Gelman A., Hill J. Data Analysis Using Regression and Multilevel/Hierarchical Models

Cambridge: Cambridge University Press, 2006. — 648 p. — (Analytical Methods for Social Research). — ISBN: 978-0-511-26878-6.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. 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.Why?
Concepts and methods from basic probability and statistics
Single-level regression
Linear regression: the basics
Linear regression: before and after fitting the model
Logistic regression
Generalized linear models
Working with regression inferences
Simulation of probability models and statistical inferences
Simulation for checking statistical procedures and model fits
Causal inference using regression on the treatment variable
Causal inference using more advanced models
Multilevel regression
Multilevel structures
Multilevel linear models: the basics
Multilevel linear models: varying slopes, non-nested models, and other complexities
Multilevel logistic regression
Multilevel generalized linear models
Fitting multilevel models
Multilevel modeling in Bugs and R: the basics
Fitting multilevel linear and generalized linear models in Bugs and R
Likelihood and Bayesian inference and computation
Debugging and speeding convergence
From data collection to model understanding to model checking
Sample size and power calculations
Understanding and summarizing the fitted models
Analysis of variance
Causal inference using multilevel models
Model checking and comparison
Missing-data imputationSix quick tips to improve your regression modeling
Statistical graphics for research and presentation
Software