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<!DOCTYPE html>
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<div id="header">
<h1 class="title toc-ignore">Regression and Other Stories - Examples</h1>
<h4 class="author">Andrew Gelman, Jennifer Hill, Aki Vehtari</h4>
<h4 class="date">Page updated: 2022-02-24</h4>
</div>
<hr />
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<ul>
<li>The code and data are provided to fully reproduce the examples and figures in the book. They can be a good way to see what the code does. Different people have different styles of code. The code here is not supposed to be a model. The statistical analyses and graphs in the book are intended to be models for good practice, but the code here is meant to be simple with minimal dependencies.</li>
<li><p>For R programming basics see Appendix A of Regression and Other Stories. If you want to learn more, see our recommendations for <a href="R_visualizaton.html">R programming and visualization with R</a>.</p></li>
<li>The folders below (ending /) point to the code (.R and .Rmd) and <code>data</code> folders (.csv or .txt) in github, and .html -files point to knitted notebooks.</li>
<li>Most examples have cleaned data in .csv file in <code>data</code> subfolder for easy experimenting. For completeness and reproducibility, the data subfolders have also the raw data and <code>*_setup.R</code> file showing how the data pre-processing has been done (to do the exercises and follow along with the examples, you don’t need to worry about the setup code).</li>
<li><p>For easy access to data sets, there is an R package <code>rosdata</code>. You can install it with a command <code>remotes::install_github("avehtari/ROS-Examples",subdir = "rpackage")</code>. Then you can access data, for example, as <code>library(rosdata)</code>, <code>data(wells)</code>, <code>head(wells)</code>. You can get the list of data sets with <code>?rosdata</code>.</p></li>
<li>When running the notebooks, to avoid need to switch the working directory, <code>rprojroot</code> package is used to set the project root directory. The downloaded git repository can be placed anywhere you like and you can rename the ROS-Examples directory if you wish. When running the code, it is sufficient that the working directory is any directory in the ROS-Examples (or renamed). Running</li>
</ul>
<pre><code>library("rprojroot")
root<-has_file(".ROS-Examples-root")$make_fix_file()</code></pre>
<p>will find the file <code>.ROS-Examples-root</code> which is in the <code>ROS-Examples</code> directory, and will set the full path according to that. Then, for example,</p>
<pre><code>wells <- read.csv(root("Arsenic/data","wells.csv"))</code></pre>
<p>finds the <code>wells.csv</code> file, no matter where you have placed or renamed the <code>ROS-Examples</code> directory. When you switch to another example, there is no need to switch the working directory.</p>
<hr />
</div>
<div id="examples-by-chapters" class="section level2">
<h2>Examples by chapters</h2>
<div id="introduction-1" class="section level3">
<h3>1 Introduction</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/">ElectionsEconomy/</a>
<ul>
<li><a href="ElectionsEconomy/hibbs.html">hibbs.html</a> - Predicting presidential vote share from the economy</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectricCompany/">ElectricCompany/</a>
<ul>
<li><a href="ElectricCompany/electric.html">electric.html</a> - Analysis of “Electric company” data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Peacekeeping/">Peacekeeping/</a>
<ul>
<li><a href="Peacekeeping/peace.html">peace.html</a> - Outcomes after civil war in countries with and without United Nations peacekeeping</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/SimpleCausal/">SimpleCausal/</a>
<ul>
<li><a href="SimpleCausal/causal.html">causal.html</a> - Simple graphs illustrating regression for causal inference</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Helicopters/">Helicopters/</a>
<ul>
<li><a href="Helicopters/helicopters.html">helicopters.html</a> - Example data file for helicopter flying time exercise</li>
</ul></li>
</ul>
</div>
<div id="data-and-measurement" class="section level3">
<h3>2 Data and measurement</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/HDI/">HDI/</a>
<ul>
<li><a href="HDI/hdi.html">hdi.html</a> - Human Development Index - Looking at data in different ways</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Pew/">Pew/</a>
<ul>
<li><a href="Pew/pew.html">pew.html</a> - Miscellaneous analyses using raw Pew data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/HealthExpenditure/">HealthExpenditure/</a>
<ul>
<li><a href="HealthExpenditure/healthexpenditure.html">healthexpenditure.html</a> - Discovery through graphs of data and models</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Names/">Names/</a>
<ul>
<li><a href="Names/names.html">names.html</a> - Names - Distributions of names of American babies</li>
<li><a href="Names/lastletters.html">lastletters.html</a> - Last letters - Distributions of last letters of names of American babies</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/AgePeriodCohort/">AgePeriodCohort/</a>
<ul>
<li><a href="AgePeriodCohort/births.html">births.html</a> - Age adjustment</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Congress/">Congress/</a>
<ul>
<li><a href="Congress/congress_plots.html">congress_plots.html</a> - Predictive uncertainty for congressional elections</li>
</ul></li>
</ul>
</div>
<div id="some-basic-methods-in-mathematics-and-probability" class="section level3">
<h3>3 Some basic methods in mathematics and probability</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Mile/">Mile/</a>
<ul>
<li><a href="Mile/mile.html">mile.html</a> - Trend of record times in the mile run</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Metabolic/">Metabolic/</a>
<ul>
<li><a href="Metabolic/metabolic.html">metabolic.html</a> - How to interpret a power law or log-log regression</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Earnings/">Earnings/</a>
<ul>
<li><a href="Earnings/height_and_weight.html">height_and_weight.html</a> - Predict weight</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/CentralLimitTheorem/">CentralLimitTheorem/</a>
<ul>
<li><a href="CentralLimitTheorem/heightweight.html">heightweight.html</a> - Illustrate central limit theorem and normal distribution</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Stents/">Stents/</a>
<ul>
<li><a href="Stents/stents.html">stents.html</a> - Stents - comparing distributions</li>
</ul></li>
</ul>
</div>
<div id="generative-models-and-statistical-inference" class="section level3">
<h3>4 Generative models and statistical inference</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Coverage/">Coverage/</a>
<ul>
<li><a href="Coverage/coverage.html">coverage.html</a> - Example of coverage</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Death/">Death/</a>
<ul>
<li><a href="Death/polls.html">polls.html</a> - Proportion of American adults supporting the death penalty</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Coop/">Coop/</a>
<ul>
<li><a href="Coop/riverbay.html">riverbay.html</a> - Example of hypothesis testing</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Girls/">Girls/</a></li>
</ul>
</div>
<div id="simulation" class="section level3">
<h3>5 Simulation</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ProbabilitySimulation/">ProbabilitySimulation/</a>
<ul>
<li><a href="ProbabilitySimulation/probsim.html">probsim.html</a> - Simulation of probability models</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Earnings/">Earnings/</a>
<ul>
<li><a href="Earnings/earnings_bootstrap.html">earnings_bootstrap.html</a> - Bootstrapping to simulate the sampling distribution</li>
</ul></li>
</ul>
</div>
<div id="background-on-regression-modeling" class="section level3">
<h3>6 Background on regression modeling</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Simplest/">Simplest/</a>
<ul>
<li><a href="Simplest/simplest.html">simplest.html</a> - Linear regression with a single predictor</li>
<li><a href="Simplest/simplest_lm.html">simplest_lm.html</a> - Linear least squares regression with a single predictor</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Earnings/">Earnings/</a>
<ul>
<li><a href="Earnings/earnings_regression.html">earnings_regression.html</a> - Predict respondents’ yearly earnings using survey data from 1990.</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/PearsonLee/">PearsonLee/</a>
<ul>
<li><a href="PearsonLee/heights.html">heights.html</a> - The heredity of height. Published in 1903 by Karl Pearson and Alice Lee.</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/FakeMidtermFinal/">FakeMidtermFinal/</a>
<ul>
<li><a href="FakeMidtermFinal/simulation.html">simulation.html</a> - Fake dataset of 1000 students’ scores on a midterm and final exam</li>
</ul></li>
</ul>
</div>
<div id="linear-regression-with-a-single-predictor" class="section level3">
<h3>7 Linear regression with a single predictor</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/">ElectionsEconomy/</a>
<ul>
<li><a href="ElectionsEconomy/hibbs.html">hibbs.html</a> - Predicting presidential vote share from the economy</li>
<li><a href="ElectionsEconomy/hills.html">hills.html</a> - Present uncertainty in parameter estimates</li>
<li><a href="ElectionsEconomy/hibbs_coverage.html">hibbs_coverage.html</a> - Checking the coverage of intervals</li>
<li><a href="Simplest/">Simplest/</a></li>
<li><a href="Simplest/simplest.html">simplest.html</a> - Linear regression with a single predictor</li>
<li><a href="Simplest/simplest_lm.html">simplest_lm.html</a> - Linear least squares regression with a single predictor</li>
</ul></li>
</ul>
</div>
<div id="fitting-regression-models" class="section level3">
<h3>8 Fitting regression models</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/">ElectionsEconomy/</a>
<ul>
<li><a href="ElectionsEconomy/hibbs.html">hibbs.html</a> - Predicting presidential vote share from the economy</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Influence/">Influence/</a>
<ul>
<li><a href="Influence/influence.html">influence.html</a> - Influence of individual points in a fitted regression</li>
</ul></li>
</ul>
</div>
<div id="prediction-and-bayesian-inference" class="section level3">
<h3>9 Prediction and Bayesian inference</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/">ElectionsEconomy/</a>
<ul>
<li><a href="ElectionsEconomy/hibbs.html">hibbs.html</a> - Predicting presidential vote share from the economy</li>
<li><a href="ElectionsEconomy/bayes.html">bayes.html</a> - Demonstration of Bayesian information aggregation</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/SexRatio/">SexRatio/</a>
<ul>
<li><a href="SexRatio/sexratio.html">sexratio.html</a> - Example where an informative prior makes a difference</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Earnings/">Earnings/</a>
<ul>
<li><a href="Earnings/height_and_weight.html">height_and_weight.html</a> - Predict weight</li>
<li><a href="Earnings/earnings_regression.html">earnings_regression.html</a> - Predict respondents’ yearly earnings using survey data from 1990.</li>
</ul></li>
</ul>
</div>
<div id="linear-regression-with-multiple-predictors" class="section level3">
<h3>10 Linear regression with multiple predictors</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/KidIQ/">KidIQ/</a>
<ul>
<li><a href="KidIQ/kidiq.html">kidiq.html</a> - Linear regression with multiple predictors</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Earnings/">Earnings/</a>
<ul>
<li><a href="Earnings/height_and_weight.html">height_and_weight.html</a> - Predict weight</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Congress/">Congress/</a>
<ul>
<li><a href="Congress/congress.html">congress.html</a> - Predictive uncertainty for congressional elections</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/NES/">NES/</a>
<ul>
<li><a href="NES/nes_linear.html">nes_linear.html</a> - Fitting the same regression to many datasets</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Beauty/">Beauty/</a>
<ul>
<li><a href="Beauty/beauty.html">beauty.html</a> - Student evaluations of instructors’ beauty and teaching quality</li>
</ul></li>
</ul>
</div>
<div id="assumptions-diagnostics-and-model-evaluation" class="section level3">
<h3>11 Assumptions, diagnostics, and model evaluation</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/KidIQ/">KidIQ/</a>
<ul>
<li><a href="KidIQ/kidiq.html">kidiq.html</a> - Linear regression with multiple predictors</li>
<li><a href="KidIQ/kidiq_loo.html">kidiq_loo.html</a> - Linear regression and leave-one-out cross-validation</li>
<li><a href="KidIQ/kidiq_R2.html">kidiq_R2.html</a> - Linear regression and Bayes-R2 and LOO-R2</li>
<li><a href="KidIQ/kidiq_kcv.html">kidiq_kcv.html</a> - Linear regression and K-fold cross-validation</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Residuals/">Residuals/</a>
<ul>
<li><a href="Residuals/residuals.html">residuals.html</a> - Plotting the data and fitted model</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Introclass/">Introclass/</a>
<ul>
<li><a href="Introclass/residual_plots.html">residual_plots.html</a> - Plot residuals vs. predicted values, or residuals vs. observed values?</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Newcomb/">Newcomb/</a>
<ul>
<li><a href="Newcomb/newcomb.html">newcomb.html</a> - Posterior predictive checking of Normal model for Newcomb’s speed of light data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Unemployment/">Unemployment/</a>
<ul>
<li><a href="Unemployment/unemployment.html">unemployment.html</a> - Time series fit and posterior predictive model checking for unemployment series</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Rsquared/">Rsquared/</a>
<ul>
<li><a href="Rsquared/rsquared.html">rsquared.html</a> - Bayesian R^2</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/CrossValidation/">CrossValidation/</a>
<ul>
<li><a href="CrossValidation/crossvalidation.html">crossvalidation.html</a> - Demonstration of cross validation</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/FakeKCV/">FakeKCV/</a>
<ul>
<li><a href="FakeKCV/fake_kcv.html">fake_kcv.html</a> - Demonstration of <span class="math inline">\(K\)</span>-fold cross-validation using simulated data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Pyth/">Pyth/</a></li>
</ul>
</div>
<div id="transformations" class="section level3">
<h3>12 Transformations</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/KidIQ/">KidIQ/</a>
<ul>
<li><a href="KidIQ/kidiq.html">kidiq.html</a> - Linear regression with multiple predictors</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Earnings/">Earnings/</a>
<ul>
<li><a href="Earnings/earnings_regression.html">earnings_regression.html</a> - Predict respondents’ yearly earnings using survey data from 1990.</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Gay/">Gay/</a>
<ul>
<li><a href="Gay/gay_simple.html">gay_simple.html</a> - Simple models (linear and discretized age) and political attitudes as a function of age</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Mesquite/">Mesquite/</a>
<ul>
<li><a href="Mesquite/mesquite.html">mesquite.html</a> - Predicting the yields of mesquite bushes</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Student/">Student/</a>
<ul>
<li><a href="Student/student.html">student.html</a> - Models for regression coefficients</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Pollution/">Pollution/</a>
<ul>
<li><a href="Pollution/pollution.html">pollution.html</a> - Pollution data.</li>
</ul></li>
</ul>
</div>
<div id="logistic-regression" class="section level3">
<h3>13 Logistic regression</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/NES/">NES/</a>
<ul>
<li><a href="NES/nes_logistic.html">nes_logistic.html</a> - Logistic regression, identifiability, and separation</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/LogisticPriors/">LogisticPriors/</a>
<ul>
<li><a href="LogisticPriors/logistic_priors.html">logistic_priors.html</a> - Effect of priors in logistic regression</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Arsenic/">Arsenic/</a>
<ul>
<li><a href="Arsenic/arsenic_logistic_building.html">arsenic_logistic_building.html</a> - Building a logistic regression model: wells in Bangladesh</li>
</ul></li>
</ul>
</div>
<div id="working-with-logistic-regression" class="section level3">
<h3>14 Working with logistic regression</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/LogitGraphs/">LogitGraphs/</a>
<ul>
<li><a href="LogitGraphs/logitgraphs.html">logitgraphs.html</a> - Different ways of displaying logistic regression</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/NES/">NES/</a>
<ul>
<li><a href="NES/nes_logistic.html">nes_logistic.html</a> - Logistic regression, identifiability, and separation</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Rodents/">Rodents/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Arsenic/">Arsenic/</a>
<ul>
<li><a href="Arsenic/arsenic_logistic_residuals.html">arsenic_logistic_residuals.html</a> - Residual plots for a logistic regression model: wells in Bangladesh</li>
<li><a href="Arsenic/arsenic_logistic_apc.html">arsenic_logistic_apc.html</a> - Average predictice comparisons for a logistic regression model: wells in Bangladesh</li>
</ul></li>
</ul>
</div>
<div id="other-generalized-linear-models" class="section level3">
<h3>15 Other generalized linear models</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/PoissonExample/">PoissonExample/</a>
<ul>
<li><a href="PoissonExample/poisson_regression.html">PoissonExample.html</a> - Demonstrate Poisson regression with simulated data.</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Roaches/">Roaches/</a>
<ul>
<li><a href="Roaches/roaches.html">roaches.html</a> - Analyse the effect of integrated pest management on reducing cockroach levels in urban apartments</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Storable/">Storable/</a>
<ul>
<li><a href="Storable/storable.html">storable.html</a> - Ordered categorical data analysis with a study from experimental economics, on the topic of ``storable votes.’’</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Robit/">Robit/</a>
<ul>
<li><a href="Robit/robit.html">robit.html</a> - Comparison of robit and logit models for binary data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Earnings/">Earnings/</a>
<ul>
<li><a href="Earnings/earnings_compound.html">earnings_compound.html</a> - Compound discrete-continuos model</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/RiskyBehavior/">RiskyBehavior/</a>
<ul>
<li><a href="RiskyBehavior/risky.html">risky.html</a> Risky behavior data.</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/NES/">NES/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Lalonde/">Lalonde/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Congress/">Congress/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/AcademyAwards/">AcademyAwards/</a></li>
</ul>
</div>
<div id="design-and-sample-size-decisions" class="section level3">
<h3>16 Design and sample size decisions</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectricCompany/">ElectricCompany/</a>
<ul>
<li><a href="ElectricCompany/electric.html">electric.html</a> - Analysis of “Electric company” data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/SampleSize/">SampleSize/</a>
<ul>
<li><a href="DataCollection/simulation.html">simulation.html</a> - Sample size simulation</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/FakeMidtermFinal/">FakeMidtermFinal/</a>
<ul>
<li><a href="FakeMidtermFinal/simulation_based_design.html">simulation_based_design.html</a> - Fake dataset of a randomized experiment on student grades</li>
</ul></li>
</ul>
</div>
<div id="poststratification-and-missing-data-imputation" class="section level3">
<h3>17 Poststratification and missing-data imputation</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Poststrat/">Poststrat/</a>
<ul>
<li><a href="Poststrat/poststrat.html">poststrat.html</a> - Poststratification after estimation</li>
<li><a href="Poststrat/poststrat2.html">poststrat2.html</a> - Poststratification after estimation</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Imputation/">Imputation/</a>
<ul>
<li><a href="Imputation/imputation.html">imputation.html</a> - Regression-based imputation for the Social Indicators Survey</li>
<li><a href="Imputation/imputation_gg.html">imputation_gg.html</a> - Regression-based imputation for the Social Indicators Survey, dplyr/ggplot version</li>
</ul></li>
</ul>
</div>
<div id="causal-inference-basics-and-randomized-experiments" class="section level3">
<h3>18 Causal inference basics and randomized experiments</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Sesame/">Sesame/</a>
<ul>
<li><a href="Sesame/sesame.html">sesame.html</a> - Causal analysis of Sesame Street experiment</li>
</ul></li>
</ul>
</div>
<div id="causal-inference-using-regression-on-the-treatment-variable" class="section level3">
<h3>19 Causal inference using regression on the treatment variable</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectricCompany/">ElectricCompany/</a>
<ul>
<li><a href="ElectricCompany/electric.html">electric.html</a> - Analysis of “Electric company” data</li>
</ul></li>
<li><a href="(https://github.com/avehtari/ROS-Examples/tree/master/Incentives/)">Incentives/</a>
<ul>
<li><a href="Incentives/incentives.html">incentives.html</a> - Simple analysis of incentives data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Cows/">Cows/</a></li>
</ul>
</div>
<div id="observational-studies-with-all-confounders-assumed-to-be-measured" class="section level3">
<h3>20 Observational studies with all confounders assumed to be measured</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectricCompany/">ElectricCompany/</a>
<ul>
<li><a href="ElectricCompany/electric.html">electric.html</a> - Analysis of “Electric company” data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Childcare/">Childcare/</a>
<ul>
<li><a href="Childcare/childcare.html">childcare.html</a> - Infant Health and Development Program (IHDP) example.</li>
</ul></li>
</ul>
</div>
<div id="more-advanced-topics-in-causal-inference" class="section level3">
<h3>21 More advanced topics in causal inference</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Sesame/">Sesame/</a>
<ul>
<li><a href="Sesame/sesame.html">sesame.html</a> - Causal analysis of Sesame Street experiment</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Pypass/">Bypass/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ChileSchools/">ChileSchools/</a>
<ul>
<li><a href="ChileSchools/chile_schools.html">chile_schools.html</a> - ChileSchools example.</li>
</ul></li>
</ul>
</div>
<div id="advanced-regression-and-multilevel-models" class="section level3">
<h3>22 Advanced regression and multilevel models</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Golf/">Golf/</a>
<ul>
<li><a href="Golf/golf.html">golf.html</a> - Gold putting accuracy: Fitting a nonlinear model using Stan</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Gay/">Gay/</a>
<ul>
<li><a href="Gay/gay.html">gay.html</a> - Nonlinear models (Loess, B-spline, GP-spline, and BART) and political attitudes as a function of age</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/">ElectionsEconomy/</a>
<ul>
<li><a href="ElectionsEconomy/hibbs.html">hibbs.html</a> - Predicting presidential vote share from the economy</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Scalability/">Scalability/</a>
<ul>
<li><a href="Scalability/scalability.html">scalability.html</a> - Demonstrate computation speed with 100 000 observations.</li>
</ul></li>
</ul>
</div>
<div id="appendix-a" class="section level3">
<h3>Appendix A</h3>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Coins/">Coins/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Mile/">Mile/</a>
<ul>
<li><a href="Mile/mile.html">mile.html</a> - Trend of record times in the mile run</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Parabola/">Parabola/</a>
<ul>
<li><a href="Parabola/parabola.html">parabola.html</a> - Demonstration of using Stan for optimization</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Restaurant/">Restaurant/</a>
<ul>
<li><a href="Restaurant/restaurant.html">restaurant.html</a> - Demonstration of using Stan for optimization</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/DifferentSoftware/">DifferentSoftware/</a>
<ul>
<li><a href="DifferentSoftware/linear.html">linear.html</a> - Linear regression using different software options</li>
</ul></li>
</ul>
<hr />
</div>
</div>
<div id="examples-alphabetically" class="section level2">
<h2>Examples alphabetically</h2>
<ul>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/AcademyAwards/">AcademyAwards/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/AgePeriodCohort/">AgePeriodCohort/</a>
<ul>
<li><a href="AgePeriodCohort/births.html">births.html</a> - Age adjustment</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Arsenic/">Arsenic/</a>
<ul>
<li><a href="Arsenic/arsenic_logistic_building.html">arsenic_logistic_building.html</a> - Building a logistic regression model: wells in Bangladesh</li>
<li><a href="Arsenic/arsenic_logistic_residuals.html">arsenic_logistic_residuals.html</a> - Residual plots for a logistic regression model: wells in Bangladesh</li>
<li><a href="Arsenic/arsenic_logistic_apc.html">arsenic_logistic_apc.html</a> - Average predictice comparisons for a logistic regression model: wells in Bangladesh</li>
<li><a href="Arsenic/arsenic_logistic_building_optimizing.html">arsenic_logistic_building_optimizing.html</a> - Building a logistic regression model: wells in Bangladesh. A version with normal approximation at the mode.</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Balance/">Balance/</a>
<ul>
<li><a href="Balance/treatcontrol.html">treatcontrol.html</a></li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Beauty/">Beauty/</a>
<ul>
<li><a href="Beauty/beauty.html">beauty.html</a> - Student evaluations of instructors’ beauty and teaching quality</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Bypass/">Bypass/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/CausalDiagram/">CausalDiagram/</a>
<ul>
<li><a href="CausalDiagram/diagrams.html">diagrams.html</a> - Plot causal diagram</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/CentralLimitTheorem/">CentralLimitTheorem/</a>
<ul>
<li><a href="CentralLimitTheorem/heightweight.html">heightweight.html</a> - Illustrate central limit theorem and normal distribution</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Childcare/">Childcare/</a>
<ul>
<li><a href="Childcare/childcare.html">childcare.html</a> - Infant Health and Development Program (IHDP) example.</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ChileSchools/">ChileSchools/</a>
<ul>
<li><a href="ChileSchools/chile_schools.html">chile_schools.html</a> - ChileSchools example.</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Coins/">Coins/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Congress/">Congress/</a>
<ul>
<li><a href="Congress/congress.html">congress.html</a> - Predictive uncertainty for congressional elections</li>
<li><a href="Congress/congress_plots.html">congress_plots.html</a> - Predictive uncertainty for congressional elections</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Coop/">Coop/</a>
<ul>
<li><a href="Coop/riverbay.html">riverbay.html</a> - Example of hypothesis testing</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Coverage/">Coverage/</a>
<ul>
<li><a href="Coverage/coverage.html">coverage.html</a> - Example of coverage</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Cows/">Cows/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/CrossValidation/">CrossValidation/</a>
<ul>
<li><a href="CrossValidation/crossvalidation.html">crossvalidation.html</a> - Demonstration of cross validation</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/SampleSize/">SampleSize/</a>
<ul>
<li><a href="DataCollection/simulation.html">simulation.html</a> - Sample size simulation</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Death/">Death/</a>
<ul>
<li><a href="Death/polls.html">polls.html</a> - Proportion of American adults supporting the death penalty</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/DifferentSoftware/">DifferentSoftware/</a>
<ul>
<li><a href="DifferentSoftware/linear.html">linear.html</a> - Linear regression using different software options</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Earnings/">Earnings/</a>
<ul>
<li><a href="Earnings/earnings_regression.html">earnings_regression.html</a> - Predict respondents’ yearly earnings using survey data from 1990.</li>
<li><a href="Earnings/earnings_bootstrap.html">earnings_bootstrap.html</a> - Bootstrapping to simulate the sampling distribution</li>
<li><a href="Earnings/earnings_compound.html">earnings_compound.html</a> - Compound discrete-continuos model</li>
<li><a href="Earnings/height_and_weight.html">height_and_weight.html</a> - Predict weight</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/">ElectionsEconomy/</a>
<ul>
<li><a href="ElectionsEconomy/bayes.html">bayes.html</a> - Demonstration of Bayesian information aggregation</li>
<li><a href="ElectionsEconomy/hibbs.html">hibbs.html</a> - Predicting presidential vote share from the economy</li>
<li><a href="ElectionsEconomy/hills.html">hills.html</a> - Present uncertainty in parameter estimates</li>
<li><a href="ElectionsEconomy/hibbs_coverage.html">hibbs_coverage.html</a> - Checking the model-fitting procedure using fake-data simulation.</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/ElectricCompany/">ElectricCompany/</a>
<ul>
<li><a href="ElectricCompany/electric.html">electric.html</a> - Analysis of “Electric company” data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/FakeKCV/">FakeKCV/</a>
<ul>
<li><a href="FakeKCV/fake_kcv.html">fake_kcv.html</a> - Demonstration of <span class="math inline">\(K\)</span>-fold cross-validation using simulated data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/FakeMidtermFinal/">FakeMidtermFinal/</a>
<ul>
<li><a href="FakeMidtermFinal/simulation.html">simulation.html</a> - Fake dataset of 1000 students’ scores on a midterm and final exam</li>
<li><a href="FakeMidtermFinal/simulation_based_design.html">simulation_based_design.html</a> - Fake dataset of a randomized experiment on student grades</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/FrenchElection/">FrenchElection/</a>
<ul>
<li><a href="FrenchElection/ps_primaire.html">ps_primaire.html</a> - French Election data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Gay/">Gay/</a>
<ul>
<li><a href="Gay/gay_simple.html">gay_simple.html</a> - Simple models (linear and discretized age) and political attitudes as a function of age</li>
<li><a href="Gay/gay.html">gay.html</a> - Nonlinear models (Loess, B-spline, GP-spline, and BART) and political attitudes as a function of age</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Girls/">Girls/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Golf/">Golf/</a>
<ul>
<li><a href="Golf/golf.html">golf.html</a> - Gold putting accuracy: Fitting a nonlinear model using Stan</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/HDI/">HDI/</a>
<ul>
<li><a href="HDI/hdi.html">hdi.html</a> - Human Development Index - Looking at data in different ways</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/HealthExpenditure/">HealthExpenditure/</a>
<ul>
<li><a href="HealthExpenditure/healthexpenditure.html">healthexpenditure.html</a> - Discovery through graphs of data and models</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Helicopters/">Helicopters/</a>
<ul>
<li><a href="Helicopters/helicopters.html">helicopters.html</a> - Example data file for helicopter flying time exercise</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Imputation/">Imputation/</a>
<ul>
<li><a href="Imputation/imputation.html">imputation.html</a> - Regression-based imputation for the Social Indicators Survey</li>
<li><a href="Imputation/imputation_gg.html">imputation_gg.html</a> - Regression-based imputation for the Social Indicators Survey, dplyr/ggplot version</li>
</ul></li>
<li><a href="(https://github.com/avehtari/ROS-Examples/tree/master/Incentives/)">Incentives/</a>
<ul>
<li><a href="Incentives/incentives.html">incentives.html</a> - Simple analysis of incentives data</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Influence/">Influence/</a>
<ul>
<li><a href="Influence/influence.html">influence.html</a> - Influence of individual points in a fitted regression</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Interactions/">Interactions/</a>
<ul>
<li><a href="Interactions/interactions.html">interactions.html</a> - Plot interaction example figure</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Introclass/">Introclass/</a>
<ul>
<li><a href="Introclass/residual_plots.html">residual_plots.html</a> - Plot residuals vs. predicted values, or residuals vs. observed values?</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/KidIQ/">KidIQ/</a>
<ul>
<li><a href="KidIQ/kidiq.html">kidiq.html</a> - Linear regression with multiple predictors</li>
<li><a href="KidIQ/kidiq_loo.html">kidiq_loo.html</a> - Linear regression and leave-one-out cross-validation</li>
<li><a href="KidIQ/kidiq_R2.html">kidiq_R2.html</a> - Linear regression and Bayes-R2 and LOO-R2</li>
<li><a href="KidIQ/kidiq_kcv.html">kidiq_kcv.html</a> - Linear regression and K-fold cross-validation</li>
</ul></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/Lalonde/">Lalonde/</a></li>
<li><a href="https://github.com/avehtari/ROS-Examples/tree/master/LogisticPriors/">LogisticPriors/</a>
<ul>
<li><a href="LogisticPriors/logistic_priors.html">logistic_priors.html</a> - Effect of priors in logistic regression</li>