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).Xiao-Li Meng, Department of Statistics, Harvard University, USA.

"I congratulate the editors on this volume; it really is an essential and very enjoyable journey with Don Rubin's statistical family." (Biometrics, September 2006) "…contains much current important work…" (Technometrics, November 2005)"This a useful reference book on an important topic with applications to a wide range of disciplines." (CHOICE, September 2005)“With this variety of papers, the reader is bound to find some papers interesting…” (Journal of Applied Statistics, Vol.32, No.3, April 2005)“I strongly recommend that libraries have a copy of this book in their reference section.” (Journal of the Royal Statistical Society Series A, June 2005)"...a very useful addition to academic libraries…" (Short Book Reviews, Vol.24, No.3, December 2004)

• Preface xiiiI Casual inference and observational studies 11 An overview of methods for causal inference from observational studies, by Sander Greenland 31.1 Introduction 31.2 Approaches based on causal models 31.3 Canonical inference 91.4 Methodologic modeling 101.5 Conclusion 132 Matching in observational studies, by Paul R. Rosenbaum 152.1 The role of matching in observational studies 152.2 Why match? 162.3 Two key issues: balance and structure 172.4 Additional issues 213 Estimating causal effects in nonexperimental studies, by Rajeev Dehejia 253.1 Introduction 253.2 Identifying and estimating the average treatment effect 273.3 The NSWdata 293.4 Propensity score estimates 313.5 Conclusions 354 Medication cost sharing and drug spending in Medicare, by Alyce S. Adams 374.1 Methods 384.2 Results 404.3 Study limitations 454.4 Conclusions and policy implications 465 A comparison of experimental and observational data analyses, by Jennifer L. Hill, Jerome P. Reiter, and Elaine L. Zanutto 495.1 Experimental sample 505.2 Constructed observational study 515.3 Concluding remarks 606 Fixing broken experiments using the propensity score, by Bruce Sacerdote 616.1 Introduction 616.2 The lottery data 626.3 Estimating the propensity scores 636.4 Results 656.5 Concluding remarks 717 The propensity score with continuous treatments, by Keisuke Hirano and Guido W. Imbens 737.1 Introduction 737.2 The basic framework 747.3 Bias removal using the GPS 767.4 Estimation and inference 787.5 Application: the Imbens–Rubin–Sacerdote lottery sample 797.6 Conclusion 838 Causal inference with instrumental variables, by Junni L. Zhang 858.1 Introduction 858.2 Key assumptions for the LATE interpretation of the IV estimand 878.3 Estimating causal effects with IV 908.4 Some recent applications 958.5 Discussion 959 Principal stratification, by Constantine E. Frangakis 979.1 Introduction: partially controlled studies 979.2 Examples of partially controlled studies 979.3 Principal stratification 1019.4 Estimands 1029.5 Assumptions 1049.6 Designs and polydesigns 107II Missing data modeling 10910 Nonresponse adjustment in government statistical agencies: constraints, inferential goals, and robustness issues, by John L. Eltinge 11110.1 Introduction: a wide spectrum of nonresponse adjustment efforts in government statistical agencies 11110.2 Constraints 11210.3 Complex estimand structures, inferential goals, and utility functions 11210.4 Robustness 11310.5 Closing remarks 11311 Bridging across changes in classification systems, by Nathaniel Schenker 11711.1 Introduction 11711.2 Multiple imputation to achieve comparability of industry and occupation codes 11811.3 Bridging the transition from single-race reporting to multiple-race reporting 12311.4 Conclusion 12812 Representing the Census undercount by multiple imputation of households, by Alan M. Zaslavsky 12912.1 Introduction 12912.2 Models 13112.3 Inference 13412.4 Simulation evaluations 13812.5 Conclusion 14013 Statistical disclosure techniques based on multiple imputation, by Roderick J. A. Little, Fang Liu, and TrivelloreE. Raghunathan 14113.1 Introduction 14113.2 Full synthesis 14313.3 SMIKe andMIKe 14413.4 Analysis of synthetic samples 14713.5 An application 14913.6 Conclusions 15214 Designs producing balanced missing data: examples from the National Assessment of Educational Progress, by Neal Thomas 15314.1 Introduction 15314.2 Statistical methods in NAEP 15514.3 Split and balanced designs for estimating population parameters 15714.4 Maximum likelihood estimation 15914.5 The role of secondary covariates 16014.6 Conclusions 16215 Propensity score estimation with missing data, by Ralph B. D'Agostino Jr. 16315.1 Introduction 16315.2 Notation 16515.3 Applied example:March of Dimes data 16815.4 Conclusion and future directions 17416 Sensitivity to nonignorability in frequentist inference, by Guoguang Ma and Daniel F. Heitjan 17516.1 Missing data in clinical trials 17516.2 Ignorability and bias 17516.3 A nonignorable selection model 17616.4 Sensitivity of the mean and variance 17716.5 Sensitivity of the power 17816.6 Sensitivity of the coverage probability 18016.7 An example 18416.8 Discussion 185III Statistical modeling and computation 18717 Statistical modeling and computation, by D. Michael Titterington 18917.1 Regression models 19017.2 Latent-variable problems 19117.3 Computation: non-Bayesian 19117.4 Computation: Bayesian 19217.5 Prospects for the future 19318 Treatment effects in before-after data, by Andrew Gelman 19518.1 Default statistical models of treatment effects 19518.2 Before-after correlation is typically larger for controls than for treated units 19618.3 A class of models for varying treatment effects 20018.4 Discussion 20119 Multimodality in mixture models and factor models, by Eric Loken 20319.1 Multimodality in mixture models 20419.2 Multimodal posterior distributions in continuous latent variable models 20919.3 Summary 21220 Modeling the covariance and correlation matrix of repeated measures, by W. John Boscardin and Xiao Zhang 21520.1 Introduction 21520.2 Modeling the covariance matrix 21620.3 Modeling the correlation matrix 21820.4 Modeling a mixed covariance-correlation matrix 22020.5 Nonzero means and unbalanced data 22020.6 Multivariate probit model 22120.7 Example: covariance modeling 22220.8 Example: mixed data 22521 Robit regression: a simple robust alternative to logistic and probit regression, by Chuanhai Liu 22721.1 Introduction 22721.2 The robit model 22821.3 Robustness of likelihood-based inference using logistic, probit, and robit regression models 23021.4 Complete data for simple maximum likelihood estimation 23121.5 Maximum likelihood estimation using EM-type algorithms 23321.6 A numerical example 23521.7 Conclusion 23822 Using EM and data augmentation for the competing risks model, by Radu V. Craiu and Thierry Duchesne 23922.1 Introduction 23922.2 The model 24022.3 EM-based analysis 24322.4 Bayesian analysis 24422.5 Example 24822.6 Discussion and further work 25023 Mixed effects models and the EM algorithm, by Florin Vaida, Xiao-Li Meng, and Ronghui Xu 25323.1 Introduction 25323.2 Binary regression with random effects 25423.3 Proportional hazards mixed-effects models 25924 The sampling/importance resampling algorithm, by Kim-Hung Li 26524.1 Introduction 26524.2 SIR algorithm 26624.3 Selection of the pool size 26724.4 Selection criterion of the importance sampling distribution 27124.5 The resampling algorithms 27224.6 Discussion 276IV Applied Bayesian inference 27725 Whither applied Bayesian inference?, by Bradley P. Carlin 27925.1 Where we've been 27925.2 Where we are 28125.3 Where we're going 28226 Efficient EM-type algorithms for fitting spectral lines in high-energy astrophysics, by David A. van Dyk and Taeyoung Park 28526.1 Application-specific statistical methods 28526.2 The Chandra X-ray observatory 28726.3 Fitting narrow emission lines 28926.4 Model checking and model selection 29427 Improved predictions of lynx trappings using a biological model, by Cavan Reilly and Angelique Zeringue 29727.1 Introduction 29727.2 The current best model 29827.3 Biological models for predator prey systems 29927.4 Some statistical models based on the Lotka-Volterra system 30027.5 Computational aspects of posterior inference 30227.6 Posterior predictive checks and model expansion 30427.7 Prediction with the posterior mode 30727.8 Discussion 30828 Record linkage using finite mixture models, by Michael D. Larsen 30928.1 Introduction to record linkage 30928.2 Record linkage 31028.3 Mixture models 31128.4 Application 31428.5 Analysis of linked files 31628.6 Bayesian hierarchical record linkage 31728.7 Summary 31829 Identifying likely duplicates by record linkage in a survey of prostitutes, by Thomas R. Belin, Hemant Ishwaran, Naihua Duan, Sandra H. Berry, and David E. Kanouse 31929.1 Concern about duplicates in an anonymous survey 31929.2 General frameworks for record linkage 32129.3 Estimating probabilities of duplication in the Los Angeles Women's Health Risk Study 32229.4 Discussion 32830 Applying structural equation models with incomplete data, by Hal S. Stern and Yoonsook Jeon 33130.1 Structural equation models 33230.2 Bayesian inference for structural equation models 33430.3 Iowa Youth and Families Project example 33930.4 Summary and discussion 34231 Perceptual scaling, by Ying Nian Wu, Cheng-En Guo, and Song Chun Zhu 34331.1 Introduction 34331.2 Sparsity and minimax entropy 34731.3 Complexity scaling law. 35331.4 Perceptibility scaling law 35631.5 Texture = imperceptible structures 35831.6 Perceptibility and sparsity 359References 361Index 401