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Statistical Analysis with Missing Data.

By: Contributor(s): Series: Wiley Series in Probability and Statistics SerPublisher: Newy York : John Wiley & Sons, Incorporated, 2002Copyright date: ©2002Edition: 2nd edDescription: 1 online resource (409 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781118625866
Subject(s): Genre/Form: Additional physical formats: Print version:: Statistical Analysis with Missing DataDDC classification:
  • 519.5
LOC classification:
  • QA276 -- .L57 2002eb
Online resources:
Contents:
Cover -- Title Page -- Copyright -- Contents -- Preface -- Part I: Overview and Basic Approaches -- Chapter 1: Introduction -- 1.1. The Problem of Missing Data -- 1.2. Missing-data Patterns -- 1.3. Mechanisms That Lead to Missing Data -- 1.4. A Taxonomy of Missing-data Methods -- Chapter 2: Missing Data in Experiments -- 2.1. Introduction -- 2.2. The Exact Least Squares Solution with Complete Data -- 2.3. The Correct Least Squares Analysis with Missing Data -- 2.4. Filling in Least Squares Estimates -- 2.4.1. Yates's Method -- 2.4.2. Using a Formula for the Missing Values -- 2.4.3. Iterating to Find the Missing Values -- 2.4.4. Ancova with Missing-value Covariates -- 2.5. Bartlett's Ancova Method -- 2.5.1. Useful Properties of Bartlett's Method -- 2.5.2. Notation -- 2.5.3. The Ancova Estimates of Parameters and Missing Y Values -- 2.5.4. Ancova Estimates of the Residual Sums of Squares and the Covariance Matrix of ß^ -- 2.6. Least Squares Estimates of Missing Values by Ancova Using Only Complete-data Methods -- 2.7. Correct Least Squares Estimates of Standard Errors and One Degree of Freedom Sums of Squares -- 2.8. Correct Least Squares Sums of Squares with More Than One Degree of Freedom -- Chapter 3: Complete-case and Available-case Analysis, Including Weighting Methods -- 3.1. Introduction -- 3.2. Complete-case Analysis -- 3.3. Weighted Complete-case Analysis -- 3.3.1. Weighting Adjustments -- 3.3.2. Added Variance from Nonresponse Weighting -- 3.3.3. Post-stratification and Raking to Known Margins -- 3.3.4. Inference from Weighted Data -- 3.3.5. Summary of Weighting Methods -- 3.4. Available-case Analysis -- Chapter 4: Single Imputation Methods -- 4.1. Introduction -- 4.2. Imputing Means from a Predictive Distribution -- 4.2.1. Unconditional Mean Imputation -- 4.2.2. Conditional Mean Imputation.
4.3. Imputing Draws from a Predictive Distribution -- 4.3.1. Draws Based on Explicit Models -- 4.3.2. Draws Based on Implicit Models -- 4.4. Conclusions -- Chapter 5: Estimation of Imputation Uncertainty -- 5.1. Introduction -- 5.2. Imputation Methods That Provide Valid Standard Errors from a Single Filled-in Data Set -- 5.3. Standard Errors for Imputed Data by Resampling -- 5.3.1 Bootstrap Standard Errors -- 5.3.2. Jackknife Standard Errors -- 5.4. Introduction to Multiple Imputation -- 5.5. Comparison of Resampling Methods and Multiple Imputation -- Part II: Likelihood-based Approaches to the Analysis of Missing Data -- Chapter 6: Theory of Inference Based on the Likelihood Function -- 6.1. Review of Likelihood-based Estimation for Complete Data -- 6.1.1. Maximum Likelihood Estimation -- 6.1.2. Rudiments of Bayes Estimation -- 6.1.3. Large-sample Maximum Likelihood and Bayes Inference -- 6.1.4. Bayes Inference Based on the Full Posterior Distribution -- 6.1.5. Simulating Draws from Posterior Distributions -- 6.2. Likelihood-based Inference with Incomplete Data -- 6.3. a Generally Flawed Alternative to Maximum Likelihood: Maximizing over the Parameters and the Missing Data -- 6.3.1. The Method -- 6.3.2. Background -- 6.3.3. Examples -- 6.4. Likelihood Theory for Coarsened Data -- Chapter 7: Factored Likelihood Methods, Ignoring the Missing-data Mechanism -- 7.1. Introduction -- 7.2. Bivariate Normal Data with One Variable Subject to Nonresponse: Ml Estimation -- 7.2.1. Ml Estimates -- 7.2.2. Large-sample Covariance Matrix -- 7.3 Bivariate Normal Monotone Data: Small-sample Inference -- 7.4 Monotone Data with More Than Two Variables -- 7.4.1. Multivariate Data with One Normal Variable Subject to Nonresponse -- 7.4.2. Factorization of the Likelihood for a General Monotone Pattern -- 7.4.3. Ml Computation for Monotone Normal Data Via the Sweep Operator.
7.4.4. Bayes Computation for Monotone Normal Data Via the Sweep Operator -- 7.5 Factorizations for Special Nonmonotone Patterns -- Chapter 8: Maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse -- 8.1. Alternative Computational Strategies -- 8.2. Introduction to the Em Algorithm -- 8.3. The E Step and the M Step of Em -- 8.4. Theory of the Em Algorithm -- 8.4.1. Convergence Properties -- 8.4.2. Em for Exponential Families -- 8.4.3. Rate of Convergence of Em -- 8.5. Extensions of Em -- 8.5.1. The Ecm Algorithm -- 8.5.2. Ecme and Aecm Algorithms -- 8.5.3. Px-em Algorithm -- 8.6. Hybrid Maximization Methods -- Chapter 9: Large-sample Inference Based on Maximum Likelihood Estimates -- 9.1. Standard Errors Based on the Information Matrix -- 9.2. Standard Errors Via Methods That Do Not Require Computing and Inverting an Estimate of the Observed Information Matrix -- 9.2.1. Supplemented Em Algorithm -- 9.2.2. Bootstrapping the Observed Data -- 9.2.3. Other Large Sample Methods -- 9.2.4. Posterior Standard Errors from Bayesian Methods -- Chapter 10: Bayes and Multiple Imputation -- 10.1. Bayesian Iterative Simulation Methods -- 10.1.1. Data Augmentation -- 10.1.2. The Gibbs' Sampler -- 10.1.3. Assessing Convergence of Iterative Simulations -- 10.1.4. Some Other Simulation Methods -- 10.2. Multiple Imputation -- 10.2.1. Large-sample Bayesian Approximations of the Posterior Mean and Variance Based on a Small Number of Draws -- 10.2.2. Approximations Using Test Statistics -- 10.2.3. Other Methods for Creating Multiple Imputations -- 10.2.4. Use of Different Models for Imputation and Analysis -- Part III: Likelihood-based Approaches to the Analysis of Incomplete Data: Some Examples -- Chapter 11: Multivariate Normal Examples, Ignoring the Missing-data Mechanism -- 11.1. Introduction.
11.2. Inference for a Mean Vector and Covariance Matrix with Missing Data Under Normality -- 11.2.1. The Em Algorithm for Incomplete Multivariate Normal Samples -- 11.2.2. Estimated Asymptotic Covariance Matrix of (θ - θ^) -- 11.2.3. Bayes Inference for the Normal Model Via Data Augmentation -- 11.3. Estimation with a Restricted Covariance Matrix -- 11.4. Multiple Linear Regression -- 11.4.1. Linear Regression with Missing Values Confined to the Dependent Variable -- 11.4.2. More General Linear Regression Problems with Missing Data -- 11.5. A General Repeated-measures Model with Missing Data -- 11.6. Time Series Models -- 11.6.1. Introduction -- 11.6.2. Autoregressive Models for Univariate Time Series with Missing Values -- 11.6.3. Kalman Filter Models -- Chapter 12: Robust Estimation -- 12.1. Introduction -- 12.2. Robust Estimation for a Univariate Sample -- 12.3. Robust Estimation of the Mean and Covariance Matrix -- 12.3.1. Multivariate Complete Data -- 12.3.2. Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values -- 12.3.3. Adaptive Robust Multivariate Estimation -- 12.3.4. Bayes Inferences for the T Model -- 12.4. Further Extensions of the T Model -- Chapter 13: Models for Partially Classified Contingency Tables, Ignoring the Missing-data Mechanism -- 13.1. Introduction -- 13.2. Factored Likelihoods for Monotone Multinomial Data -- 13.2.1. Introduction -- 13.2.2. Ml Estimation for Monotone Patterns -- 13.2.3. Precision of Estimation -- 13.3. Ml and Bayes Estimation for Multinomial Samples with General Patterns of Missing Data -- 13.4. Loglinear Models for Partially Classified Contingency Tables -- 13.4.1. The Complete-data Case -- 13.4.2. Loglinear Models for Partially Classified Tables -- 13.4.3. Goodness-of-fit Tests for Partially Classified Data.
Chapter 14: Mixed Normal and Non-normal Data with Missing Values, Ignoring the Missing-data Mechanism -- 14.1. Introduction -- 14.2. The General Location Model -- 14.2.1. The Complete-data Model and Parameter Estimates -- 14.2.2. Ml Estimation with Missing Values -- 14.2.3. Details of the E Step Calculations -- 14.2.4. Bayes Computations for the Unrestricted General Location Model -- 14.3. The General Location Model with Parameter Constraints -- 14.3.1. Introduction -- 14.3.2. Restricted Models for the Cell Means -- 14.3.3. Loglinear Models for the Cell Probabilities -- 14.3.4. Modifications to the Algorithms of Sections 14.2.2 and 14.2.3 for Parameter Restrictions -- 14.3.5. Simplifications When the Categorical Variables Are More Observed Than the Continuous Variables. -- 14.4. Regression Problems Involving Mixtures of Continuous and Categorical Variables -- 14.4.1. Normal Linear Regression with Missing Continuous or Categorical Covariates -- 14.4.2. Logistic Regression with Missing Continuous or Categorical Covariates -- 14.5. Further Extensions of the General Location Model -- Chapter 15: Nonignorable Missing-data Models -- 15.1. Introduction -- 15.2. Likelihood Theory for Nonignorable Models -- 15.3. Models with Known Nonignorable Missing-data Mechanisms: Grouped and Rounded Data -- 15.4. Normal Selection Models -- 15.5. Normal Pattern-mixture Models -- 15.5.1. Univariate Normal Pattern-mixture Models -- 15.5.2. Bivariate Normal Pattern-mixture Models Identified Via Parameter Restrictions -- 15.6. Nonignorable Models for Normal Repeated-measures Data -- 15.7. Nonignorable Models for Categorical Data -- References -- Author Index -- Subject Index.
Summary: Praise for the First Edition of Statistical Analysis with Missing Data "An important contribution to the applied statistics literature.... I give the book high marks for unifying and making accessible much of the past and current work in this important area." -William E. Strawderman, Rutgers University "This book...provide[s] interesting real-life examples, stimulating end-of-chapter exercises, and up-to-date references. It should be on every applied statistician's bookshelf." -The Statistician "The book should be studied in the statistical methods department in every statistical agency." -Journal of Official Statistics Statistical analysis of data sets with missing values is a pervasive problem for which standard methods are of limited value. The first edition of Statistical Analysis with Missing Data has been a standard reference on missing-data methods. Now, reflecting extensive developments in Bayesian methods for simulating posterior distributions, this Second Edition by two acknowledged experts on the subject offers a thoroughly up-to-date, reorganized survey of current methodology for handling missing-data problems. Blending theory and application, authors Roderick Little and Donald Rubin review historical approaches to the subject and describe rigorous yet 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 apply the theory to a wide range of important missing-data problems. The new edition now enlarges its coverage to include: Expanded coverage of Bayesian methodology, both theoretical and computational, and of multiple imputation Analysis of data with missing values where inferences are based on likelihoods derived from formal statistical models for theSummary: data-generating and missing-data mechanisms Applications of the approach in a variety of contexts including regression, factor analysis, contingency table analysis, time series, and sample survey inference Extensive references, examples, and exercises Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Statistical Analysis With Missing Data was among those chosen.
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Cover -- Title Page -- Copyright -- Contents -- Preface -- Part I: Overview and Basic Approaches -- Chapter 1: Introduction -- 1.1. The Problem of Missing Data -- 1.2. Missing-data Patterns -- 1.3. Mechanisms That Lead to Missing Data -- 1.4. A Taxonomy of Missing-data Methods -- Chapter 2: Missing Data in Experiments -- 2.1. Introduction -- 2.2. The Exact Least Squares Solution with Complete Data -- 2.3. The Correct Least Squares Analysis with Missing Data -- 2.4. Filling in Least Squares Estimates -- 2.4.1. Yates's Method -- 2.4.2. Using a Formula for the Missing Values -- 2.4.3. Iterating to Find the Missing Values -- 2.4.4. Ancova with Missing-value Covariates -- 2.5. Bartlett's Ancova Method -- 2.5.1. Useful Properties of Bartlett's Method -- 2.5.2. Notation -- 2.5.3. The Ancova Estimates of Parameters and Missing Y Values -- 2.5.4. Ancova Estimates of the Residual Sums of Squares and the Covariance Matrix of ß^ -- 2.6. Least Squares Estimates of Missing Values by Ancova Using Only Complete-data Methods -- 2.7. Correct Least Squares Estimates of Standard Errors and One Degree of Freedom Sums of Squares -- 2.8. Correct Least Squares Sums of Squares with More Than One Degree of Freedom -- Chapter 3: Complete-case and Available-case Analysis, Including Weighting Methods -- 3.1. Introduction -- 3.2. Complete-case Analysis -- 3.3. Weighted Complete-case Analysis -- 3.3.1. Weighting Adjustments -- 3.3.2. Added Variance from Nonresponse Weighting -- 3.3.3. Post-stratification and Raking to Known Margins -- 3.3.4. Inference from Weighted Data -- 3.3.5. Summary of Weighting Methods -- 3.4. Available-case Analysis -- Chapter 4: Single Imputation Methods -- 4.1. Introduction -- 4.2. Imputing Means from a Predictive Distribution -- 4.2.1. Unconditional Mean Imputation -- 4.2.2. Conditional Mean Imputation.

4.3. Imputing Draws from a Predictive Distribution -- 4.3.1. Draws Based on Explicit Models -- 4.3.2. Draws Based on Implicit Models -- 4.4. Conclusions -- Chapter 5: Estimation of Imputation Uncertainty -- 5.1. Introduction -- 5.2. Imputation Methods That Provide Valid Standard Errors from a Single Filled-in Data Set -- 5.3. Standard Errors for Imputed Data by Resampling -- 5.3.1 Bootstrap Standard Errors -- 5.3.2. Jackknife Standard Errors -- 5.4. Introduction to Multiple Imputation -- 5.5. Comparison of Resampling Methods and Multiple Imputation -- Part II: Likelihood-based Approaches to the Analysis of Missing Data -- Chapter 6: Theory of Inference Based on the Likelihood Function -- 6.1. Review of Likelihood-based Estimation for Complete Data -- 6.1.1. Maximum Likelihood Estimation -- 6.1.2. Rudiments of Bayes Estimation -- 6.1.3. Large-sample Maximum Likelihood and Bayes Inference -- 6.1.4. Bayes Inference Based on the Full Posterior Distribution -- 6.1.5. Simulating Draws from Posterior Distributions -- 6.2. Likelihood-based Inference with Incomplete Data -- 6.3. a Generally Flawed Alternative to Maximum Likelihood: Maximizing over the Parameters and the Missing Data -- 6.3.1. The Method -- 6.3.2. Background -- 6.3.3. Examples -- 6.4. Likelihood Theory for Coarsened Data -- Chapter 7: Factored Likelihood Methods, Ignoring the Missing-data Mechanism -- 7.1. Introduction -- 7.2. Bivariate Normal Data with One Variable Subject to Nonresponse: Ml Estimation -- 7.2.1. Ml Estimates -- 7.2.2. Large-sample Covariance Matrix -- 7.3 Bivariate Normal Monotone Data: Small-sample Inference -- 7.4 Monotone Data with More Than Two Variables -- 7.4.1. Multivariate Data with One Normal Variable Subject to Nonresponse -- 7.4.2. Factorization of the Likelihood for a General Monotone Pattern -- 7.4.3. Ml Computation for Monotone Normal Data Via the Sweep Operator.

7.4.4. Bayes Computation for Monotone Normal Data Via the Sweep Operator -- 7.5 Factorizations for Special Nonmonotone Patterns -- Chapter 8: Maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse -- 8.1. Alternative Computational Strategies -- 8.2. Introduction to the Em Algorithm -- 8.3. The E Step and the M Step of Em -- 8.4. Theory of the Em Algorithm -- 8.4.1. Convergence Properties -- 8.4.2. Em for Exponential Families -- 8.4.3. Rate of Convergence of Em -- 8.5. Extensions of Em -- 8.5.1. The Ecm Algorithm -- 8.5.2. Ecme and Aecm Algorithms -- 8.5.3. Px-em Algorithm -- 8.6. Hybrid Maximization Methods -- Chapter 9: Large-sample Inference Based on Maximum Likelihood Estimates -- 9.1. Standard Errors Based on the Information Matrix -- 9.2. Standard Errors Via Methods That Do Not Require Computing and Inverting an Estimate of the Observed Information Matrix -- 9.2.1. Supplemented Em Algorithm -- 9.2.2. Bootstrapping the Observed Data -- 9.2.3. Other Large Sample Methods -- 9.2.4. Posterior Standard Errors from Bayesian Methods -- Chapter 10: Bayes and Multiple Imputation -- 10.1. Bayesian Iterative Simulation Methods -- 10.1.1. Data Augmentation -- 10.1.2. The Gibbs' Sampler -- 10.1.3. Assessing Convergence of Iterative Simulations -- 10.1.4. Some Other Simulation Methods -- 10.2. Multiple Imputation -- 10.2.1. Large-sample Bayesian Approximations of the Posterior Mean and Variance Based on a Small Number of Draws -- 10.2.2. Approximations Using Test Statistics -- 10.2.3. Other Methods for Creating Multiple Imputations -- 10.2.4. Use of Different Models for Imputation and Analysis -- Part III: Likelihood-based Approaches to the Analysis of Incomplete Data: Some Examples -- Chapter 11: Multivariate Normal Examples, Ignoring the Missing-data Mechanism -- 11.1. Introduction.

11.2. Inference for a Mean Vector and Covariance Matrix with Missing Data Under Normality -- 11.2.1. The Em Algorithm for Incomplete Multivariate Normal Samples -- 11.2.2. Estimated Asymptotic Covariance Matrix of (θ - θ^) -- 11.2.3. Bayes Inference for the Normal Model Via Data Augmentation -- 11.3. Estimation with a Restricted Covariance Matrix -- 11.4. Multiple Linear Regression -- 11.4.1. Linear Regression with Missing Values Confined to the Dependent Variable -- 11.4.2. More General Linear Regression Problems with Missing Data -- 11.5. A General Repeated-measures Model with Missing Data -- 11.6. Time Series Models -- 11.6.1. Introduction -- 11.6.2. Autoregressive Models for Univariate Time Series with Missing Values -- 11.6.3. Kalman Filter Models -- Chapter 12: Robust Estimation -- 12.1. Introduction -- 12.2. Robust Estimation for a Univariate Sample -- 12.3. Robust Estimation of the Mean and Covariance Matrix -- 12.3.1. Multivariate Complete Data -- 12.3.2. Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values -- 12.3.3. Adaptive Robust Multivariate Estimation -- 12.3.4. Bayes Inferences for the T Model -- 12.4. Further Extensions of the T Model -- Chapter 13: Models for Partially Classified Contingency Tables, Ignoring the Missing-data Mechanism -- 13.1. Introduction -- 13.2. Factored Likelihoods for Monotone Multinomial Data -- 13.2.1. Introduction -- 13.2.2. Ml Estimation for Monotone Patterns -- 13.2.3. Precision of Estimation -- 13.3. Ml and Bayes Estimation for Multinomial Samples with General Patterns of Missing Data -- 13.4. Loglinear Models for Partially Classified Contingency Tables -- 13.4.1. The Complete-data Case -- 13.4.2. Loglinear Models for Partially Classified Tables -- 13.4.3. Goodness-of-fit Tests for Partially Classified Data.

Chapter 14: Mixed Normal and Non-normal Data with Missing Values, Ignoring the Missing-data Mechanism -- 14.1. Introduction -- 14.2. The General Location Model -- 14.2.1. The Complete-data Model and Parameter Estimates -- 14.2.2. Ml Estimation with Missing Values -- 14.2.3. Details of the E Step Calculations -- 14.2.4. Bayes Computations for the Unrestricted General Location Model -- 14.3. The General Location Model with Parameter Constraints -- 14.3.1. Introduction -- 14.3.2. Restricted Models for the Cell Means -- 14.3.3. Loglinear Models for the Cell Probabilities -- 14.3.4. Modifications to the Algorithms of Sections 14.2.2 and 14.2.3 for Parameter Restrictions -- 14.3.5. Simplifications When the Categorical Variables Are More Observed Than the Continuous Variables. -- 14.4. Regression Problems Involving Mixtures of Continuous and Categorical Variables -- 14.4.1. Normal Linear Regression with Missing Continuous or Categorical Covariates -- 14.4.2. Logistic Regression with Missing Continuous or Categorical Covariates -- 14.5. Further Extensions of the General Location Model -- Chapter 15: Nonignorable Missing-data Models -- 15.1. Introduction -- 15.2. Likelihood Theory for Nonignorable Models -- 15.3. Models with Known Nonignorable Missing-data Mechanisms: Grouped and Rounded Data -- 15.4. Normal Selection Models -- 15.5. Normal Pattern-mixture Models -- 15.5.1. Univariate Normal Pattern-mixture Models -- 15.5.2. Bivariate Normal Pattern-mixture Models Identified Via Parameter Restrictions -- 15.6. Nonignorable Models for Normal Repeated-measures Data -- 15.7. Nonignorable Models for Categorical Data -- References -- Author Index -- Subject Index.

Praise for the First Edition of Statistical Analysis with Missing Data "An important contribution to the applied statistics literature.... I give the book high marks for unifying and making accessible much of the past and current work in this important area." -William E. Strawderman, Rutgers University "This book...provide[s] interesting real-life examples, stimulating end-of-chapter exercises, and up-to-date references. It should be on every applied statistician's bookshelf." -The Statistician "The book should be studied in the statistical methods department in every statistical agency." -Journal of Official Statistics Statistical analysis of data sets with missing values is a pervasive problem for which standard methods are of limited value. The first edition of Statistical Analysis with Missing Data has been a standard reference on missing-data methods. Now, reflecting extensive developments in Bayesian methods for simulating posterior distributions, this Second Edition by two acknowledged experts on the subject offers a thoroughly up-to-date, reorganized survey of current methodology for handling missing-data problems. Blending theory and application, authors Roderick Little and Donald Rubin review historical approaches to the subject and describe rigorous yet 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 apply the theory to a wide range of important missing-data problems. The new edition now enlarges its coverage to include: Expanded coverage of Bayesian methodology, both theoretical and computational, and of multiple imputation Analysis of data with missing values where inferences are based on likelihoods derived from formal statistical models for the

data-generating and missing-data mechanisms Applications of the approach in a variety of contexts including regression, factor analysis, contingency table analysis, time series, and sample survey inference Extensive references, examples, and exercises Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Statistical Analysis With Missing Data was among those chosen.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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