Roderick J. A. Little, Donald B. Rubin

Statistical Analysis with Missing Data (eBook, ePUB)

• Format: ePub

Produktbeschreibung

An up-to-date, comprehensive treatment of a classic text on missing data in statistics The topic of missing data has gained considerable attention in recent decades. This new edition by two acknowledged experts on the subject offers an up-to-date account of practical methodology for handling missing data problems. Blending theory and application, authors Roderick Little and Donald Rubin review historical approaches to the subject and describe simple methods for multivariate analysis with missing values. They then provide a coherent theory for analysis of problems based on likelihoods derived from statistical models for the data and the missing data mechanism, and then they apply the theory to a wide range of important missing data problems. Statistical Analysis with Missing Data, Third Edition starts by introducing readers to the subject and approaches toward solving it. It looks at the patterns and mechanisms that create the missing data, as well as a taxonomy of missing data. It then goes on to examine missing data in experiments, before discussing complete-case and available-case analysis, including weighting methods. The new edition expands its coverage to include recent work on topics such as nonresponse in sample surveys, causal inference, diagnostic methods, and sensitivity analysis, among a host of other topics. * An updated "classic" written by renowned authorities on the subject * Features over 150 exercises (including many new ones) * Covers recent work on important methods like multiple imputation, robust alternatives to weighting, and Bayesian methods * Revises previous topics based on past student feedback and class experience * Contains an updated and expanded bibliography The authors were awarded The Karl Pearson Prize in 2017 by the International Statistical Institute, for a research contribution that has had profound influence on statistical theory, methodology or applications. Their work "has been no less than defining and transforming." (ISI) Statistical Analysis with Missing Data, Third Edition is an ideal textbook for upper undergraduate and/or beginning graduate level students of the subject. It is also an excellent source of information for applied statisticians and practitioners in government and industry.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 462
• Erscheinungstermin: 21. März 2019
• Englisch
• ISBN-13: 9781118595695
• Artikelnr.: 56060435

Autorenporträt

Roderick J. A. Little, PhD., is Richard D. Remington Distinguished University Professor of Biostatistics, Professor of Statistics, and Research Professor, Institute for Social Research, at the University of Michigan. Donald B. Rubin, PhD., is Professor, Yau Mathematical Sciences Center, Tsinghua University; Murray Shusterman Senior Research Fellow, Department of Statistical Science, Fox School of Business at Temple University; and Professor Emeritus, Harvard University.

Inhaltsangabe

Preface to the Third Edition xi Part I Overview and Basic Approaches 1 1
Introduction 3 1.1 The Problem of Missing Data 3 1.2 Missingness Patterns
and Mechanisms 8 1.3 Mechanisms That Lead to Missing Data 13 1.4 A Taxonomy
of Missing Data Methods 23 2 Missing Data in Experiments 29 2.1
Introduction 29 2.2 The Exact Least Squares Solution with Complete Data 30
2.3 The Correct Least Squares Analysis with Missing Data 32 2.4 Filling in
Least Squares Estimates 33 2.4.1 Yates's Method 33 2.4.2 Using a Formula
for the Missing Values 34 2.4.3 Iterating to Find the Missing Values 34
2.4.4 ANCOVA with Missing Value Covariates 35 2.5 Bartlett's ANCOVA Method
35 2.5.1 Useful Properties of Bartlett's Method 35 2.5.2 Notation 36 2.5.3
The ANCOVA Estimates of Parameters and Missing Y-Values 36 2.5.4 ANCOVA
Estimates of the Residual Sums of Squares and the Covariance Matrix of beta
37 2.6 Least Squares Estimates of Missing Values by ANCOVA Using Only
Complete-Data Methods 38 2.7 Correct Least Squares Estimates of Standard
Errors and One Degree of Freedom Sums of Squares 40 2.8 Correct
Least-Squares Sums of Squares with More Than One Degree of Freedom 42 3
Complete-Case and Available-Case Analysis, Including Weighting Methods 47
3.1 Introduction 47 3.2 Complete-Case Analysis 47 3.3 Weighted
Complete-Case Analysis 50 3.3.1 Weighting Adjustments 50 3.3.2
Poststratification and Raking to Known Margins 58 3.3.3 Inference from
Weighted Data 60 3.3.4 Summary of Weighting Methods 61 3.4 Available-Case
Analysis 61 4 Single Imputation Methods 67 4.1 Introduction 67 4.2 Imputing
Means from a Predictive Distribution 69 4.2.1 Unconditional Mean Imputation
69 4.2.2 Conditional Mean Imputation 70 4.3 Imputing Draws from a
Predictive Distribution 73 4.3.1 Draws Based on Explicit Models 73 4.3.2
Draws Based on Implicit Models - Hot Deck Methods 76 4.4 Conclusion 81 5
Accounting for Uncertainty from Missing Data 85 5.1 Introduction 85 5.2
Imputation Methods that Provide Valid Standard Errors from a Single
Filled-in Data Set 86 5.3 Standard Errors for Imputed Data by Resampling 90
5.3.1 Bootstrap Standard Errors 90 5.3.2 Jackknife Standard Errors 92 5.4
Introduction to Multiple Imputation 95 5.5 Comparison of Resampling Methods
and Multiple Imputation 100 Part II Likelihood-Based Approaches to the
Analysis of Data with Missing Values 107 6 Theory of Inference Based on the
Likelihood Function 109 6.1 Review of Likelihood-Based Estimation for
Complete Data 109 6.1.1 Maximum Likelihood Estimation 109 6.1.2 Inference
Based on the Likelihood 118 6.1.3 Large Sample Maximum Likelihood and Bayes
Inference 119 6.1.4 Bayes Inference Based on the Full Posterior
Distribution 126 6.1.5 Simulating Posterior Distributions 130 6.2
Likelihood-Based Inference with Incomplete Data 132 6.3 A Generally Flawed
Alternative to Maximum Likelihood: Maximizing over the Parameters and the
Missing Data 141 6.3.1 The Method 141 6.3.2 Background 142 6.3.3 Examples
143 6.4 Likelihood Theory for Coarsened Data 145 7 Factored Likelihood
Methods When the Missingness Mechanism Is Ignorable 151 7.1 Introduction
151 7.2 Bivariate Normal Data with One Variable Subject to Missingness: ML
Estimation 153 7.2.1 ML Estimates 153 7.2.2 Large-Sample Covariance Matrix
157 7.3 Bivariate Normal Monotone Data: Small-Sample Inference 158 7.4
Monotone Missingness with More Than Two Variables 161 7.4.1 Multivariate
Data with One Normal Variable Subject to Missingness 161 7.4.2 The Factored
Likelihood for a General Monotone Pattern 162 7.4.3 ML Computation for
Monotone Normal Data via the Sweep Operator 166 7.4.4 Bayes Computation
forMonotone Normal Data via the Sweep Operator 174 7.5 Factored Likelihoods
for Special Nonmonotone Patterns 175 8 Maximum Likelihood for General
Patterns of Missing Data: Introduction and Theory with Ignorable
Nonresponse 185 8.1 Alternative Computational Strategies 185 8.2
Introduction to the EM Algorithm 187 8.3 The E Step and The M Step of EM
188 8.4 Theory of the EM Algorithm 193 8.4.1 Convergence Properties of EM
193 8.4.2 EM for Exponential Families 196 8.4.3 Rate of Convergence of EM
198 8.5 Extensions of EM 200 8.5.1 The ECM Algorithm 200 8.5.2 The ECME and
AECM Algorithms 205 8.5.3 The PX-EM Algorithm 206 8.6 Hybrid Maximization
Methods 208 9 Large-Sample Inference Based on Maximum Likelihood Estimates
213 9.1 Standard Errors Based on The Information Matrix 213 9.2 Standard
Errors via Other Methods 214 9.2.1 The Supplemented EM Algorithm 214 9.2.2
Bootstrapping the Observed Data 219 9.2.3 Other Large-Sample Methods 220
9.2.4 Posterior Standard Errors from Bayesian Methods 221 10 Bayes and
Multiple Imputation 223 10.1 Bayesian Iterative Simulation Methods 223
10.1.1 Data Augmentation 223 10.1.2 The Gibbs' Sampler 226 10.1.3 Assessing
Convergence of Iterative Simulations 230 10.1.4 Some Other Simulation
Methods 231 10.2 Multiple Imputation 232 10.2.1 Large-Sample Bayesian
Approximations of the Posterior Mean and Variance Based on a Small Number
of Draws 232 10.2.2 Approximations Using Test Statistics or p-Values 235
10.2.3 Other Methods for Creating Multiple Imputations 238 10.2.4
Chained-Equation Multiple Imputation 241 10.2.5 Using Different Models for
Imputation and Analysis 243 Part III Likelihood-Based Approaches to the
Analysis of Incomplete Data: Some Examples 247 11 Multivariate Normal
Examples, Ignoring the Missingness Mechanism 249 11.1 Introduction 249 11.2
Inference for a Mean Vector and Covariance Matrix with Missing Data Under
Normality 249 11.2.1 The EM Algorithm for Incomplete Multivariate Normal
Samples 250 11.2.2 Estimated Asymptotic Covariance Matrix of (theta . theta
hat) 252 11.2.3 Bayes Inference and Multiple Imputation for the Normal
Model 253 11.3 The Normal Model with a Restricted Covariance Matrix 257
11.4 Multiple Linear Regression 264 11.4.1 Linear Regression with
Missingness Confined to the Dependent Variable 264 11.4.2 More General
Linear Regression Problems with Missing Data 266 11.5 A General
Repeated-Measures Model with Missing Data 269 11.6 Time Series Models 273
11.6.1 Introduction 273 11.6.2 Autoregressive Models for Univariate Time
Series with Missing Values 273 11.6.3 Kalman Filter Models 276 11.7
Measurement Error Formulated as Missing Data 277 12 Models for Robust
Estimation 285 12.1 Introduction 285 12.2 Reducing the Influence of
Outliers by Replacing the Normal Distribution by a Longer-Tailed
Distribution 286 12.2.1 Estimation for a Univariate Sample 286 12.2.2
Robust Estimation of the Mean and Covariance Matrix with Complete Data 288
12.2.3 Robust Estimation of the Mean and Covariance Matrix from Data with
Missing Values 290 12.2.4 Adaptive Robust Multivariate Estimation 291
12.2.5 Bayes Inference for the t Model 292 12.2.6 Further Extensions of the
t Model 294 12.3 Penalized Spline of Propensity Prediction 298 13 Models
for Partially Classified Contingency Tables, Ignoring the Missingness
Mechanism 301 13.1 Introduction 301 13.2 Factored Likelihoods for Monotone
Multinomial Data 302 13.2.1 Introduction 302 13.2.2 ML and Bayes for
Monotone Patterns 303 13.2.3 Precision of Estimation 312 13.3 ML and Bayes
Estimation for Multinomial Samples with General Patterns of Missingness 313
13.4 Loglinear Models for Partially Classified Contingency Tables 317
13.4.1 The Complete-Data Case 317 13.4.2 Loglinear Models for Partially
Classified Tables 320 13.4.3 Goodness-of-Fit Tests for Partially Classified
Data 326 14 Mixed Normal and Nonnormal Data with Missing Values, Ignoring
the Missingness Mechanism 329 14.1 Introduction 329 14.2 The General
Location Model 329 14.2.1 The Complete-DataModel and Parameter Estimates
329 14.2.2 ML Estimation with Missing Values 331 14.2.3 Details of the E
Step Calculations 334 14.2.4 Bayes' Computation for the Unrestricted
General Location Model 335 14.3 The General Location Model with Parameter
Constraints 337 14.3.1 Introduction 337 14.3.2 Restricted Models for the
Cell Means 340 14.3.3 LoglinearModels for the Cell Probabilities 340 14.3.4
Modifications to the Algorithms of Previous Sections to Accommodate
Parameter Restrictions 340 14.3.5 SimplificationsWhen Categorical Variables
are More Observed than Continuous Variables 343 14.4 Regression Problems
InvolvingMixtures of Continuous and Categorical Variables 344 14.4.1 Normal
Linear Regression with Missing Continuous or Categorical Covariates 344
14.4.2 Logistic Regression with Missing Continuous or Categorical
Covariates 346 14.5 Further Extensions of the General Location Model 347 15
Missing Not at RandomModels 351 15.1 Introduction 351 15.2 Models with
Known MNAR Missingness Mechanisms: Grouped and Rounded Data 355 15.3 Normal
Models for MNAR Missing Data 362 15.3.1 Normal Selection and
Pattern-Mixture Models for Univariate Missingness 362 15.3.2 Following up a
Subsample of Nonrespondents 364 15.3.3 The Bayesian Approach 366 15.3.4
Imposing Restrictions on Model Parameters 369 15.3.5 Sensitivity Analysis
376 15.3.6 Subsample Ignorable Likelihood for Regression with Missing Data
379 15.4 Other Models and Methods for MNAR Missing Data 382 15.4.1 MNAR
Models for Repeated-Measures Data 382 15.4.2 MNAR Models for Categorical
Data 385 15.4.3 Sensitivity Analyses for Chained-Equation Multiple
Imputations 391 15.4.4 Sensitivity Analyses in Pharmaceutical Applications
396 References 405 Author Index 429 Subject Index 437