Data Analysis Using Regression and Multilevel/Hierarchical Models, first published in 2007, is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout.
Andrew Gelman is Professor of Statistics and Professor of Political Science at Columbia University. He has published over 150 articles in statistical theory, methods, and computation, and in applications areas including decision analysis, survey sampling, political science, public health, and policy. His other books are Bayesian Data Analysis (1995, second edition 2003) and Teaching Statistics: A Bag of Tricks (2002). Jennifer Hill is Assistant Professor of Public Affairs in the Department of International and Public Affairs at Columbia University. She has co-authored articles that have appeared in the Journal of the American Statistical Association, American Political Science Review, American Journal of Public Health, Developmental Psychology, the Economic Journal and the Journal of Policy Analysis and Management, among others.
1. Why?; 2. Concepts and methods from basic probability and statistics; Part I. A. Single-Level Regression: 3. Linear regression: the basics; 4. Linear regression: before and after fitting the model; 5. Logistic regression; 6. Generalized linear models; Part I. B. Working with Regression Inferences: 7. Simulation of probability models and statistical inferences; 8. Simulation for checking statistical procedures and model fits; 9. Causal inference using regression on the treatment variable; 10. Causal inference using more advanced models; Part II. A. Multilevel Regression: 11. Multilevel structures; 12. Multilevel linear models: the basics; 13. Multilevel linear models: varying slopes, non-nested models and other complexities; 14. Multilevel logistic regression; 15. Multilevel generalized linear models; Part II. B. Fitting Multilevel Models: 16. Multilevel modeling in bugs and R: the basics; 17. Fitting multilevel linear and generalized linear models in bugs and R; 18. Likelihood and Bayesian inference and computation; 19. Debugging and speeding convergence; Part III. From Data Collection to Model Understanding to Model Checking: 20. Sample size and power calculations; 21. Understanding and summarizing the fitted models; 22. Analysis of variance; 23. Causal inference using multilevel models; 24. Model checking and comparison; 25. Missing data imputation; Appendixes: A. Six quick tips to improve your regression modeling; B. Statistical graphics for research and presentation; C. Software; References.