level4">
<h4>Full summary</h4>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model_summary =<span class="st"> </span><span class="kw">summary</span>(model, <span class="dt">use_cache =</span> <span class="ot">FALSE</span>, <span class="dt">priors =</span> <span class="ot">TRUE</span>)
<span class="kw">print</span>(model_summary)</code></pre></div>
<pre><code>## Family: poisson(log)
## Formula: children ~ paternalage + age_at_1st_child + age_at_last_child + birth_cohort + male + maternalage.factor + paternalage.mean + paternal_loss + maternal_loss + older_siblings + nr.siblings + last_born + (1 | idParents)
## Data: model_data (Number of observations: 101944)
## Samples: 6 chains, each with iter = 800; warmup = 300; thin = 1;
## total post-warmup samples = 3000
## WAIC: Not computed
##
## Priors:
## b ~ normal(0,5)
## sd ~ student_t(3, 0, 5)
##
## Group-Level Effects:
## ~idParents (Number of levels: 68647)
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sd(Intercept) 0 0 0 0.01 3000 1
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample
## Intercept 0.47 0.02 0.44 0.51 3000
## paternalage 0.00 0.01 -0.03 0.02 1003
## age_at_1st_child -0.54 0.00 -0.55 -0.53 3000
## age_at_last_child 0.51 0.00 0.51 0.52 3000
## birth_cohort1950M1955 0.02 0.01 0.01 0.03 3000
## birth_cohort1955M1960 0.06 0.01 0.05 0.07 3000
## male1 0.00 0.00 -0.01 0.01 3000
## maternalage.factor1420 -0.01 0.01 -0.03 0.00 3000
## maternalage.factor3561 0.01 0.01 0.00 0.02 3000
## paternalage.mean 0.02 0.01 0.00 0.05 992
## paternal_loss01 -0.14 0.21 -0.56 0.26 3000
## paternal_loss15 -0.03 0.06 -0.15 0.09 3000
## paternal_loss510 -0.02 0.03 -0.08 0.04 3000
## paternal_loss1015 -0.02 0.02 -0.05 0.02 3000
## paternal_loss1520 -0.02 0.01 -0.05 0.01 3000
## paternal_loss2025 -0.02 0.01 -0.04 0.00 3000
## paternal_loss2530 -0.01 0.01 -0.03 0.00 3000
## paternal_loss3035 -0.01 0.01 -0.03 0.01 3000
## paternal_loss3540 -0.01 0.01 -0.03 0.00 3000
## paternal_loss4045 -0.01 0.01 -0.02 0.01 3000
## paternal_lossunclear 0.01 0.01 0.00 0.02 3000
## maternal_loss01 -0.06 0.22 -0.52 0.36 3000
## maternal_loss15 0.02 0.10 -0.17 0.20 3000
## maternal_loss510 0.01 0.04 -0.07 0.09 3000
## maternal_loss1015 0.00 0.03 -0.05 0.06 3000
## maternal_loss1520 -0.01 0.02 -0.05 0.03 3000
## maternal_loss2025 0.00 0.02 -0.04 0.03 3000
## maternal_loss2530 -0.01 0.01 -0.03 0.02 3000
## maternal_loss3035 0.00 0.01 -0.02 0.03 3000
## maternal_loss3540 -0.01 0.01 -0.03 0.01 3000
## maternal_loss4045 0.00 0.01 -0.02 0.01 3000
## maternal_lossunclear 0.01 0.01 0.00 0.02 3000
## older_siblings1 0.00 0.01 -0.01 0.01 1188
## older_siblings2 0.00 0.01 -0.02 0.02 1113
## older_siblings3 0.00 0.02 -0.03 0.03 913
## older_siblings4 -0.01 0.02 -0.06 0.03 1258
## older_siblings5P -0.03 0.03 -0.09 0.02 1110
## nr.siblings 0.01 0.00 0.00 0.02 1180
## last_born1 0.00 0.00 -0.01 0.01 3000
## Rhat
## Intercept 1
## paternalage 1
## age_at_1st_child 1
## age_at_last_child 1
## birth_cohort1950M1955 1
## birth_cohort1955M1960 1
## male1 1
## maternalage.factor1420 1
## maternalage.factor3561 1
## paternalage.mean 1
## paternal_loss01 1
## paternal_loss15 1
## paternal_loss510 1
## paternal_loss1015 1
## paternal_loss1520 1
## paternal_loss2025 1
## paternal_loss2530 1
## paternal_loss3035 1
## paternal_loss3540 1
## paternal_loss4045 1
## paternal_lossunclear 1
## maternal_loss01 1
## maternal_loss15 1
## maternal_loss510 1
## maternal_loss1015 1
## maternal_loss1520 1
## maternal_loss2025 1
## maternal_loss2530 1
## maternal_loss3035 1
## maternal_loss3540 1
## maternal_loss4045 1
## maternal_lossunclear 1
## older_siblings1 1
## older_siblings2 1
## older_siblings3 1
## older_siblings4 1
## older_siblings5P 1
## nr.siblings 1
## last_born1 1
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).</code></pre>
</div>
<div id="table-of-fixed-effects-1" class="section level4">
<h4>Table of fixed effects</h4>
<p>Estimates are <code>exp(b)</code>. When they are referring to the hurdle (hu) component, or a dichotomous outcome, they are odds ratios, when they are referring to a Poisson component, they are hazard ratios. In both cases, they are presented with 95% credibility intervals. To see the effects on the response scale (probability or number of children), consult the marginal effect plots.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">fixed_eff =<span class="st"> </span><span class="kw">data.frame</span>(model_summary$fixed, <span class="dt">check.names =</span> F)
fixed_eff$Est.Error =<span class="st"> </span>fixed_eff$Eff.Sample =<span class="st"> </span>fixed_eff$Rhat =<span class="st"> </span><span class="ot">NULL</span>
fixed_eff$<span class="st">`</span><span class="dt">Odds/hazard ratio</span><span class="st">`</span> =<span class="st"> </span><span class="kw">exp</span>(fixed_eff$Estimate)
fixed_eff$<span class="st">`</span><span class="dt">OR/HR low 95%</span><span class="st">`</span> =<span class="st"> </span><span class="kw">exp</span>(fixed_eff$<span class="st">`</span><span class="dt">l-95% CI</span><span class="st">`</span>)
fixed_eff$<span class="st">`</span><span class="dt">OR/HR high 95%</span><span class="st">`</span> =<span class="st"> </span><span class="kw">exp</span>(fixed_eff$<span class="st">`</span><span class="dt">u-95% CI</span><span class="st">`</span>)
fixed_eff =<span class="st"> </span>fixed_eff %>%<span class="st"> </span><span class="kw">select</span>(<span class="st">`</span><span class="dt">Odds/hazard ratio</span><span class="st">`</span>, <span class="st">`</span><span class="dt">OR/HR low 95%</span><span class="st">`</span>, <span class="st">`</span><span class="dt">OR/HR high 95%</span><span class="st">`</span>)
pander::<span class="kw">pander</span>(fixed_eff)</code></pre></div>
<table>
<colgroup>
<col width="35%" />
<col width="24%" />
<col width="19%" />
<col width="19%" />
</colgroup>
<thead>
<tr class="header">
<th align="center"> </th>
<th align="center">Odds/hazard ratio</th>
<th align="center">OR/HR low 95%</th>
<th align="center">OR/HR high 95%</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center"><strong>Intercept</strong></td>
<td align="center">1.607</td>
<td align="center">1.549</td>
<td align="center">1.666</td>
</tr>
<tr class="even">
<td align="center"><strong>paternalage</strong></td>
<td align="center">0.9963</td>
<td align="center">0.9703</td>
<td align="center">1.023</td>
</tr>
<tr class="odd">
<td align="center"><strong>age_at_1st_child</strong></td>
<td align="center">0.5841</td>
<td align="center">0.5791</td>
<td align="center">0.5893</td>
</tr>
<tr class="even">
<td align="center"><strong>age_at_last_child</strong></td>
<td align="center">1.669</td>
<td align="center">1.658</td>
<td align="center">1.681</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1950M1955</strong></td>
<td align="center">1.021</td>
<td align="center">1.01</td>
<td align="center">1.032</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1955M1960</strong></td>
<td align="center">1.065</td>
<td align="center">1.053</td>
<td align="center">1.077</td>
</tr>
<tr class="odd">
<td align="center"><strong>male1</strong></td>
<td align="center">1</td>
<td align="center">0.9921</td>
<td align="center">1.009</td>
</tr>
<tr class="even">
<td align="center"><strong>maternalage.factor1420</strong></td>
<td align="center">0.9871</td>
<td align="center">0.9716</td>
<td align="center">1.002</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternalage.factor3561</strong></td>
<td align="center">1.01</td>
<td align="center">0.9954</td>
<td align="center">1.024</td>
</tr>
<tr class="even">
<td align="center"><strong>paternalage.mean</strong></td>
<td align="center">1.023</td>
<td align="center">0.9964</td>
<td align="center">1.051</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss01</strong></td>
<td align="center">0.8711</td>
<td align="center">0.5735</td>
<td align="center">1.291</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss15</strong></td>
<td align="center">0.9709</td>
<td align="center">0.8604</td>
<td align="center">1.09</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss510</strong></td>
<td align="center">0.9806</td>
<td align="center">0.9247</td>
<td align="center">1.037</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss1015</strong></td>
<td align="center">0.9847</td>
<td align="center">0.9511</td>
<td align="center">1.02</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss1520</strong></td>
<td align="center">0.9804</td>
<td align="center">0.9557</td>
<td align="center">1.007</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss2025</strong></td>
<td align="center">0.9778</td>
<td align="center">0.9578</td>
<td align="center">0.9983</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss2530</strong></td>
<td align="center">0.9852</td>
<td align="center">0.9684</td>
<td align="center">1.003</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss3035</strong></td>
<td align="center">0.9898</td>
<td align="center">0.9738</td>
<td align="center">1.006</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss3540</strong></td>
<td align="center">0.9897</td>
<td align="center">0.9751</td>
<td align="center">1.005</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss4045</strong></td>
<td align="center">0.9915</td>
<td align="center">0.9762</td>
<td align="center">1.006</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_lossunclear</strong></td>
<td align="center">1.009</td>
<td align="center">0.9981</td>
<td align="center">1.02</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss01</strong></td>
<td align="center">0.9444</td>
<td align="center">0.5949</td>
<td align="center">1.429</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss15</strong></td>
<td align="center">1.022</td>
<td align="center">0.8448</td>
<td align="center">1.227</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss510</strong></td>
<td align="center">1.012</td>
<td align="center">0.93</td>
<td align="center">1.096</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss1015</strong></td>
<td align="center">1.003</td>
<td align="center">0.9495</td>
<td align="center">1.059</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss1520</strong></td>
<td align="center">0.9896</td>
<td align="center">0.9518</td>
<td align="center">1.028</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss2025</strong></td>
<td align="center">0.9951</td>
<td align="center">0.9646</td>
<td align="center">1.027</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss2530</strong></td>
<td align="center">0.9931</td>
<td align="center">0.9661</td>
<td align="center">1.02</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss3035</strong></td>
<td align="center">1.003</td>
<td align="center">0.9799</td>
<td align="center">1.027</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss3540</strong></td>
<td align="center">0.9902</td>
<td align="center">0.971</td>
<td align="center">1.01</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss4045</strong></td>
<td align="center">0.9954</td>
<td align="center">0.977</td>
<td align="center">1.015</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_lossunclear</strong></td>
<td align="center">1.006</td>
<td align="center">0.9959</td>
<td align="center">1.016</td>
</tr>
<tr class="odd">
<td align="center"><strong>older_siblings1</strong></td>
<td align="center">1.001</td>
<td align="center">0.9876</td>
<td align="center">1.015</td>
</tr>
<tr class="even">
<td align="center"><strong>older_siblings2</strong></td>
<td align="center">0.9997</td>
<td align="center">0.9772</td>
<td align="center">1.023</td>
</tr>
<tr class="odd">
<td align="center"><strong>older_siblings3</strong></td>
<td align="center">0.9999</td>
<td align="center">0.9666</td>
<td align="center">1.033</td>
</tr>
<tr class="even">
<td align="center"><strong>older_siblings4</strong></td>
<td align="center">0.9895</td>
<td align="center">0.9457</td>
<td align="center">1.034</td>
</tr>
<tr class="odd">
<td align="center"><strong>older_siblings5P</strong></td>
<td align="center">0.9688</td>
<td align="center">0.9144</td>
<td align="center">1.024</td>
</tr>
<tr class="even">
<td align="center"><strong>nr.siblings</strong></td>
<td align="center">1.01</td>
<td align="center">1.005</td>
<td align="center">1.015</td>
</tr>
<tr class="odd">
<td align="center"><strong>last_born1</strong></td>
<td align="center">1.003</td>
<td align="center">0.9942</td>
<td align="center">1.013</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="paternal-age-effect-1" class="section level3">
<h3>Paternal age effect</h3>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">pander::<span class="kw">pander</span>(<span class="kw">paternal_age_10y_effect</span>(model))</code></pre></div>
<table style="width:89%;">
<colgroup>
<col width="27%" />
<col width="25%" />
<col width="18%" />
<col width="18%" />
</colgroup>
<thead>
<tr class="header">
<th align="center">effect</th>
<th align="center">median_estimate</th>
<th align="center">ci_95</th>
<th align="center">ci_80</th>
</tr>