examples.Rmd

---
title: "Regression and Other Stories - Examples"
author: "Andrew Gelman, Jennifer Hill, Aki Vehtari"
date: "Page updated: `r format.Date(file.mtime('index.Rmd'),'%Y-%m-%d')`"
---

-------------

## Introduction

- 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.
- For R programming basics see Appendix A of Regression and Other Stories. If you want to learn more, see our recommendations for [R programming and visualization with R](R_visualizaton.html).

- The folders below (ending /) point to the code (.R and .Rmd)
  and `data` folders (.csv or .txt) in github, and .html -files
  point to knitted notebooks.
- Most examples have cleaned data in .csv file in `data` subfolder
  for easy experimenting. For completeness and reproducibility, the
  data subfolders have also the raw data and `*_setup.R` 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).
- For easy access to data sets, there is an R package `rosdata`. You can install it with a command `remotes::install_github("avehtari/ROS-Examples",subdir = "rpackage")`. Then you can access data, for example, as
`library(rosdata)`, `data(wells)`, `head(wells)`. You can get the list of data sets with `?rosdata`.

- When running the notebooks, to avoid need to switch the working directory, `rprojroot` 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
```
library("rprojroot")
root<-has_file(".ROS-Examples-root")$make_fix_file()
```
will find the file `.ROS-Examples-root` which is in the `ROS-Examples` directory, and will set the full path according to that. Then, for example,
```
wells <- read.csv(root("Arsenic/data","wells.csv"))
```
finds the `wells.csv` file, no matter where you have placed or renamed the `ROS-Examples` directory. When you switch to another example, there is no need to switch the working directory.

-------------

## Examples by chapters

### 1  Introduction
- [ElectionsEconomy/](https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/)
    - [hibbs.html](ElectionsEconomy/hibbs.html) - Predicting presidential vote share from the economy
- [ElectricCompany/](https://github.com/avehtari/ROS-Examples/tree/master/ElectricCompany/)
    - [electric.html](ElectricCompany/electric.html) - Analysis of "Electric company" data
- [Peacekeeping/](https://github.com/avehtari/ROS-Examples/tree/master/Peacekeeping/)
    - [peace.html](Peacekeeping/peace.html) - Outcomes after civil war in countries with and without United Nations peacekeeping
- [SimpleCausal/](https://github.com/avehtari/ROS-Examples/tree/master/SimpleCausal/)
    - [causal.html](SimpleCausal/causal.html) - Simple graphs illustrating regression for causal inference
- [Helicopters/](https://github.com/avehtari/ROS-Examples/tree/master/Helicopters/)
    - [helicopters.html](Helicopters/helicopters.html) - Example data file for helicopter flying time exercise

### 2  Data and measurement
- [HDI/](https://github.com/avehtari/ROS-Examples/tree/master/HDI/)
    - [hdi.html](HDI/hdi.html) - Human Development Index - Looking at data in different ways
- [Pew/](https://github.com/avehtari/ROS-Examples/tree/master/Pew/)
    - [pew.html](Pew/pew.html) - Miscellaneous analyses using raw Pew data
- [HealthExpenditure/](https://github.com/avehtari/ROS-Examples/tree/master/HealthExpenditure/)
    - [healthexpenditure.html](HealthExpenditure/healthexpenditure.html) - Discovery through graphs of data and models
- [Names/](https://github.com/avehtari/ROS-Examples/tree/master/Names/)
    - [names.html](Names/names.html) - Names - Distributions of names of American babies
    - [lastletters.html](Names/lastletters.html) - Last letters - Distributions of last letters of names of American babies
- [AgePeriodCohort/](https://github.com/avehtari/ROS-Examples/tree/master/AgePeriodCohort/)
    - [births.html](AgePeriodCohort/births.html) - Age adjustment
- [Congress/](https://github.com/avehtari/ROS-Examples/tree/master/Congress/)
    - [congress_plots.html](Congress/congress_plots.html) - Predictive uncertainty for congressional elections

### 3  Some basic methods in mathematics and probability
- [Mile/](https://github.com/avehtari/ROS-Examples/tree/master/Mile/)
    - [mile.html](Mile/mile.html) - Trend of record times in the mile run
- [Metabolic/](https://github.com/avehtari/ROS-Examples/tree/master/Metabolic/)
    - [metabolic.html](Metabolic/metabolic.html) - How to interpret a power law or log-log regression
- [Earnings/](https://github.com/avehtari/ROS-Examples/tree/master/Earnings/)
    - [height_and_weight.html](Earnings/height_and_weight.html) - Predict weight
- [CentralLimitTheorem/](https://github.com/avehtari/ROS-Examples/tree/master/CentralLimitTheorem/)
    - [heightweight.html](CentralLimitTheorem/heightweight.html) - Illustrate central limit theorem and normal distribution
- [Stents/](https://github.com/avehtari/ROS-Examples/tree/master/Stents/)
    - [stents.html](Stents/stents.html) - Stents - comparing distributions

### 4  Generative models and statistical inference
- [Coverage/](https://github.com/avehtari/ROS-Examples/tree/master/Coverage/)
    - [coverage.html](Coverage/coverage.html) - Example of coverage
- [Death/](https://github.com/avehtari/ROS-Examples/tree/master/Death/)
    - [polls.html](Death/polls.html) - Proportion of American adults supporting the death penalty
- [Coop/](https://github.com/avehtari/ROS-Examples/tree/master/Coop/)
    - [riverbay.html](Coop/riverbay.html) - Example of hypothesis testing
- [Girls/](https://github.com/avehtari/ROS-Examples/tree/master/Girls/)

### 5  Simulation
- [ProbabilitySimulation/](https://github.com/avehtari/ROS-Examples/tree/master/ProbabilitySimulation/)
    - [probsim.html](ProbabilitySimulation/probsim.html) - Simulation of probability models
- [Earnings/](https://github.com/avehtari/ROS-Examples/tree/master/Earnings/)
    - [earnings_bootstrap.html](Earnings/earnings_bootstrap.html) - Bootstrapping to simulate the sampling distribution

### 6  Background on regression modeling
- [Simplest/](https://github.com/avehtari/ROS-Examples/tree/master/Simplest/)
    - [simplest.html](Simplest/simplest.html) - Linear regression with a single predictor
    - [simplest_lm.html](Simplest/simplest_lm.html) - Linear least squares regression with a single predictor
- [Earnings/](https://github.com/avehtari/ROS-Examples/tree/master/Earnings/)
    - [earnings_regression.html](Earnings/earnings_regression.html) - Predict respondents' yearly earnings using survey data from 1990.
- [PearsonLee/](https://github.com/avehtari/ROS-Examples/tree/master/PearsonLee/)
    - [heights.html](PearsonLee/heights.html) - The heredity of height. Published in 1903 by Karl Pearson and Alice Lee.
- [FakeMidtermFinal/](https://github.com/avehtari/ROS-Examples/tree/master/FakeMidtermFinal/)
    - [simulation.html](FakeMidtermFinal/simulation.html) - Fake dataset of 1000 students' scores on a midterm and final exam

### 7  Linear regression with a single predictor
- [ElectionsEconomy/](https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/)
    - [hibbs.html](ElectionsEconomy/hibbs.html) - Predicting presidential vote share from the economy
    - [hills.html](ElectionsEconomy/hills.html) - Present uncertainty in parameter estimates
    - [hibbs_coverage.html](ElectionsEconomy/hibbs_coverage.html) - Checking the coverage of intervals
   - [Simplest/](Simplest/)
    - [simplest.html](Simplest/simplest.html) - Linear regression with a single predictor
    - [simplest_lm.html](Simplest/simplest_lm.html) - Linear least squares regression with a single predictor

### 8 Fitting regression models
- [ElectionsEconomy/](https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/)
    - [hibbs.html](ElectionsEconomy/hibbs.html) - Predicting presidential vote share from the economy
- [Influence/](https://github.com/avehtari/ROS-Examples/tree/master/Influence/)
    - [influence.html](Influence/influence.html) - Influence of individual points in a fitted regression

### 9 Prediction and Bayesian inference 
- [ElectionsEconomy/](https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/)
    - [hibbs.html](ElectionsEconomy/hibbs.html) - Predicting presidential vote share from the economy
    - [bayes.html](ElectionsEconomy/bayes.html) - Demonstration of Bayesian information aggregation
- [SexRatio/](https://github.com/avehtari/ROS-Examples/tree/master/SexRatio/)
    - [sexratio.html](SexRatio/sexratio.html) - Example where an informative prior makes a difference
- [Earnings/](https://github.com/avehtari/ROS-Examples/tree/master/Earnings/)
    - [height_and_weight.html](Earnings/height_and_weight.html) - Predict weight
    - [earnings_regression.html](Earnings/earnings_regression.html) - Predict respondents' yearly earnings using survey data from 1990.

### 10  Linear regression with multiple predictors
- [KidIQ/](https://github.com/avehtari/ROS-Examples/tree/master/KidIQ/)
    - [kidiq.html](KidIQ/kidiq.html) - Linear regression with multiple predictors
- [Earnings/](https://github.com/avehtari/ROS-Examples/tree/master/Earnings/)
    - [height_and_weight.html](Earnings/height_and_weight.html) - Predict weight
- [Congress/](https://github.com/avehtari/ROS-Examples/tree/master/Congress/)
    - [congress.html](Congress/congress.html) - Predictive uncertainty for congressional elections
- [NES/](https://github.com/avehtari/ROS-Examples/tree/master/NES/)
    - [nes_linear.html](NES/nes_linear.html) - Fitting the same regression to many datasets
- [Beauty/](https://github.com/avehtari/ROS-Examples/tree/master/Beauty/)
    - [beauty.html](Beauty/beauty.html) - Student evaluations of instructors’ beauty and teaching quality

### 11  Assumptions, diagnostics, and model evaluation
- [KidIQ/](https://github.com/avehtari/ROS-Examples/tree/master/KidIQ/)
    - [kidiq.html](KidIQ/kidiq.html) - Linear regression with multiple predictors
    - [kidiq_loo.html](KidIQ/kidiq_loo.html) - Linear regression and leave-one-out cross-validation
    - [kidiq_R2.html](KidIQ/kidiq_R2.html) - Linear regression and Bayes-R2 and LOO-R2
    - [kidiq_kcv.html](KidIQ/kidiq_kcv.html) - Linear regression and K-fold cross-validation
- [Residuals/](https://github.com/avehtari/ROS-Examples/tree/master/Residuals/)
    - [residuals.html](Residuals/residuals.html) - Plotting the data and fitted model
- [Introclass/](https://github.com/avehtari/ROS-Examples/tree/master/Introclass/)
    - [residual_plots.html](Introclass/residual_plots.html) - Plot residuals vs.\ predicted values, or residuals vs.\ observed values?
- [Newcomb/](https://github.com/avehtari/ROS-Examples/tree/master/Newcomb/)
    - [newcomb.html](Newcomb/newcomb.html) - Posterior predictive checking of Normal model for Newcomb's speed of light data
- [Unemployment/](https://github.com/avehtari/ROS-Examples/tree/master/Unemployment/)
    - [unemployment.html](Unemployment/unemployment.html) - Time series fit and posterior predictive model checking for unemployment series
- [Rsquared/](https://github.com/avehtari/ROS-Examples/tree/master/Rsquared/)
    - [rsquared.html](Rsquared/rsquared.html) - Bayesian R^2
- [CrossValidation/](https://github.com/avehtari/ROS-Examples/tree/master/CrossValidation/)
    - [crossvalidation.html](CrossValidation/crossvalidation.html) - Demonstration of cross validation
- [FakeKCV/](https://github.com/avehtari/ROS-Examples/tree/master/FakeKCV/)
    - [fake_kcv.html](FakeKCV/fake_kcv.html) - Demonstration of $K$-fold cross-validation using simulated data
- [Pyth/](https://github.com/avehtari/ROS-Examples/tree/master/Pyth/)

### 12  Transformations
- [KidIQ/](https://github.com/avehtari/ROS-Examples/tree/master/KidIQ/)
    - [kidiq.html](KidIQ/kidiq.html) - Linear regression with multiple predictors
- [Earnings/](https://github.com/avehtari/ROS-Examples/tree/master/Earnings/)
    - [earnings_regression.html](Earnings/earnings_regression.html) - Predict respondents' yearly earnings using survey data from 1990.
- [Gay/](https://github.com/avehtari/ROS-Examples/tree/master/Gay/)
    - [gay_simple.html](Gay/gay_simple.html) - Simple models (linear and discretized age) and political attitudes as a function of age
- [Mesquite/](https://github.com/avehtari/ROS-Examples/tree/master/Mesquite/)
    - [mesquite.html](Mesquite/mesquite.html) - Predicting the yields of mesquite bushes
- [Student/](https://github.com/avehtari/ROS-Examples/tree/master/Student/)
    - [student.html](Student/student.html) - Models for regression coefficients
- [Pollution/](https://github.com/avehtari/ROS-Examples/tree/master/Pollution/)
    - [pollution.html](Pollution/pollution.html) - Pollution data.

### 13  Logistic regression
- [NES/](https://github.com/avehtari/ROS-Examples/tree/master/NES/)
    - [nes_logistic.html](NES/nes_logistic.html) - Logistic regression, identifiability, and separation
- [LogisticPriors/](https://github.com/avehtari/ROS-Examples/tree/master/LogisticPriors/)
    - [logistic_priors.html](LogisticPriors/logistic_priors.html) - Effect of priors in logistic regression
- [Arsenic/](https://github.com/avehtari/ROS-Examples/tree/master/Arsenic/)
    - [arsenic_logistic_building.html](Arsenic/arsenic_logistic_building.html) - Building a logistic regression model: wells in Bangladesh

### 14  Working with logistic regression
- [LogitGraphs/](https://github.com/avehtari/ROS-Examples/LogitGraphs/)
    - [logitgraphs.html](LogitGraphs/logitgraphs.html) - Different ways of displaying logistic regression
- [NES/](https://github.com/avehtari/ROS-Examples/tree/master/NES/)
    - [nes_logistic.html](NES/nes_logistic.html) - Logistic regression, identifiability, and separation
- [Rodents/](https://github.com/avehtari/ROS-Examples/tree/master/Rodents/)
- [Arsenic/](https://github.com/avehtari/ROS-Examples/tree/master/Arsenic/)
    - [arsenic_logistic_residuals.html](Arsenic/arsenic_logistic_residuals.html) - Residual plots for a logistic regression model: wells in Bangladesh
    - [arsenic_logistic_apc.html](Arsenic/arsenic_logistic_apc.html) - Average predictice comparisons for a logistic regression model: wells in Bangladesh

### 15  Other generalized linear models
- [PoissonExample/](https://github.com/avehtari/ROS-Examples/tree/master/PoissonExample/)
    - [PoissonExample.html](PoissonExample/poisson_regression.html) - Demonstrate Poisson regression with simulated data.
- [Roaches/](https://github.com/avehtari/ROS-Examples/tree/master/Roaches/)
    - [roaches.html](Roaches/roaches.html) - Analyse the effect of integrated pest management on reducing cockroach levels in urban apartments
- [Storable/](https://github.com/avehtari/ROS-Examples/tree/master/Storable/) 
    - [storable.html](Storable/storable.html) - Ordered categorical data analysis with a study from experimental economics, on the topic of ``storable votes.''
- [Robit/](https://github.com/avehtari/ROS-Examples/tree/master/Robit/)
    - [robit.html](Robit/robit.html) - Comparison of robit and logit models for binary data
- [Earnings/](https://github.com/avehtari/ROS-Examples/tree/master/Earnings/)
    - [earnings_compound.html](Earnings/earnings_compound.html) - Compound discrete-continuos model
- [RiskyBehavior/](https://github.com/avehtari/ROS-Examples/tree/master/RiskyBehavior/)
    - [risky.html](RiskyBehavior/risky.html) Risky behavior data.
- [NES/](https://github.com/avehtari/ROS-Examples/tree/master/NES/)
- [Lalonde/](https://github.com/avehtari/ROS-Examples/tree/master/Lalonde/)
- [Congress/](https://github.com/avehtari/ROS-Examples/tree/master/Congress/)
- [AcademyAwards/](https://github.com/avehtari/ROS-Examples/tree/master/AcademyAwards/)

### 16  Design and sample size decisions
- [ElectricCompany/](https://github.com/avehtari/ROS-Examples/tree/master/ElectricCompany/)
    - [electric.html](ElectricCompany/electric.html) - Analysis of "Electric company" data
- [SampleSize/](https://github.com/avehtari/ROS-Examples/tree/master/SampleSize/)
    - [simulation.html](DataCollection/simulation.html) - Sample size simulation
- [FakeMidtermFinal/](https://github.com/avehtari/ROS-Examples/tree/master/FakeMidtermFinal/)
    - [simulation_based_design.html](FakeMidtermFinal/simulation_based_design.html) - Fake dataset of a randomized experiment on student grades

### 17  Poststratification and missing-data imputation
- [Poststrat/](https://github.com/avehtari/ROS-Examples/tree/master/Poststrat/)
    - [poststrat.html](Poststrat/poststrat.html) - Poststratification after estimation
    - [poststrat2.html](Poststrat/poststrat2.html) - Poststratification after estimation
- [Imputation/](https://github.com/avehtari/ROS-Examples/tree/master/Imputation/)
    - [imputation.html](Imputation/imputation.html) - Regression-based imputation for the Social Indicators Survey
    - [imputation_gg.html](Imputation/imputation_gg.html) - Regression-based imputation for the Social Indicators Survey, dplyr/ggplot version

### 18  Causal inference basics and randomized experiments
- [Sesame/](https://github.com/avehtari/ROS-Examples/tree/master/Sesame/)
    - [sesame.html](Sesame/sesame.html) - Causal analysis of Sesame Street experiment

### 19  Causal inference using regression on the treatment variable
- [ElectricCompany/](https://github.com/avehtari/ROS-Examples/tree/master/ElectricCompany/)
    - [electric.html](ElectricCompany/electric.html) - Analysis of "Electric company" data
- [Incentives/]((https://github.com/avehtari/ROS-Examples/tree/master/Incentives/))
    - [incentives.html](Incentives/incentives.html) - Simple analysis of incentives data
- [Cows/](https://github.com/avehtari/ROS-Examples/tree/master/Cows/)

### 20  Observational studies with all confounders assumed to be measured
- [ElectricCompany/](https://github.com/avehtari/ROS-Examples/tree/master/ElectricCompany/)
    - [electric.html](ElectricCompany/electric.html) - Analysis of "Electric company" data
- [Childcare/](https://github.com/avehtari/ROS-Examples/tree/master/Childcare/)
    - [childcare.html](Childcare/childcare.html) - Infant Health and Development Program (IHDP) example.

### 21  More advanced topics in causal inference
- [Sesame/](https://github.com/avehtari/ROS-Examples/tree/master/Sesame/)
    - [sesame.html](Sesame/sesame.html) - Causal analysis of Sesame Street experiment
- [Bypass/](https://github.com/avehtari/ROS-Examples/tree/master/Pypass/)
- [ChileSchools/](https://github.com/avehtari/ROS-Examples/tree/master/ChileSchools/)
    - [chile_schools.html](ChileSchools/chile_schools.html) - ChileSchools example.

### 22  Advanced regression and multilevel models
- [Golf/](https://github.com/avehtari/ROS-Examples/tree/master/Golf/)
    - [golf.html](Golf/golf.html) - Gold putting accuracy: Fitting a nonlinear model using Stan
- [Gay/](https://github.com/avehtari/ROS-Examples/tree/master/Gay/)
    - [gay.html](Gay/gay.html) - Nonlinear models (Loess, B-spline, GP-spline, and BART) and political attitudes as a function of age
- [ElectionsEconomy/](https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/)
    - [hibbs.html](ElectionsEconomy/hibbs.html) - Predicting presidential vote share from the economy
- [Scalability/](https://github.com/avehtari/ROS-Examples/tree/master/Scalability/)
    - [scalability.html](Scalability/scalability.html) - Demonstrate computation speed with 100 000 observations.

### Appendix A
- [Coins/](https://github.com/avehtari/ROS-Examples/tree/master/Coins/)
- [Mile/](https://github.com/avehtari/ROS-Examples/tree/master/Mile/)
    - [mile.html](Mile/mile.html) - Trend of record times in the mile run
- [Parabola/](https://github.com/avehtari/ROS-Examples/tree/master/Parabola/)
    - [parabola.html](Parabola/parabola.html) - Demonstration of using Stan for optimization
- [Restaurant/](https://github.com/avehtari/ROS-Examples/tree/master/Restaurant/)
    - [restaurant.html](Restaurant/restaurant.html) - Demonstration of using Stan for optimization
- [DifferentSoftware/](https://github.com/avehtari/ROS-Examples/tree/master/DifferentSoftware/)
    - [linear.html](DifferentSoftware/linear.html) - Linear regression using different software options

-------------

## Examples alphabetically

- [AcademyAwards/](https://github.com/avehtari/ROS-Examples/tree/master/AcademyAwards/)
- [AgePeriodCohort/](https://github.com/avehtari/ROS-Examples/tree/master/AgePeriodCohort/)
    - [births.html](AgePeriodCohort/births.html) - Age adjustment
- [Arsenic/](https://github.com/avehtari/ROS-Examples/tree/master/Arsenic/)
    - [arsenic_logistic_building.html](Arsenic/arsenic_logistic_building.html) - Building a logistic regression model: wells in Bangladesh
    - [arsenic_logistic_residuals.html](Arsenic/arsenic_logistic_residuals.html) - Residual plots for a logistic regression model: wells in Bangladesh
    - [arsenic_logistic_apc.html](Arsenic/arsenic_logistic_apc.html) - Average predictice comparisons for a logistic regression model: wells in Bangladesh
    - [arsenic_logistic_building_optimizing.html](Arsenic/arsenic_logistic_building_optimizing.html) - Building a logistic regression model: wells in Bangladesh. A version with normal approximation at the mode.
- [Balance/](https://github.com/avehtari/ROS-Examples/tree/master/Balance/)
    - [treatcontrol.html](Balance/treatcontrol.html)
- [Beauty/](https://github.com/avehtari/ROS-Examples/tree/master/Beauty/)
    - [beauty.html](Beauty/beauty.html) - Student evaluations of instructors’ beauty and teaching quality
- [Bypass/](https://github.com/avehtari/ROS-Examples/tree/master/Bypass/)
- [CausalDiagram/](https://github.com/avehtari/ROS-Examples/tree/master/CausalDiagram/)
    - [diagrams.html](CausalDiagram/diagrams.html) - Plot causal diagram
- [CentralLimitTheorem/](https://github.com/avehtari/ROS-Examples/tree/master/CentralLimitTheorem/)
    - [heightweight.html](CentralLimitTheorem/heightweight.html) - Illustrate central limit theorem and normal distribution
- [Childcare/](https://github.com/avehtari/ROS-Examples/tree/master/Childcare/)
    - [childcare.html](Childcare/childcare.html) - Infant Health and Development Program (IHDP) example.
- [ChileSchools/](https://github.com/avehtari/ROS-Examples/tree/master/ChileSchools/)
    - [chile_schools.html](ChileSchools/chile_schools.html) - ChileSchools example.
- [Coins/](https://github.com/avehtari/ROS-Examples/tree/master/Coins/)
- [Congress/](https://github.com/avehtari/ROS-Examples/tree/master/Congress/)
    - [congress.html](Congress/congress.html) - Predictive uncertainty for congressional elections
    - [congress_plots.html](Congress/congress_plots.html) - Predictive uncertainty for congressional elections
- [Coop/](https://github.com/avehtari/ROS-Examples/tree/master/Coop/)
    - [riverbay.html](Coop/riverbay.html) - Example of hypothesis testing
- [Coverage/](https://github.com/avehtari/ROS-Examples/tree/master/Coverage/)
    - [coverage.html](Coverage/coverage.html) - Example of coverage
- [Cows/](https://github.com/avehtari/ROS-Examples/tree/master/Cows/)
- [CrossValidation/](https://github.com/avehtari/ROS-Examples/tree/master/CrossValidation/)
    - [crossvalidation.html](CrossValidation/crossvalidation.html) - Demonstration of cross validation
- [SampleSize/](https://github.com/avehtari/ROS-Examples/tree/master/SampleSize/)
    - [simulation.html](DataCollection/simulation.html) - Sample size simulation
- [Death/](https://github.com/avehtari/ROS-Examples/tree/master/Death/)
    - [polls.html](Death/polls.html) - Proportion of American adults supporting the death penalty
- [DifferentSoftware/](https://github.com/avehtari/ROS-Examples/tree/master/DifferentSoftware/)
    - [linear.html](DifferentSoftware/linear.html) - Linear regression using different software options
- [Earnings/](https://github.com/avehtari/ROS-Examples/tree/master/Earnings/)
    - [earnings_regression.html](Earnings/earnings_regression.html) - Predict respondents' yearly earnings using survey data from 1990.
    - [earnings_bootstrap.html](Earnings/earnings_bootstrap.html) - Bootstrapping to simulate the sampling distribution
    - [earnings_compound.html](Earnings/earnings_compound.html) - Compound discrete-continuos model
    - [height_and_weight.html](Earnings/height_and_weight.html) - Predict weight
- [ElectionsEconomy/](https://github.com/avehtari/ROS-Examples/tree/master/ElectionsEconomy/)
    - [bayes.html](ElectionsEconomy/bayes.html) - Demonstration of Bayesian information aggregation
    - [hibbs.html](ElectionsEconomy/hibbs.html) - Predicting presidential vote share from the economy
    - [hills.html](ElectionsEconomy/hills.html) - Present uncertainty in parameter estimates
    - [hibbs_coverage.html](ElectionsEconomy/hibbs_coverage.html) - Checking the model-fitting procedure using fake-data simulation.
- [ElectricCompany/](https://github.com/avehtari/ROS-Examples/tree/master/ElectricCompany/)
    - [electric.html](ElectricCompany/electric.html) - Analysis of "Electric company" data
- [FakeKCV/](https://github.com/avehtari/ROS-Examples/tree/master/FakeKCV/)
    - [fake_kcv.html](FakeKCV/fake_kcv.html) - Demonstration of $K$-fold cross-validation using simulated data
- [FakeMidtermFinal/](https://github.com/avehtari/ROS-Examples/tree/master/FakeMidtermFinal/)
    - [simulation.html](FakeMidtermFinal/simulation.html) - Fake dataset of 1000 students' scores on a midterm and final exam
    - [simulation_based_design.html](FakeMidtermFinal/simulation_based_design.html) - Fake dataset of a randomized experiment on student grades
- [FrenchElection/](https://github.com/avehtari/ROS-Examples/tree/master/FrenchElection/)
    - [ps_primaire.html](FrenchElection/ps_primaire.html) - French Election data
- [Gay/](https://github.com/avehtari/ROS-Examples/tree/master/Gay/)
    - [gay_simple.html](Gay/gay_simple.html) - Simple models (linear and discretized age) and political attitudes as a function of age
    - [gay.html](Gay/gay.html) - Nonlinear models (Loess, B-spline, GP-spline, and BART) and political attitudes as a function of age
- [Girls/](https://github.com/avehtari/ROS-Examples/tree/master/Girls/)
- [Golf/](https://github.com/avehtari/ROS-Examples/tree/master/Golf/)
    - [golf.html](Golf/golf.html) - Gold putting accuracy: Fitting a nonlinear model using Stan
- [HDI/](https://github.com/avehtari/ROS-Examples/HDI/)
    - [hdi.html](HDI/hdi.html) - Human Development Index - Looking at data in different ways
- [HealthExpenditure/](https://github.com/avehtari/ROS-Examples/tree/master/HealthExpenditure/)
    - [healthexpenditure.html](HealthExpenditure/healthexpenditure.html) - Discovery through graphs of data and models
- [Helicopters/](https://github.com/avehtari/ROS-Examples/tree/master/Helicopters/)
    - [helicopters.html](Helicopters/helicopters.html) - Example data file for helicopter flying time exercise
- [Imputation/](https://github.com/avehtari/ROS-Examples/tree/master/Imputation/)
    - [imputation.html](Imputation/imputation.html) - Regression-based imputation for the Social Indicators Survey
    - [imputation_gg.html](Imputation/imputation_gg.html) - Regression-based imputation for the Social Indicators Survey, dplyr/ggplot version
- [Incentives/]((https://github.com/avehtari/ROS-Examples/tree/master/Incentives/))
    - [incentives.html](Incentives/incentives.html) - Simple analysis of incentives data
- [Influence/](https://github.com/avehtari/ROS-Examples/tree/master/Influence/)
    - [influence.html](Influence/influence.html) - Influence of individual points in a fitted regression
- [Interactions/](https://github.com/avehtari/ROS-Examples/tree/master/Interactions/)
    - [interactions.html](Interactions/interactions.html) - Plot interaction example figure
- [Introclass/](https://github.com/avehtari/ROS-Examples/tree/master/Introclass/)
    - [residual_plots.html](Introclass/residual_plots.html) - Plot residuals vs.\ predicted values, or residuals vs.\ observed values?
- [KidIQ/](https://github.com/avehtari/ROS-Examples/tree/master/KidIQ/)
    - [kidiq.html](KidIQ/kidiq.html) - Linear regression with multiple predictors
    - [kidiq_loo.html](KidIQ/kidiq_loo.html) - Linear regression and leave-one-out cross-validation
    - [kidiq_R2.html](KidIQ/kidiq_R2.html) - Linear regression and Bayes-R2 and LOO-R2
    - [kidiq_kcv.html](KidIQ/kidiq_kcv.html) - Linear regression and K-fold cross-validation
- [Lalonde/](https://github.com/avehtari/ROS-Examples/tree/master/Lalonde/)
- [LogisticPriors/](https://github.com/avehtari/ROS-Examples/tree/master/LogisticPriors/)
    - [logistic_priors.html](LogisticPriors/logistic_priors.html) - Effect of priors in logistic regression
- [Mesquite/](https://github.com/avehtari/ROS-Examples/tree/master/Mesquite/)
    - [mesquite.html](Mesquite/mesquite.html) - Predicting the yields of mesquite bushes
- [Metabolic/](https://github.com/avehtari/ROS-Examples/tree/master/Metabolic/)
    - [metabolic.html](Metabolic/metabolic.html) - How to interpret a power law or log-log regression
- [Mile/](https://github.com/avehtari/ROS-Examples/tree/master/Mile/)
    - [mile.html](Mile/mile.html) - Trend of record times in the mile run
- [Names/](https://github.com/avehtari/ROS-Examples/tree/master/Names/)
    - [names.html](Names/names.html) - Names - Distributions of names of American babies
    - [lastletters.html](Names/lastletters.html) - Last letters - Distributions of last letters of names of American babies
- [NES/](https://github.com/avehtari/ROS-Examples/tree/master/NES/)
    - [nes_linear.html](NES/nes_linear.html) - Fitting the same regression to many datasets
    - [nes_logistic.html](NES/nes_logistic.html) - Logistic regression, identifiability, and separation
- [Newcomb/](https://github.com/avehtari/ROS-Examples/tree/master/Newcomb/)
    - [newcomb.html](Newcomb/newcomb.html) - Posterior predictive checking of Normal model for Newcomb's speed of light data
- [Parabola/](https://github.com/avehtari/ROS-Examples/tree/master/Parabola/)
    - [parabola.html](Parabola/parabola.html) - Demonstration of using Stan for optimization
- [Peacekeeping/](https://github.com/avehtari/ROS-Examples/tree/master/Peacekeeping/)
    - [peace.html](Peacekeeping/peace.html) - Outcomes after civil war in countries with and without United Nations peacekeeping
- [PearsonLee/](https://github.com/avehtari/ROS-Examples/tree/master/PearsonLee/)
    - [heights.html](PearsonLee/heights.html) - The heredity of height. Published in 1903 by Karl Pearson and Alice Lee.
- [Pew/](https://github.com/avehtari/ROS-Examples/tree/master/Pew/)
    - [pew.html](Pew/pew.html) - Miscellaneous analyses using raw Pew data
- [PoissonExample/](https://github.com/avehtari/ROS-Examples/tree/master/PoissonExample/)
    - [poissonexample.html](PoissonExample/poissonexample.html) - Demonstrate Poisson regression with simulated data.
- [Pollution/](https://github.com/avehtari/ROS-Examples/tree/master/Pollution/)
    - [pollution.html](Pollution/pollution.html) - Pollution data.
- [Poststrat/](https://github.com/avehtari/ROS-Examples/tree/master/Poststrat/)
    - [poststrat.html](Poststrat/poststrat.html) - Poststratification after estimation
    - [poststrat2.html](Poststrat/poststrat2.html) - Poststratification after estimation
- [ProbabilitySimulation/](https://github.com/avehtari/ROS-Examples/tree/master/ProbabilitySimulation/)
    - [probsim.html](ProbabilitySimulation/probsim.html) - Simulation of probability models
- [Pyth/](https://github.com/avehtari/ROS-Examples/tree/master/Pyth/)
- [Redistricting/](https://github.com/avehtari/ROS-Examples/tree/master/Redistricting/)
- [Residuals/](https://github.com/avehtari/ROS-Examples/tree/master/Residuals/)
    - [residuals.html](Residuals/residuals.html) - Plotting the data and fitted model
- [Restaurant/](https://github.com/avehtari/ROS-Examples/tree/master/Restaurant/)
    - [restaurant.html](Restaurant/restaurant.html) - Demonstration of using Stan for optimization
- [RiskyBehavior/](https://github.com/avehtari/ROS-Examples/tree/master/RiskyBehavior/)
    - [risky.html](RiskyBehavior/risky.html) Risky behavior data.
- [Roaches/](https://github.com/avehtari/ROS-Examples/tree/master/Roaches/)
    - [roaches.html](Roaches/roaches.html) - Analyse the effect of integrated pest management on reducing cockroach levels in urban apartments
- [Robit/](https://github.com/avehtari/ROS-Examples/tree/master/Robit/)
    - [robit.html](Robit/robit.html) - Comparison of robit and logit models for binary data
- [Rodents/](https://github.com/avehtari/ROS-Examples/tree/master/Rodents/)
- [Rsquared/](https://github.com/avehtari/ROS-Examples/tree/master/Rsquared/)
    - [rsquared.html](Rsquared/rsquared.html) - Bayesian R^2
- [Sesame/](https://github.com/avehtari/ROS-Examples/tree/master/Sesame/)
    - [sesame.html](Sesame/sesame.html) - Causal analysis of Sesame Street experiment
- [SexRatio/](https://github.com/avehtari/ROS-Examples/tree/master/SexRatio/)
    - [sexratio.html](SexRatio/sexratio.html) - Example where an informative prior makes a difference
- [SimpleCausal/](https://github.com/avehtari/ROS-Examples/tree/master/SimpleCausal/)
    - [causal.html](SimpleCausal/causal.html) - Simple graphs illustrating regression for causal inference
- [Simplest/](https://github.com/avehtari/ROS-Examples/tree/master/Simplest/)
    - [simplest.html](Simplest/simplest.html) - Linear regression with a single predictor
    - [simplest_lm.html](Simplest/simplest_lm.html) - Linear least squares regression with a single predictor
- [Stents/](https://github.com/avehtari/ROS-Examples/tree/master/Stents/)
    - [stents.html](Stents/stents.html) - Stents - comparing distributions
- [Storable/](https://github.com/avehtari/ROS-Examples/tree/master/Storable/)
    - [storable.html](Storable/storable.html) - Ordered categorical data analysis with a study from experimental economics, on the topic of ``storable votes.''
- [Student/](https://github.com/avehtari/ROS-Examples/tree/master/Student/)
    - [student.html](Student/student.html) - Models for regression coefficients
- [Unemployment/](https://github.com/avehtari/ROS-Examples/tree/master/Unemployment/)
    - [unemployment.html](Unemployment/unemployment.html) - Time series fit and posterior predictive model checking for unemployment series

-------------

## Download code and data

- [Git repo for the code and data](https://github.com/avehtari/ROS-Examples)
- [Download all code and data as a ZIP file](https://codeload.github.com/avehtari/ROS-Examples/zip/master)

## Tidyverse code

Bill Behrman has revised all the example code to use Tidyverse

- [Regression and Other Stories - Tidyverse Examples](https://github.com/behrman/ros)
- [Style guide used by Behrman](http://dcl-workflow.stanford.edu/style-guide.html)

## brms + tidyverse code

Solomon A. Kurz is revising all the example code to use brms and tidyverse

- [Working through Regression and other stories](https://github.com/ASKurz/Working-through-Regression-and-other-stories)

## Python code

Ravin Kumar, Tomás Capretto, and Osvaldo Martin are porting ROS
examples to Python using bambi (BAyesian Model-Building Interface)
which has similar formula syntax as rstanarm and brms.

- [Bambi resources](https://github.com/bambinos/Bambi_resources)

## Julia code

Rob J. Goedman is porting ROS examples to Julia.

- [RegressionAndOtherStories.jl](https://github.com/RegressionAndOtherStoriesJulia/RegressionAndOtherStories.jl)