Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives

by Gelman, Andrew; Meng, Xiao-Li

• ISBN13: 9780470090435
• ISBN10: 047009043X
• Edition: 1st
• Format: Hardcover
• Copyright: 2004-09-03
• Publisher: WILEY

Summary

This book brings together a collection of articles on statistical methods relating to missing data analysis, including multiple imputation, propensity scores, instrumental variables, and Bayesian inference. Covering new research topics and real-world examples which do not feature in many standard texts. The book is dedicated to Professor Don Rubin (Harvard). Don Rubin has made fundamental contributions to the study of missing data. Key features of the book include: Comprehensive coverage of an imporant area for both research and applications. Adopts a pragmatic approach to describing a wide range of intermediate and advanced statistical techniques. Covers key topics such as multiple imputation, propensity scores, instrumental variables and Bayesian inference. Includes a number of applications from the social and health sciences. Edited and authored by highly respected researchers in the area.

Author Biography

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).

Table of Contents

Preface	p. xiii
Casual inference and observational studies	p. 1
An overview of methods for causal inference from observational studies	p. 3
Introduction	p. 3
Approaches based on causal models	p. 3
Canonical inference	p. 9
Methodologic modeling	p. 10
Conclusion	p. 13
Matching in observational studies	p. 15
The role of matching in observational studies	p. 15
Why match?	p. 16
Two key issues: balance and structure	p. 17
Additional issues	p. 21
Estimating causal effects in nonexperimental studies	p. 25
Introduction	p. 25
Identifying and estimating the average treatment effect	p. 27
The NSW data	p. 29
Propensity score estimates	p. 31
Conclusions	p. 35
Medication cost sharing and drug spending in Medicare	p. 37
Methods	p. 38
Results	p. 40
Study limitations	p. 45
Conclusions and policy implications	p. 46
A comparison of experimental and observational data analyses	p. 49
Experimental sample	p. 50
Constructed observational study	p. 51
Concluding remarks	p. 60
Fixing broken experiments using the propensity score	p. 61
Introduction	p. 61
The lottery data	p. 62
Estimating the propensity scores	p. 63
Results	p. 65
Concluding remarks	p. 71
The propensity score with continuous treatments	p. 73
Introduction	p. 73
The basic framework	p. 74
Bias removal using the GPS	p. 76
Estimation and inference	p. 78
Application: the Imbens-Rubin-Sacerdote lottery sample	p. 79
Conclusion	p. 83
Causal inference with instrumental variables	p. 85
Introduction	p. 85
Key assumptions for the LATE interpretation of the IV estimand	p. 87
Estimating causal effects with IV	p. 90
Some recent applications	p. 95
Discussion	p. 95
Principal stratification	p. 97
Introduction: partially controlled studies	p. 97
Examples of partially controlled studies	p. 97
Principal stratification	p. 101
Estimands	p. 102
Assumptions	p. 104
Designs and polydesigns	p. 107
Missing data modeling	p. 109
Nonresponse adjustment in government statistical agencies: constraints, inferential goals, and robustness issues	p. 111
Introduction: a wide spectrum of nonresponse adjustment efforts in government statistical agencies	p. 111
Constraints	p. 112
Complex estimand structures, inferential goals, and utility functions	p. 112
Robustness	p. 113
Closing remarks	p. 113
Bridging across changes in classification systems	p. 117
Introduction	p. 117
Multiple imputation to achieve comparability of industry and occupation codes	p. 118
Bridging the transition from single-race reporting to multiple-race reporting	p. 123
Conclusion	p. 128
Representing the Census undercount by multiple imputation of households	p. 129
Introduction	p. 129
Models	p. 131
Inference	p. 134
Simulation evaluations	p. 138
Conclusion	p. 140
Statistical disclosure techniques based on multiple imputation	p. 141
Introduction	p. 141
Full synthesis	p. 143
SMIKe and MIKe	p. 144
Analysis of synthetic samples	p. 147
An application	p. 149
Conclusions	p. 152
Designs producing balanced missing data: examples from the National Assessment of Educational Progress	p. 153
Introduction	p. 153
Statistical methods in NAEP	p. 155
Split and balanced designs for estimating population parameters	p. 157
Maximum likelihood estimation	p. 159
The role of secondary covariates	p. 160
Conclusions	p. 162
Propensity score estimation with missing data	p. 163
Introduction	p. 163
Notation	p. 165
Applied example: March of Dimes data	p. 168
Conclusion and future directions	p. 174
Sensitivity to nonignorability in frequentist inference	p. 175
Missing data in clinical trials	p. 175
Ignorability and bias	p. 175
A nonignorable selection model	p. 176
Sensitivity of the mean and variance	p. 177
Sensitivity of the power	p. 178
Sensitivity of the coverage probability	p. 180
An example	p. 184
Discussion	p. 185
Statistical modeling and computation	p. 187
Statistical modeling and computation	p. 189
Regression models	p. 190
Latent-variable problems	p. 191
Computation: non-Bayesian	p. 191
Computation: Bayesian	p. 192
Prospects for the future	p. 193
Treatment effects in before-after data	p. 195
Default statistical models of treatment effects	p. 195
Before-after correlation is typically larger for controls than for treated units	p. 196
A class of models for varying treatment effects	p. 200
Discussion	p. 201
Multimodality in mixture models and factor models	p. 203
Multimodality in mixture models	p. 204
Multimodal posterior distributions in continuous latent variable models	p. 209
Summary	p. 212
Modeling the covariance and correlation matrix of repeated measures	p. 215
Introduction	p. 215
Modeling the covariance matrix	p. 216
Modeling the correlation matrix	p. 218
Modeling a mixed covariance-correlation matrix	p. 220
Nonzero means and unbalanced data	p. 220
Multivariate probit model	p. 221
Example: covariance modeling	p. 222
Example: mixed data	p. 225
Robit regression: a simple robust alternative to logistic and probit regression	p. 227
Introduction	p. 227
The robit model	p. 228
Robustness of likelihood-based inference using logistic, probit, and robit regression models	p. 230
Complete data for simple maximum likelihood estimation	p. 231
Maximum likelihood estimation using EM-type algorithms	p. 233
A numerical example	p. 235
Conclusion	p. 238
Using EM and data augmentation for the competing risks model	p. 239
Introduction	p. 239
The model	p. 240
EM-based analysis	p. 243
Bayesian analysis	p. 244
Example	p. 248
Discussion and further work	p. 250
Mixed effects models and the EM algorithm	p. 253
Introduction	p. 253
Binary regression with random effects	p. 254
Proportional hazards mixed-effects models	p. 259
The sampling/importance resampling algorithm	p. 265
Introduction	p. 265
SIR algorithm	p. 266
Selection of the pool size	p. 267
Selection criterion of the importance sampling distribution	p. 271
The resampling algorithms	p. 272
Discussion	p. 276
Applied Bayesian inference	p. 277
Whither applied Bayesian inference?	p. 279
Where we've been	p. 279
Where we are	p. 281
Where we're going	p. 282
Efficient EM-type algorithms for fitting spectral lines in high-energy astrophysics	p. 285
Application-specific statistical methods	p. 285
The Chandra X-ray observatory	p. 287
Fitting narrow emission lines	p. 289
Model checking and model selection	p. 294
Improved predictions of lynx trappings using a biological model	p. 297
Introduction	p. 297
The current best model	p. 298
Biological models for predator prey systems	p. 299
Some statistical models based on the Lotka-Volterra system	p. 300
Computational aspects of posterior inference	p. 302
Posterior predictive checks and model expansion	p. 304
Prediction with the posterior mode	p. 307
Discussion	p. 308
Record linkage using finite mixture models	p. 309
Introduction to record linkage	p. 309
Record linkage	p. 310
Mixture models	p. 311
Application	p. 314
Analysis of linked files	p. 316
Bayesian hierarchical record linkage	p. 317
Summary	p. 318
Identifying likely duplicates by record linkage in a survey of prostitutes	p. 319
Concern about duplicates in an anonymous survey	p. 319
General frameworks for record linkage	p. 321
Estimating probabilities of duplication in the Los Angeles Women's Health Risk Study	p. 322
Discussion	p. 328
Applying structural equation models with incomplete data	p. 331
Structural equation models	p. 332
Bayesian inference for structural equation models	p. 334
Iowa Youth and Families Project example	p. 339
Summary and discussion	p. 342
Perceptual scaling	p. 343
Introduction	p. 343
Sparsity and minimax entropy	p. 347
Complexity scaling law	p. 353
Perceptibility scaling law	p. 356
Texture = imperceptible structures	p. 358
Perceptibility and sparsity	p. 359
References	p. 361
Index	p. 401
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