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<title>Paternal Age and Offspring Fitness</title>
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<body>
<div class="container-fluid main-container">
<div class="row">
<div class="col-xs-3 krummhoern" style="border-top:solid #E2A674 20px">
</div>
<div class="col-xs-3 rpqa" style="border-top:solid #9F3B2B 20px">
</div>
<div class="col-xs-3 hist_sweden" style="border-top:solid #21523B 20px">
</div>
<div class="col-xs-3 mod_sweden" style="border-top:solid #8A846C 20px">
</div>
</div>
<div id="paternal-age-effects-on-offspring-fitness-in-four-populations" class="section level3 tab-content">
<h3>Paternal age effects on offspring fitness <small>in four populations</small></h3>
<div id="main-result" class="section level4">
<h4>Main result</h4>
<div id="paternal-age-effect-in-a-sibling-comparison-design-adjusting-for-average-paternal-age-maternal-age-number-of-siblings-number-of-older-siblings-being-last-born-birth-cohort-and-parental-loss." class="section level5">
<h5><small>Paternal age effect in a <abbr title="i.e. random effects for each union/parents" data-toggle="tooltip">sibling comparison design</abbr>, adjusting for <abbr title="i.e. averaged over siblings" data-toggle="tooltip">average paternal age</abbr>, <abbr title="in three categories: 14 to 20, 20 to 35, 35 and older" data-toggle="tooltip">maternal age</abbr>, <abbr title="Same for all siblings" data-toggle="tooltip">number of siblings</abbr>, <abbr title="In six categories: 0-5, 5+" data-toggle="tooltip">number of older siblings</abbr>, being last born, <abbr title="grouped into up to five-year bins by birth year, small bins lumped" data-toggle="tooltip">birth cohort</abbr>, and <abbr title="we modelled the loss of either the father or the mother with two separate predictors in bins (0-1, 2-5, 6-10, …, 41-45, 45+, unknown)" data-toggle="tooltip">parental loss</abbr></small>.</h5>
<p>We find that the children of older fathers consistently have fewer childrens in all four populations, when compared to their siblings.</p>
<div class="row">
<div class="col-md-12">
<p><a href="2_compare_main_models.html"><img src="library/mcmc_comp.png" alt="Main model results"><br></a></p>
</div>
</div>
</div>
</div>
<div id="by-population" class="section level4">
<h4>By Population</h4>
<div class="row krmh">
<div class="col-md-3" style="border-top: solid #E2A674;border-width:20px 0px">
<p><strong><big>Krummhörn</big></strong><br> <img src="library/krmh.jpg" alt="Krmh"></p>
<div class="row">
<div class="col-md-12">
<div class="well well-sm">
<a title=" Loading, merging, transforming, wrangling data, predictor calculation, etc. " data-toggle="tooltip" href=" 0_krmh_massage.html "> Data Wrangling </a>
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<a title=" Descriptive statistics for this population " data-toggle="tooltip" href=" 1_krmh_descriptives.html "> Descriptives </a>
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<a title=" Main models " data-toggle="tooltip" href=" 2_krmh_main_models.html "> Main Models </a>
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<div class="well well-sm">
<a title=" Selective episode models " data-toggle="tooltip" href=" 3_krmh_selective_episodes.html "> Selective Episodes </a>
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<a title=" Robustness analyses to check various modelling assumptions " data-toggle="tooltip" href=" 5_krmh_robustness.html "> Robustness </a>
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<a title=" Sensitivity analyses to test potential pathways " data-toggle="tooltip" href=" 6_krmh_sensitivity.html "> Sensitivity </a>
</div>
</div>
</div>
</div>
<div class="col-md-3 rpqa" style="border-top: solid #9F3B2B;border-width:20px 0px">
<p><strong><big>Québec</big></strong><br> <img src="library/rpqa.jpg" alt="RPQA"></p>
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<a title=" Loading, merging, transforming, wrangling data, predictor calculation, etc. " data-toggle="tooltip" href=" 0_rpqa_massage.html "> Data Wrangling </a>
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<a title=" Descriptive statistics for this population " data-toggle="tooltip" href=" 1_rpqa_descriptives.html "> Descriptives </a>
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<div class="well well-sm">
<a title=" Main models " data-toggle="tooltip" href=" 2_rpqa_main_models.html "> Main Models </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Selective episode models " data-toggle="tooltip" href=" 3_rpqa_selective_episodes.html "> Selective Episodes </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Grandpaternal age effect model " data-toggle="tooltip" href=" 4_rpqa_grandparents.html "> Grandparents </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Robustness analyses to check various modelling assumptions " data-toggle="tooltip" href=" 5_rpqa_robustness.html "> Robustness </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Sensitivity analyses to test potential pathways " data-toggle="tooltip" href=" 6_rpqa_sensitivity.html "> Sensitivity </a>
</div>
</div>
</div>
</div>
<div class="col-md-3 hist_sweden" style="border-top: solid #21523B;border-width:20px 0px">
<p><strong><big>Historical Sweden</big></strong><br> <img src="library/ddb.jpg" alt="DDB"></p>
<div class="row">
<div class="col-md-12">
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<a title=" Loading, merging, transforming, wrangling data, predictor calculation, etc. " data-toggle="tooltip" href=" 0_ddb_massage.html "> Data Wrangling </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Descriptive statistics for this population " data-toggle="tooltip" href=" 1_ddb_descriptives.html "> Descriptives </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Main models " data-toggle="tooltip" href=" 2_ddb_main_models.html "> Main Models </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Selective episode models " data-toggle="tooltip" href=" 3_ddb_selective_episodes.html "> Selective Episodes </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm" style="background:none;border-color:transparent;box-shadow:none">
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Robustness analyses to check various modelling assumptions " data-toggle="tooltip" href=" 5_ddb_robustness.html "> Robustness </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Sensitivity analyses to test potential pathways " data-toggle="tooltip" href=" 6_ddb_sensitivity.html "> Sensitivity </a>
</div>
</div>
</div>
</div>
<div class="col-md-3 mod_sweden" style="border-top: solid #8A846C;border-width:20px 0px">
<p><strong><big>20<sup>th</sup>-century Sweden</big></strong><br> <img src="library/swed.jpg" alt="SCB Örebro"></p>
<div class="row">
<div class="col-md-12">
<div class="well well-sm">
<a title=" Loading, merging, transforming, wrangling data, predictor calculation, etc. " data-toggle="tooltip" href=" 0_swed_massage.html "> Data Wrangling </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Descriptive statistics for this population " data-toggle="tooltip" href=" 1_swed_descriptives.html "> Descriptives </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Main models " data-toggle="tooltip" href=" 2_swed_main_models.html "> Main Models </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Selective episode models " data-toggle="tooltip" href=" 3_swed_selective_episodes.html "> Selective Episodes </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm" style="background:none;border-color:transparent;box-shadow:none">
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Robustness analyses to check various modelling assumptions " data-toggle="tooltip" href=" 5_swed_robustness.html "> Robustness </a>
</div>
</div>
<div class="col-md-12">
<div class="well well-sm">
<a title=" Sensitivity analyses to test potential pathways " data-toggle="tooltip" href=" 6_swed_sensitivity.html "> Sensitivity </a>
</div>
</div>
</div>
</div>
</div>
</div>
<div id="reproductive-timing" class="section level4">
<h4>Reproductive timing</h4>
<p>Much reporting on increasing parental ages tends to focus on ages at <strong>first birth</strong> (dashed lines) and hence seems at times unduly alarmist. Parental ages at <strong>all births</strong> (solid lines) show an increase since 1970 too, but are still lower than in the four Swedish regions of our historical Swedish data (1737-1880). The biggest difference is in fact not the slight delay of age at first birth in modern Sweden, but the much earlier reproductive stoppage (ages at <strong>last birth</strong>, dotted lines).</p>
<p>Hence, contrary to many people’s intutitions, in modern Sweden (1947-1959, gray) the average child was born to a younger parent than in our pre-industrial populations (1737-1880, green). This is mostly because people stopped having children earlier and to a lesser degree because people started having children ca. 1 year earlier. In contemporary Sweden (2010), the average parental age for both mothers and fathers is still lower than in our historical Swedish data.</p>
<div class="row">
<div class="col-md-12">
<p><a href="1_compare_descriptives.html"> <img src="library/rep_timing_comp.png" alt="Age at first child slightly lower in modern Sweden"> </a></p>
</div>
</div>
<p>In the below plot, we have compared all four populations ages at first and last births. The data for modern Sweden focuses on children born 1947 to 1959. Especially, mothers’ ages at last births stand out: In all historical datasets, it was still common for mothers to reproduce beyond the age of 40, reproductive stoppage for both men and women occurs much earlier in modern Sweden. <a href="1_compare_descriptives.html">Further descriptive comparisons on reproductive timing and other parameters</a>.</p>
<div class="row">
<div class="col-md-6">
<p><a href="1_compare_descriptives.html"> <img src="library/age_at_1st_child.png" alt="Age at first child slightly lower in modern Sweden"></a></p>
</div>
<div class="col-md-6">
<p><a href="1_compare_descriptives.html"> <img src="library/age_at_last_child.png" alt="Age at last child much lower in modern Sweden"></a></p>
</div>
</div>
</div>
<div id="comparisons" class="section level4">
<h4>Comparisons</h4>
<div id="descriptives" class="section level5">
<h5><a href="1_compare_descriptives.html">Descriptives</a></h5>
<p>Comparison of descriptives across populations.</p>
</div>
<div id="main-models" class="section level5">
<h5><a href="2_compare_main_models.html">Main models</a></h5>
<p>Comparison of the main models across populations.</p>
</div>
<div id="selective-episodes" class="section level5">
<h5><a href="3_compare_selective_episodes.html">Selective episodes</a></h5>
<p>Comparison of the selective episode models across populations. <img src="library/episode_comparison.png" alt="Selective episode comparison" /></p>
</div>
<div id="robustness" class="section level5">
<h5><a href="5_compare_robustness.html">Robustness</a></h5>
<p>Comparison of the results of robustness checks in different populations. <img src="library/robustness_comparison.png" alt="Robustness check comparison" /></p>
</div>
<div id="plausibility-checks" class="section level5">
<h5><a href="7_plausibility_simulations.html">Plausibility checks</a></h5>
<p>How do the obtained effect sizes on number of children compare to estimates of genome-wide deleterious mutation rate times the mean selection coefficient against a deleterious heterozygous mutation (Hayward et al., 2015) and how to the effect sizes on infant survival compare to calculations of the mutation-attributable effect size computed in Gratten et al. (2016).</p>
</div>
</div>
<div id="helpers" class="section level4">
<h4>Helpers</h4>
<p>In this document, all <a href="0__helpers.html" title="Helper functions" data-toggle="tooltip">Helper functions</a> functions that are used throughout, are documented.</p>
<p>This <a href="0__make.html" title="Script for generating this website" data-toggle="tooltip">make file</a> was used to generate this website (some code was run manually on the cluster).</p>
<p>The statistical models using brms were documented in a standardised fashion, this is documented here, <a href="0__model_summary.html" title="Model summary rmarkdown component" data-toggle="tooltip">model summary</a>.</p>
<p>The <a href="0__main_models.html" title="documentation for main model summaries and comparisons" data-toggle="tooltip">main model reports</a>, <a href="0__selective_episodes.html" title="documentation for selective epsiode summaries" data-toggle="tooltip">selective episode reports</a>, <a href="0__robustness_checks.html" title="documentation for main model summaries and comparisons" data-toggle="tooltip">main model reports</a> were also generated in a standardised fashion.</p>
</div>
<div id="authors-acknowledgements" class="section level4 tab-content">
<h4>Authors & Acknowledgements</h4>
<p>Corresponding author: <a href="mailto:ruben.arslan@gmail.com">Ruben C. Arslan</a>, Georg August University Göttingen<br />
Kai P. Willführ, Emma M. Frans, Karin J. H. Verweij, Paul-Christian Bürkner, Mikko Myrskylä, Eckart Voland, Catarina Almqvist, Brendan Zietsch, & Lars Penke</p>
<p>This supplementary website has been archived on Zenodo.org <a href="https://zenodo.org/badge/latestdoi/18913/rubenarslan/paternal_age_fitness"><img src="https://zenodo.org/badge/18913/rubenarslan/paternal_age_fitness.svg" alt="DOI" /></a>.</p>
<p>RCA thanks Holger Sennhenn-Reulen, <a href="http://jarrod.bio.ed.ac.uk/jarrod.html">Jarrod Hadfield</a>, author of MCMCglmm, and <a href="http://ms.mcmaster.ca/~bolker/">Ben Bolker</a>, co-author of lme4, for their statistical advice.</p>
<div id="license" class="section level5">
<h5>License</h5>
<p><a rel="license" href="http://creativecommons.org/licenses/by/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by/4.0/88x31.png" /></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</a>.</p>
</div>
<div id="image-credits" class="section level5 tab-content">
<h5>Image credits</h5>
<div id="kreuzkirche-pilsum-krummhorn" class="section level6">
<h6>Kreuzkirche Pilsum, Krummhörn</h6>
<p>
<a href="https://commons.wikimedia.org/wiki/File:Pilsumer_Kirche_2010.jpg#/media/File:Pilsumer_Kirche_2010.jpg"><img src="library/krmh.jpg" alt="Pilsumer Kirche 2010.jpg" height="124" width="220"></a><br>„<a href="https://commons.wikimedia.org/wiki/File:Pilsumer_Kirche_2010.jpg#/media/File:Pilsumer_Kirche_2010.jpg">Pilsumer Kirche 2010</a>“ von <a href="//commons.wikimedia.org/wiki/User:Carschten" title="User:Carschten">kaʁstn</a> <a href="//commons.wikimedia.org/wiki/User_talk:Carschten" title="User talk:Carschten">Disk</a>/<a href="//commons.wikimedia.org/wiki/Category:User:Carschten" title="Category:User:Carschten">Cat</a> - <span class="int-own-work" lang="de">Eigenes Werk</span>. Lizenziert unter <a href="http://creativecommons.org/licenses/by-sa/3.0/de/deed.en" title="Creative Commons Attribution-Share Alike 3.0 de">CC BY-SA 3.0 de</a> über <a href="//commons.wikimedia.org/wiki/">Wikimedia Commons</a>.
</p>
</div>
<div id="basilica-of-sainte-anne-de-beaupre-quebec" class="section level6">
<h6>Basilica of Sainte-Anne-de-Beaupré, Québec</h6>
<p>
<a href="https://commons.wikimedia.org/wiki/File:Church_of_Sainte_Anne_de_Beaupre.jpg#/media/File:Church_of_Sainte_Anne_de_Beaupre.jpg"><img src="library/rpqa.jpg" alt="Church of Sainte Anne de Beaupre.jpg" height="145" width="187"></a><br>“<a href="https://commons.wikimedia.org/wiki/File:Church_of_Sainte_Anne_de_Beaupre.jpg#/media/File:Church_of_Sainte_Anne_de_Beaupre.jpg">Church of Sainte Anne de Beaupre</a>” by Detroit Publishing - <a rel="nofollow" class="external free" href="http://hdl.loc.gov/loc.pnp/ppmsca.18107">http://hdl.loc.gov/loc.pnp/ppmsca.18107</a>. Licensed under Public Domain via <a href="//commons.wikimedia.org/wiki/">Wikimedia Commons</a>.
</p>
</div>
<div id="skelleftea-landsforsamlings-kyrka-sweden" class="section level6">
<h6>Skellefteå landsförsamlings kyrka, Sweden</h6>
<p>
<a href="https://commons.wikimedia.org/wiki/File:Skelleftea_landskyrka_main_view.jpg#/media/File:Skelleftea_landskyrka_main_view.jpg"><img src="library/ddb.jpg" alt="Skellefteå landsförsamlings kyrka (2010)." height="145" width="194"></a><br>“<a href="https://commons.wikimedia.org/wiki/File:Skelleftea_landskyrka_main_view.jpg#/media/File:Skelleftea_landskyrka_main_view.jpg">Skelleftea landskyrka main view</a>” av <a href="//commons.wikimedia.org/wiki/User:Xauxa" title="User:Xauxa">Xauxa</a> Håkan Svensson - <span class="int-own-work" lang="sv">Eget arbete</span>. Licensierad under <a href="http://creativecommons.org/licenses/by-sa/3.0" title="Creative Commons Attribution-Share Alike 3.0">CC BY-SA 3.0</a> via <a href="//commons.wikimedia.org/wiki/">Wikimedia Commons</a>.
</p>
</div>
<div id="statistics-sweden-statistiska-centralbyran-orebro-office-sweden" class="section level6">
<h6>Statistics Sweden, Statistiska centralbyrån, Örebro Office, Sweden</h6>
<p>
<a href="https://commons.wikimedia.org/wiki/File:SCB_%C3%96rebro.JPG#/media/File:SCB_%C3%96rebro.JPG"><img src="library/swed.jpg" alt="SCB Örebro" height="145" width="109"></a><br>“<a href="https://commons.wikimedia.org/wiki/File:SCB_%C3%96rebro.JPG#/media/File:SCB_%C3%96rebro.JPG">SCB Örebro</a>” by Edaen. Licensed under <a href="http://creativecommons.org/licenses/by/3.0" title="Creative Commons Attribution 3.0">CC BY 3.0</a> via <a href="//commons.wikimedia.org/wiki/">Wikimedia Commons</a>.
</p>
</div>
</div>
<div id="package-bibliography" class="section level5">
<h5>Package bibliography</h5>
<div id="session-info-with-package-versions" class="section level6 accordion">
<h6>Session info (with package versions)</h6>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(brms, <span class="dt">warn.conflicts =</span> F, <span class="dt">quietly =</span> T)
<span class="kw">library</span>(bayesplot, <span class="dt">warn.conflicts =</span> F, <span class="dt">quietly =</span> T)</code></pre></div>
<pre><code>## This is bayesplot version 1.2.0</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">sessionInfo</span>()</code></pre></div>
<pre><code>## R version 3.3.2 (2016-10-31)
## Platform: x86_64-apple-darwin13.4.0 (64-bit)
## Running under: OS X El Capitan 10.11.6
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] bayesplot_1.2.0 brms_1.7.0 Rcpp_0.12.9 pander_0.6.0
## [5] broom_0.4.1.9000 dtplyr_0.0.1 dplyr_0.5.0 data.table_1.9.6
## [9] knitr_1.16 plyr_1.8.4 reshape2_1.4.2 stringi_1.1.2
## [13] stringr_1.1.0 lubridate_1.6.0 formr_0.4.2 QuantPsyc_1.5
## [17] MASS_7.3-45 boot_1.3-18 psych_1.6.9 car_2.1-3
## [21] Hmisc_4.0-0 ggplot2_2.2.1 Formula_1.2-1 survival_2.40-1
## [25] lattice_0.20-34 foreign_0.8-67 formatR_1.4 rmarkdown_1.2
##
## loaded via a namespace (and not attached):
## [1] tidyr_0.6.0 assertthat_0.1 rprojroot_1.1
## [4] digest_0.6.11 packrat_0.4.8-1 R6_2.2.0
## [7] chron_2.3-47 backports_1.0.4 acepack_1.4.1
## [10] MatrixModels_0.4-1 stats4_3.3.2 coda_0.19-1
## [13] evaluate_0.10 lazyeval_0.2.0 minqa_1.2.4
## [16] SparseM_1.74 nloptr_1.0.4 rpart_4.1-10
## [19] Matrix_1.2-7.1 labeling_0.3 splines_3.3.2
## [22] lme4_1.1-12 loo_1.1.0 munsell_0.4.3
## [25] rstan_2.15.1 mnormt_1.5-5 mgcv_1.8-16
## [28] rstantools_1.2.0 htmltools_0.3.5 nnet_7.3-12
## [31] tibble_1.2 gridExtra_2.2.1 htmlTable_1.7
## [34] matrixStats_0.51.0 grid_3.3.2 nlme_3.1-128
## [37] gtable_0.2.0 DBI_0.5-1 magrittr_1.5
## [40] StanHeaders_2.15.0-1 scales_0.4.1 latticeExtra_0.6-28
## [43] RColorBrewer_1.1-2 tools_3.3.2 abind_1.4-5
## [46] parallel_3.3.2 pbkrtest_0.4-6 yaml_2.1.14
## [49] inline_0.3.14 colorspace_1.3-2 cluster_2.0.5
## [52] quantreg_5.29</code></pre>
</div>
<div id="references" class="section level6 unnumbered">
<h6>References</h6>
<div id="refs" class="references">
<div id="ref-brms">
<p>1. Bürkner, P.-C. in press brms: An R package for bayesian multilevel models using stan. <em>Journal of Statistical Software</em> </p>
</div>
<div id="ref-MCMCglmm">
<p>2. Hadfield, J. D. 2010 MCMC methods for multi-response generalized linear mixed models: The MCMCglmm R package. <em>Journal of Statistical Software</em> <strong>33</strong>, 1–22. </p>
</div>
<div id="ref-lme4">
<p>3. Bates, D., Mächler, M., Bolker, B. & Walker, S. 2015 Fitting linear mixed-effects models using lme4. <em>Journal of Statistical Software</em> <strong>67</strong>, 1–48. (doi:<a href="https://doi.org/10.18637/jss.v067.i01">10.18637/jss.v067.i01</a>)</p>
</div>
<div id="ref-rmarkdown">
<p>4. Allaire, J., Cheng, J., Xie, Y., McPherson, J., Chang, W., Allen, J., Wickham, H., Atkins, A. & Hyndman, R. 2016 <em>Rmarkdown: Dynamic documents for r</em>. </p>
</div>
<div id="ref-formatR">
<p>5. Xie, Y. 2016 <em>FormatR: Format r code automatically</em>. </p>
</div>
<div id="ref-foreign">
<p>6. R Core Team 2016 <em>Foreign: Read data stored by minitab, s, sas, spss, stata, systat, weka, dBase, .</em> </p>
</div>
<div id="ref-Hmisc">
<p>7. Harrell Jr, F. E., Charles Dupont & others. 2016 <em>Hmisc: Harrell miscellaneous</em>. </p>
</div>
<div id="ref-car">
<p>8. Fox, J. & Weisberg, S. 2011 <em>An R companion to applied regression</em>. Second. Thousand Oaks CA: Sage. </p>
</div>
<div id="ref-psych">
<p>9. Revelle, W. 2016 <em>Psych: Procedures for psychological, psychometric, and personality research</em>. Evanston, Illinois: Northwestern University. </p>
</div>
<div id="ref-QuantPsyc">
<p>10. Fletcher, T. D. 2012 <em>QuantPsyc: Quantitative psychology tools</em>. </p>
</div>
<div id="ref-formr">
<p>11. Arslan, R. 2014 <em>Formr: Formr survey framework</em>. </p>
</div>
<div id="ref-ggplot2">
<p>12. Wickham, H. 2009 <em>Ggplot2: Elegant graphics for data analysis</em>. Springer-Verlag New York. </p>
</div>
<div id="ref-lubridate">
<p>13. Grolemund, G. & Wickham, H. 2011 Dates and times made easy with lubridate. <em>Journal of Statistical Software</em> <strong>40</strong>, 1–25. </p>
</div>
<div id="ref-stringr">
<p>14. Wickham, H. 2016 <em>Stringr: Simple, consistent wrappers for common string operations</em>. </p>
</div>
<div id="ref-stringi">
<p>15. Gagolewski, M. & Tartanus, B. 2016 <em>R package stringi: Character string processing facilities</em>. </p>
</div>
<div id="ref-reshape2">
<p>16. Wickham, H. 2007 Reshaping data with the reshape package. <em>Journal of Statistical Software</em> <strong>21</strong>, 1–20. </p>
</div>
<div id="ref-plyr">
<p>17. Wickham, H. 2011 The split-apply-combine strategy for data analysis. <em>Journal of Statistical Software</em> <strong>40</strong>, 1–29. </p>
</div>
<div id="ref-knitr">
<p>18. Xie, Y. 2016 <em>Knitr: A general-purpose package for dynamic report generation in r</em>. </p>
</div>
<div id="ref-data.table">
<p>19. Dowle, M., Srinivasan, A., Short, T., R Saporta, S. L. with contributions from & Antonyan, E. 2015 <em>Data.table: Extension of data.frame</em>. </p>
</div>
<div id="ref-dplyr">
<p>20. Wickham, H. & Francois, R. 2016 <em>Dplyr: A grammar of data manipulation</em>. </p>
</div>
<div id="ref-dtplyr">
<p>21. Wickham, H. 2016 <em>Dtplyr: Data table back-end for ’dplyr’</em>. </p>
</div>
<div id="ref-broom">
<p>22. Robinson, D. 2016 <em>Broom: Convert statistical analysis objects into tidy data frames</em>. </p>
</div>
<div id="ref-pander">
<p>23. Daróczi, G. & Tsegelskyi, R. 2015 <em>Pander: An r pandoc writer</em>. </p>
</div>
<div id="ref-DT">
<p>24. Xie, Y. 2016 <em>DT: A wrapper of the javascript library ’datatables’</em>. </p>
</div>
<div id="ref-bayesplot">
<p>25. Gabry, J. 2016 <em>Bayesplot: Plotting for bayesian models</em>. </p>
</div>
</div>
</div>
</div>
</div>
</div>
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