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<!DOCTYPE html>
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<title>Québec Selective Episodes</title>
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<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>
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<div id="quebec-registre-de-la-population-du-quebec-ancien-1630-1750-selective-episodes" class="section level1 tab-content">
<h1>Québec (Registre de la Population du Québec Ancien 1630-1750), selective episodes</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$<span class="kw">set</span>(<span class="dt">warning=</span><span class="ot">TRUE</span>, <span class="dt">cache =</span> <span class="ot">FALSE</span>,<span class="dt">tidy=</span><span class="ot">FALSE</span>,<span class="dt">dev=</span><span class="kw">c</span>(<span class="st">'png'</span>),<span class="dt">fig.width=</span><span class="dv">20</span>,<span class="dt">fig.height=</span><span class="fl">12.5</span>)
make_path =<span class="st"> </span>function(file) {
<span class="kw">get_coefficient_path</span>(file, <span class="st">"rpqa"</span>)
}
<span class="co"># options for each chunk calling knit_child</span>
opts_chunk$<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>rpqa.1</code> dataset contains only those participants where paternal age is known and the birthdate is between 1630 and 1750.</p>
</div>
<div id="model-description" class="section level3">
<h3>Model description</h3>
<p>All of the following models have the following in common:</p>
<div id="estimation" class="section level4">
<h4>Estimation</h4>
<p>We fit all models using <code>brms</code> v. 1.2.0, a Bayesian regression analysis statistical package. <code>brms</code> uses <code>Stan</code>, a probabilistic programming langugage to fit models using Hamiltonian Monte Carlo.</p>
</div>
<div id="covariates" class="section level4">
<h4>Covariates</h4>
<p>As in our main models we adjust for average paternal age in the family, birth cohort (birth years in five equally large bins), for male sex, for age at paternal and maternal loss (0-1, 2-5, 6-10, …, 41-45, 45+, unknown), for maternal age (bins of 14-20, 20-35 and 35-50), for the number of siblings, for the number of older siblings (0-5, 5+) and for being last born.</p>
</div>
<div id="model-stratification" class="section level4">
<h4>Model stratification</h4>
<p>We added random intercepts for each family (father-mother dyad). We then controlled for the average paternal age in the family. Hence, the paternal age effects in the plot are split into those between families and those within families or between siblings. We are interested in the effect of paternal age between siblings, as this effect cannot be explained by e.g. genetic propensities of the father to reproduce late.</p>
</div>
</div>
</div>
<div id="e1_survive1y" class="section level2 tab-content">
<h2><em>e1</em>: Survival to first year</h2>
<p>Here, we predict the probability that the anchor survives the first year of life. All children born to this father are compared, if their death date is known or their survival can be inferred (from later marriage or children).</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>)
<span class="kw">print</span>(model_summary)</code></pre></div>
<pre><code>## Family: bernoulli(cauchit)
## Formula: survive1y ~ paternalage + 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: 61493)
## 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: 11940)
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sd(Intercept) 1.06 0.03 1 1.12 623 1
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample
## Intercept 3.74 0.25 3.26 4.25 398
## paternalage -0.44 0.07 -0.58 -0.31 789
## birth_cohort1675M1680 0.20 0.30 -0.37 0.77 627
## birth_cohort1680M1685 -0.57 0.24 -1.07 -0.08 435
## birth_cohort1685M1690 -1.46 0.22 -1.90 -1.04 349
## birth_cohort1690M1695 -0.84 0.22 -1.29 -0.40 366
## birth_cohort1695M1700 -0.83 0.22 -1.27 -0.42 349
## birth_cohort1700M1705 -1.30 0.21 -1.75 -0.89 320
## birth_cohort1705M1710 -0.78 0.22 -1.22 -0.36 349
## birth_cohort1710M1715 -1.43 0.21 -1.87 -1.03 317
## birth_cohort1715M1720 -1.29 0.21 -1.71 -0.89 315
## birth_cohort1720M1725 -1.28 0.21 -1.71 -0.90 314
## birth_cohort1725M1730 -1.65 0.20 -2.07 -1.26 309
## birth_cohort1730M1735 -1.87 0.20 -2.28 -1.47 201
## birth_cohort1735M1740 -1.67 0.20 -2.09 -1.28 312
## male1 -0.42 0.03 -0.49 -0.36 3000
## maternalage.factor1420 -0.18 0.07 -0.32 -0.04 2048
## maternalage.factor3550 -0.09 0.06 -0.19 0.02 1510
## paternalage.mean 0.54 0.07 0.40 0.69 856
## paternal_loss01 -1.02 0.11 -1.24 -0.79 1413
## paternal_loss15 -0.47 0.10 -0.67 -0.28 1287
## paternal_loss510 -0.35 0.09 -0.53 -0.18 1164
## paternal_loss1015 -0.23 0.08 -0.39 -0.06 1142
## paternal_loss1520 -0.33 0.08 -0.47 -0.18 1045
## paternal_loss2025 -0.16 0.07 -0.30 -0.01 1055
## paternal_loss2530 -0.25 0.07 -0.38 -0.11 1119
## paternal_loss3035 -0.18 0.07 -0.32 -0.05 1131
## paternal_loss3540 -0.16 0.07 -0.29 -0.03 1195
## paternal_loss4045 -0.03 0.08 -0.18 0.12 1565
## paternal_lossunclear -0.36 0.08 -0.50 -0.21 1140
## maternal_loss01 -2.20 0.10 -2.41 -2.00 996
## maternal_loss15 -0.70 0.09 -0.87 -0.53 994
## maternal_loss510 -0.44 0.08 -0.60 -0.28 1063
## maternal_loss1015 -0.41 0.08 -0.56 -0.25 1092
## maternal_loss1520 -0.39 0.08 -0.53 -0.23 1326
## maternal_loss2025 -0.27 0.08 -0.42 -0.12 1145
## maternal_loss2530 -0.17 0.07 -0.31 -0.03 1188
## maternal_loss3035 -0.21 0.07 -0.34 -0.08 1007
## maternal_loss3540 -0.24 0.06 -0.36 -0.12 1219
## maternal_loss4045 -0.03 0.07 -0.16 0.11 1549
## maternal_lossunclear -0.27 0.08 -0.42 -0.13 1348
## older_siblings1 0.45 0.06 0.33 0.56 1665
## older_siblings2 0.54 0.06 0.42 0.66 1354
## older_siblings3 0.79 0.07 0.65 0.94 1186
## older_siblings4 0.83 0.08 0.68 0.98 1071
## older_siblings5P 1.02 0.09 0.84 1.20 912
## nr.siblings -0.09 0.01 -0.11 -0.08 1267
## last_born1 0.00 0.05 -0.10 0.10 3000
## Rhat
## Intercept 1.02
## paternalage 1.00
## birth_cohort1675M1680 1.01
## birth_cohort1680M1685 1.02
## birth_cohort1685M1690 1.02
## birth_cohort1690M1695 1.02
## birth_cohort1695M1700 1.02
## birth_cohort1700M1705 1.02
## birth_cohort1705M1710 1.02
## birth_cohort1710M1715 1.02
## birth_cohort1715M1720 1.02
## birth_cohort1720M1725 1.03
## birth_cohort1725M1730 1.03
## birth_cohort1730M1735 1.03
## birth_cohort1735M1740 1.03
## male1 1.00
## maternalage.factor1420 1.00
## maternalage.factor3550 1.00
## paternalage.mean 1.00
## paternal_loss01 1.00
## paternal_loss15 1.00
## paternal_loss510 1.00
## paternal_loss1015 1.00
## paternal_loss1520 1.00
## paternal_loss2025 1.00
## paternal_loss2530 1.00
## paternal_loss3035 1.00
## paternal_loss3540 1.00
## paternal_loss4045 1.00
## paternal_lossunclear 1.00
## maternal_loss01 1.00
## maternal_loss15 1.01
## maternal_loss510 1.00
## maternal_loss1015 1.01
## maternal_loss1520 1.00
## maternal_loss2025 1.01
## maternal_loss2530 1.00
## maternal_loss3035 1.01
## maternal_loss3540 1.00
## maternal_loss4045 1.00
## maternal_lossunclear 1.00
## older_siblings1 1.00
## older_siblings2 1.00
## older_siblings3 1.00
## older_siblings4 1.00
## older_siblings5P 1.00
## nr.siblings 1.00
## last_born1 1.00
##
## 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">42.3</td>
<td align="center">25.95</td>
<td align="center">69.83</td>
</tr>
<tr class="even">
<td align="center"><strong>paternalage</strong></td>
<td align="center">0.643</td>
<td align="center">0.5615</td>
<td align="center">0.7354</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1675M1680</strong></td>
<td align="center">1.216</td>
<td align="center">0.6914</td>
<td align="center">2.169</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1680M1685</strong></td>
<td align="center">0.5651</td>
<td align="center">0.3431</td>
<td align="center">0.9193</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1685M1690</strong></td>
<td align="center">0.2332</td>
<td align="center">0.1501</td>
<td align="center">0.3541</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1690M1695</strong></td>
<td align="center">0.4322</td>
<td align="center">0.2765</td>
<td align="center">0.6711</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1695M1700</strong></td>
<td align="center">0.435</td>
<td align="center">0.2812</td>
<td align="center">0.6595</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1700M1705</strong></td>
<td align="center">0.2719</td>
<td align="center">0.1746</td>
<td align="center">0.4095</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1705M1710</strong></td>
<td align="center">0.4602</td>
<td align="center">0.2951</td>
<td align="center">0.6991</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1710M1715</strong></td>
<td align="center">0.2394</td>
<td align="center">0.1543</td>
<td align="center">0.3556</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1715M1720</strong></td>
<td align="center">0.2765</td>
<td align="center">0.1808</td>
<td align="center">0.4088</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1720M1725</strong></td>
<td align="center">0.2774</td>
<td align="center">0.1807</td>
<td align="center">0.4085</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1725M1730</strong></td>
<td align="center">0.1919</td>
<td align="center">0.1263</td>
<td align="center">0.2825</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1730M1735</strong></td>
<td align="center">0.1548</td>
<td align="center">0.1023</td>
<td align="center">0.2302</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1735M1740</strong></td>
<td align="center">0.189</td>
<td align="center">0.1238</td>
<td align="center">0.2783</td>
</tr>
<tr class="even">
<td align="center"><strong>male1</strong></td>
<td align="center">0.6559</td>
<td align="center">0.6155</td>
<td align="center">0.696</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternalage.factor1420</strong></td>
<td align="center">0.837</td>
<td align="center">0.7272</td>
<td align="center">0.9602</td>
</tr>
<tr class="even">
<td align="center"><strong>maternalage.factor3550</strong></td>
<td align="center">0.9167</td>
<td align="center">0.824</td>
<td align="center">1.024</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternalage.mean</strong></td>
<td align="center">1.721</td>
<td align="center">1.491</td>
<td align="center">1.985</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss01</strong></td>
<td align="center">0.3594</td>
<td align="center">0.2895</td>
<td align="center">0.4522</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss15</strong></td>
<td align="center">0.6225</td>
<td align="center">0.5097</td>
<td align="center">0.7536</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss510</strong></td>
<td align="center">0.7041</td>
<td align="center">0.589</td>
<td align="center">0.8371</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss1015</strong></td>
<td align="center">0.7978</td>
<td align="center">0.6802</td>
<td align="center">0.9426</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss1520</strong></td>
<td align="center">0.7197</td>
<td align="center">0.6219</td>
<td align="center">0.8363</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss2025</strong></td>
<td align="center">0.8561</td>
<td align="center">0.7422</td>
<td align="center">0.9897</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss2530</strong></td>
<td align="center">0.7824</td>
<td align="center">0.6809</td>
<td align="center">0.8994</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss3035</strong></td>
<td align="center">0.8313</td>
<td align="center">0.7246</td>
<td align="center">0.952</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss3540</strong></td>
<td align="center">0.8524</td>
<td align="center">0.7461</td>
<td align="center">0.9733</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss4045</strong></td>
<td align="center">0.9682</td>
<td align="center">0.8331</td>
<td align="center">1.124</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_lossunclear</strong></td>
<td align="center">0.7006</td>
<td align="center">0.6048</td>
<td align="center">0.8104</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss01</strong></td>
<td align="center">0.1109</td>
<td align="center">0.09014</td>
<td align="center">0.1348</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss15</strong></td>
<td align="center">0.4959</td>
<td align="center">0.4178</td>
<td align="center">0.5909</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss510</strong></td>
<td align="center">0.6449</td>
<td align="center">0.5486</td>
<td align="center">0.758</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss1015</strong></td>
<td align="center">0.6664</td>
<td align="center">0.5726</td>
<td align="center">0.7758</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss1520</strong></td>
<td align="center">0.6804</td>
<td align="center">0.5876</td>
<td align="center">0.7912</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss2025</strong></td>
<td align="center">0.7636</td>
<td align="center">0.6577</td>
<td align="center">0.891</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss2530</strong></td>
<td align="center">0.8454</td>
<td align="center">0.7305</td>
<td align="center">0.9682</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss3035</strong></td>
<td align="center">0.8086</td>
<td align="center">0.7136</td>
<td align="center">0.9186</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_loss3540</strong></td>
<td align="center">0.7885</td>
<td align="center">0.7008</td>
<td align="center">0.8899</td>
</tr>
<tr class="even">
<td align="center"><strong>maternal_loss4045</strong></td>
<td align="center">0.9697</td>
<td align="center">0.8537</td>
<td align="center">1.111</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternal_lossunclear</strong></td>
<td align="center">0.761</td>
<td align="center">0.656</td>
<td align="center">0.8802</td>
</tr>
<tr class="even">
<td align="center"><strong>older_siblings1</strong></td>
<td align="center">1.562</td>
<td align="center">1.392</td>
<td align="center">1.75</td>
</tr>
<tr class="odd">
<td align="center"><strong>older_siblings2</strong></td>
<td align="center">1.718</td>
<td align="center">1.518</td>
<td align="center">1.944</td>
</tr>
<tr class="even">
<td align="center"><strong>older_siblings3</strong></td>
<td align="center">2.211</td>
<td align="center">1.924</td>
<td align="center">2.561</td>
</tr>
<tr class="odd">
<td align="center"><strong>older_siblings4</strong></td>
<td align="center">2.29</td>
<td align="center">1.964</td>
<td align="center">2.67</td>
</tr>
<tr class="even">
<td align="center"><strong>older_siblings5P</strong></td>
<td align="center">2.78</td>
<td align="center">2.326</td>
<td align="center">3.321</td>
</tr>
<tr class="odd">
<td align="center"><strong>nr.siblings</strong></td>
<td align="center">0.9103</td>
<td align="center">0.8977</td>
<td align="center">0.9226</td>
</tr>
<tr class="even">
<td align="center"><strong>last_born1</strong></td>
<td align="center">0.9954</td>
<td align="center">0.9039</td>
<td align="center">1.102</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:92%;">
<colgroup>
<col width="27%" />
<col width="25%" />
<col width="19%" />
<col width="19%" />
</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">0.92</td>
<td align="center">[0.91;0.93]</td>
<td align="center">[0.91;0.92]</td>
</tr>
<tr class="even">
<td align="center">estimate father 35y</td>
<td align="center">0.91</td>
<td align="center">[0.9;0.92]</td>
<td align="center">[0.9;0.91]</td>
</tr>
<tr class="odd">
<td align="center">percentage change</td>
<td align="center">-1.03</td>
<td align="center">[-1.51;-0.67]</td>
<td align="center">[-1.32;-0.78]</td>
</tr>
<tr class="even">
<td align="center">OR/IRR</td>
<td align="center">0.64</td>
<td align="center">[0.56;0.74]</td>
<td align="center">[0.59;0.7]</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="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-12-1.png" /><img src="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-12-2.png" /><img src="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-12-3.png" /><img src="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-12-4.png" /><img src="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-12-5.png" /><img src="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-12-6.png" /><img src="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-12-7.png" /><img src="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-12-8.png" /><img src="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-12-9.png" /><img src="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-12-10.png" /></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="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-13-1.png" /></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="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-14-1.png" /></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="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-14-2.png" /></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="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-15-1.png" /></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="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-16-1.png" /></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/rpqa/e1_survive1y.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="e1_survive1y.html">Cluster script</a><img src="3_rpqa_selective_episodes_files/figure-html/unnamed-chunk-2-1.png" /></p>
</div>
</div>
</div>
<div id="e2_surviveR" class="section level2 tab-content">
<h2><em>e2</em>: Probability of surviving the first 15 years of life</h2>
<p>Here, we predict the probability that the anchor survives the first fifteen of life. All children born to this father who lived at least one year are compared, if their death date is known or their survival can be inferred (from later marriage or children).</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: bernoulli(cauchit)
## Formula: surviveR ~ paternalage + 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: 49246)
## 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: 11383)
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
## sd(Intercept) 1.1 0.04 1.01 1.19 957 1
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Eff.Sample
## Intercept 5.29 0.47 4.44 6.26 430
## paternalage 0.09 0.12 -0.15 0.31 1143
## birth_cohort1675M1680 -1.23 0.48 -2.27 -0.36 518
## birth_cohort1680M1685 -1.80 0.45 -2.77 -0.99 443
## birth_cohort1685M1690 -1.91 0.45 -2.88 -1.10 396
## birth_cohort1690M1695 -1.26 0.46 -2.25 -0.43 483
## birth_cohort1695M1700 -1.77 0.44 -2.73 -0.98 392
## birth_cohort1700M1705 -2.00 0.44 -2.98 -1.23 409
## birth_cohort1705M1710 -1.82 0.44 -2.78 -1.05 391
## birth_cohort1710M1715 -2.51 0.43 -3.46 -1.76 381
## birth_cohort1715M1720 -1.81 0.44 -2.77 -1.05 431
## birth_cohort1720M1725 -2.36 0.43 -3.31 -1.59 376
## birth_cohort1725M1730 -3.01 0.43 -3.96 -2.27 400
## birth_cohort1730M1735 -2.66 0.43 -3.62 -1.91 379
## birth_cohort1735M1740 -2.16 0.43 -3.11 -1.40 378
## male1 -0.22 0.05 -0.32 -0.13 3000
## maternalage.factor1420 0.08 0.12 -0.15 0.33 3000
## maternalage.factor3550 0.10 0.08 -0.07 0.26 3000
## paternalage.mean -0.06 0.12 -0.30 0.19 1071
## paternal_loss01 -0.90 0.18 -1.24 -0.56 3000
## paternal_loss15 -0.55 0.15 -0.83 -0.27 1955
## paternal_loss510 -0.71 0.13 -0.96 -0.45 1660
## paternal_loss1015 -0.40 0.13 -0.65 -0.15 1733
## paternal_loss1520 -0.49 0.12 -0.72 -0.26 1792
## paternal_loss2025 -0.41 0.11 -0.64 -0.18 1698
## paternal_loss2530 -0.32 0.11 -0.54 -0.10 1669
## paternal_loss3035 -0.15 0.12 -0.38 0.07 1628
## paternal_loss3540 -0.03 0.12 -0.26 0.20 1936
## paternal_loss4045 0.05 0.13 -0.20 0.30 2013
## paternal_lossunclear -0.48 0.11 -0.70 -0.27 1691
## maternal_loss01 -0.60 0.19 -0.96 -0.22 3000
## maternal_loss15 -0.85 0.12 -1.08 -0.61 3000
## maternal_loss510 -0.52 0.11 -0.74 -0.29 2516
## maternal_loss1015 -0.52 0.11 -0.72 -0.30 3000
## maternal_loss1520 -0.22 0.12 -0.45 0.02 3000
## maternal_loss2025 -0.02 0.12 -0.25 0.22 3000
## maternal_loss2530 -0.09 0.11 -0.30 0.13 3000
## maternal_loss3035 -0.14 0.10 -0.34 0.06 3000
## maternal_loss3540 -0.12 0.10 -0.30 0.08 3000
## maternal_loss4045 -0.21 0.10 -0.40 -0.01 3000
## maternal_lossunclear -0.11 0.11 -0.33 0.11 3000
## older_siblings1 -0.06 0.09 -0.25 0.12 2082
## older_siblings2 -0.09 0.10 -0.29 0.11 1437
## older_siblings3 -0.09 0.11 -0.31 0.14 1371
## older_siblings4 -0.07 0.12 -0.31 0.18 1104
## older_siblings5P -0.07 0.15 -0.37 0.24 804
## nr.siblings 0.01 0.01 -0.02 0.03 1260
## last_born1 -0.16 0.08 -0.31 -0.01 3000
## Rhat
## Intercept 1.01
## paternalage 1.00
## birth_cohort1675M1680 1.01
## birth_cohort1680M1685 1.01
## birth_cohort1685M1690 1.01
## birth_cohort1690M1695 1.01
## birth_cohort1695M1700 1.01
## birth_cohort1700M1705 1.01
## birth_cohort1705M1710 1.01
## birth_cohort1710M1715 1.01
## birth_cohort1715M1720 1.01
## birth_cohort1720M1725 1.01
## birth_cohort1725M1730 1.01
## birth_cohort1730M1735 1.01
## birth_cohort1735M1740 1.01
## male1 1.00
## maternalage.factor1420 1.00
## maternalage.factor3550 1.00
## paternalage.mean 1.00
## paternal_loss01 1.00
## paternal_loss15 1.00
## paternal_loss510 1.00
## paternal_loss1015 1.00
## paternal_loss1520 1.00
## paternal_loss2025 1.00
## paternal_loss2530 1.00
## paternal_loss3035 1.00
## paternal_loss3540 1.00
## paternal_loss4045 1.00
## paternal_lossunclear 1.00
## maternal_loss01 1.00
## maternal_loss15 1.00
## maternal_loss510 1.00
## maternal_loss1015 1.00
## maternal_loss1520 1.00
## maternal_loss2025 1.00
## maternal_loss2530 1.00
## maternal_loss3035 1.00
## maternal_loss3540 1.00
## maternal_loss4045 1.00
## maternal_lossunclear 1.00
## older_siblings1 1.00
## older_siblings2 1.00
## older_siblings3 1.00
## older_siblings4 1.00
## older_siblings5P 1.01
## nr.siblings 1.00
## last_born1 1.00
##
## 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">197.6</td>
<td align="center">84.56</td>
<td align="center">523.3</td>
</tr>
<tr class="even">
<td align="center"><strong>paternalage</strong></td>
<td align="center">1.092</td>
<td align="center">0.858</td>
<td align="center">1.37</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1675M1680</strong></td>
<td align="center">0.2936</td>
<td align="center">0.1038</td>
<td align="center">0.7002</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1680M1685</strong></td>
<td align="center">0.1657</td>
<td align="center">0.0624</td>
<td align="center">0.3715</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1685M1690</strong></td>
<td align="center">0.1483</td>
<td align="center">0.05632</td>
<td align="center">0.3334</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1690M1695</strong></td>
<td align="center">0.2837</td>
<td align="center">0.1051</td>
<td align="center">0.6515</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1695M1700</strong></td>
<td align="center">0.1699</td>
<td align="center">0.06522</td>
<td align="center">0.375</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1700M1705</strong></td>
<td align="center">0.1357</td>
<td align="center">0.05104</td>
<td align="center">0.291</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1705M1710</strong></td>
<td align="center">0.1618</td>
<td align="center">0.06179</td>
<td align="center">0.3492</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1710M1715</strong></td>
<td align="center">0.08141</td>
<td align="center">0.03152</td>
<td align="center">0.172</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1715M1720</strong></td>
<td align="center">0.1632</td>
<td align="center">0.06272</td>
<td align="center">0.3483</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1720M1725</strong></td>
<td align="center">0.09458</td>
<td align="center">0.03658</td>
<td align="center">0.2036</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1725M1730</strong></td>
<td align="center">0.04918</td>
<td align="center">0.01898</td>
<td align="center">0.1029</td>
</tr>
<tr class="even">
<td align="center"><strong>birth_cohort1730M1735</strong></td>
<td align="center">0.07026</td>
<td align="center">0.02684</td>
<td align="center">0.1475</td>
</tr>
<tr class="odd">
<td align="center"><strong>birth_cohort1735M1740</strong></td>
<td align="center">0.1158</td>
<td align="center">0.04447</td>
<td align="center">0.2454</td>
</tr>
<tr class="even">
<td align="center"><strong>male1</strong></td>
<td align="center">0.7998</td>
<td align="center">0.7291</td>
<td align="center">0.8792</td>
</tr>
<tr class="odd">
<td align="center"><strong>maternalage.factor1420</strong></td>
<td align="center">1.086</td>
<td align="center">0.8583</td>
<td align="center">1.392</td>
</tr>
<tr class="even">
<td align="center"><strong>maternalage.factor3550</strong></td>
<td align="center">1.103</td>
<td align="center">0.9343</td>
<td align="center">1.298</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternalage.mean</strong></td>
<td align="center">0.9464</td>
<td align="center">0.7442</td>
<td align="center">1.215</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss01</strong></td>
<td align="center">0.4059</td>
<td align="center">0.2891</td>
<td align="center">0.5736</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss15</strong></td>
<td align="center">0.5786</td>
<td align="center">0.4351</td>
<td align="center">0.7667</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss510</strong></td>
<td align="center">0.4923</td>
<td align="center">0.3848</td>
<td align="center">0.6375</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss1015</strong></td>
<td align="center">0.6685</td>
<td align="center">0.5218</td>
<td align="center">0.8586</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss1520</strong></td>
<td align="center">0.6127</td>
<td align="center">0.4861</td>
<td align="center">0.7736</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss2025</strong></td>
<td align="center">0.6608</td>
<td align="center">0.5275</td>
<td align="center">0.8324</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss2530</strong></td>
<td align="center">0.7239</td>
<td align="center">0.5841</td>
<td align="center">0.9043</td>
</tr>
<tr class="odd">
<td align="center"><strong>paternal_loss3035</strong></td>
<td align="center">0.8594</td>
<td align="center">0.6829</td>
<td align="center">1.075</td>
</tr>
<tr class="even">
<td align="center"><strong>paternal_loss3540</strong></td>