Data Analysis Using Regression and Multilevel / Hierarchical Models 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. Data Analysis Using Regression and Multilevel / Hierarchical Models 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.
"Data Analysis Using Regression and Multilevel/ Hierarchical Models [...] careful yet mathematically accessible style is generously illustrated with examples and graphical displays, making it ideal for either classroom use or self-study. It appears destined to adorn the shelves of a great many applied statisticians and social scientists for years to come."
- Brad Carlin, University of Minnesota
"Gelman and Hill have written what may be the first truly modern book on modeling. Containing practical as well as methodological insights into both Bayesian and traditional approaches, Data Analysis Using Regression and Multilevel / Hierarchical Models provides useful guidance into the process of building and evaluating models. For the social scientist and other applied statisticians interested in linear and logistic regression, causal inference, and hierarchical models, it should prove invaluable either as a classroom text or as an addition to the research bookshelf."
- Richard De Veaux, Williams College
"The theme of Gelman and Hill's engaging and nontechnical introduction to statistical modeling is 'Be flexible.' Using a broad array of examples written in R and WinBugs, the authors illustrate the many ways in which readers can build more flexibility into their predictive and causal models. This hands-on textbook is sure to become a popular choice in applied regression courses."
- Donald Green, Yale University
"Simply put, Data Analysis Using Regression and Multilevel / Hierarchical Models is the best place to learn how to do serious empirical research. Gelman and Hill have written a much needed book that is sophisticated about research design without being technical. Data Analysis Using Regression and Multilevel / Hierarchical Models is destined to be a classic!"
- Alex Tabarrok, George Mason University
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
A. Six quick tips to improve your regression modeling
B. Statistical graphics for research and presentation
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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.