Regression and Other Stories

Most textbooks on regression focus on theory and the simplest of examples. Real statistical problems, however, are complex and subtle. This is not a book about the theory of regression. It is about using regression to solve real problems of comparison, estimation, prediction, and causal inference. Unlike other books, it focuses on practical issues such as sample size and missing data and a wide range of goals and techniques. It jumps right in to methods and computer code you can use immediately. Real examples, real stories from the authors' experience demonstrate what regression can do and its limitations, with practical advice for understanding assumptions and implementing methods for experiments and observational studies. They make a smooth transition to logistic regression and GLM. The emphasis is on computation in R and Stan rather than derivations, with code available online. Graphics and presentation aid understanding of the models and model fitting.

Preface; Part I. Fundamentals: 1. Overview; 2. Data and measurement; 3. Some basic methods in mathematics and probability; 4. Statistical inference; 5. Simulation; Part II. Linear Regression: 6. Background on regression modeling; 7. Linear regression with a single predictor; 8. Fitting regression models; 9. Prediction and Bayesian inference; 10. Linear regression with multiple predictors; 11. Assumptions, diagnostics, and model evaluation; 12. Transformations and regression; Part III. Generalized Linear Models: 13. Logistic regression; 14. Working with logistic regression; 15. Other generalized linear models; Part IV. Before and After Fitting a Regression: 16. Design and sample size decisions; 17. Poststratification and missing-data imputation; Part V. Causal Inference: 18. Causal inference and randomized experiments; 19. Causal inference using regression on the treatment variable; 20. Observational studies with all confounders assumed to be measured; 21. Additional topics in causal inference; Part VI. What Comes Next?: 22. Advanced regression and multilevel models; Appendices: A. Computing in R; B. 10 quick tips to improve your regression modelling; References; Author index; Subject index.

The authors are experienced researchers who have published articles in hundreds of different scientific journals in fields including statistics, computer science, policy, public health, political science, economics, sociology, and engineering. They have also published articles in the Washington Post, New York Times, Slate, and other public venues. Their previous books include Bayesian Data Analysis, Teaching Statistics: A Bag of Tricks, and Data Analysis and Regression Using Multilevel/Hierarchical Models. Andrew Gelman is Higgins Professor of Statistics and Professor of Political Science at Columbia University.
Jennifer Hill is Professor of Applied Statistics at New York University.
Aki Vehtari is Associate Professor in Computational Probabilistic Modeling at Aalto University, Finland.