Statistical Analysis with Missing Data, 3rd Ed.

Statistical Analysis with Missing Data
Contents
Preface to the Third Edition
Part I Overview and Basic Approaches
	1 Introduction
		1.1 The Problem of Missing Data
		1.2 Missingness Patterns and Mechanisms
		1.3 Mechanisms That Lead to Missing Data
		1.4 A Taxonomy of Missing Data Methods
		Problems
		Note
	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 Yatess 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 Bartletts ANCOVA Method
			2.5.1 Useful Properties of Bartletts 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 ????
		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
		Problems
	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 Poststratification and Raking to Known Margins
			3.3.3 Inference from Weighted Data
			3.3.4 Summary of Weighting Methods
		3.4 Available-Case Analysis
		Problems
	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–Hot Deck Methods
		4.4 Conclusion
		Problems
	5 Accounting for Uncertainty from Missing Data
		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
		Problems
Part II Likelihood-Based Approaches to the Analysis of Data with Missing Values
	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 Inference Based on the Likelihood
			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 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
		Problems
		Notes
	7 Factored Likelihood Methods When the Missingness Mechanism Is Ignorable
		7.1 Introduction
		7.2 Bivariate Normal Data with One Variable Subject to Missingness: 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 Missingness with More Than Two Variables
			7.4.1 Multivariate Data with One Normal Variable Subject to Missingness
			7.4.2 The Factored 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 Factored Likelihoods for Special Nonmonotone Patterns
		Problems
	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 of EM
			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 The ECME and AECM Algorithms
			8.5.3 The PX-EM Algorithm
		8.6 Hybrid Maximization Methods
		Problems
	9 Large-Sample Inference Based on Maximum Likelihood Estimates
		9.1 Standard Errors Based on The Information Matrix
		9.2 Standard Errors via Other Methods
			9.2.1 The 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
		Problems
	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 or p-Values
			10.2.3 Other Methods for Creating Multiple Imputations
			10.2.4 Chained-Equation Multiple Imputation
			10.2.5 Using Different Models for Imputation and Analysis
		Problems
		Notes
Part III Likelihood-Based Approaches to the Analysis of Incomplete Data: Some Examples
	11 Multivariate Normal Examples, Ignoring the Missingness 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 (???? − ̂????)
			11.2.3 Bayes Inference and Multiple Imputation for the Normal Model
		11.3 The Normal Model with a Restricted Covariance Matrix
		11.4 Multiple Linear Regression
			11.4.1 Linear Regression with Missingness 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
		11.7 Measurement Error Formulated as Missing Data
		Problems
	12 Models for Robust Estimation
		12.1 Introduction
		12.2 Reducing the Influence of Outliers by Replacing the Normal Distribution by a Longer-Tailed Distribution
			12.2.1 Estimation for a Univariate Sample
			12.2.2 Robust Estimation of the Mean and Covariance Matrix with Complete Data
			12.2.3 Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values
			12.2.4 Adaptive Robust Multivariate Estimation
			12.2.5 Bayes Inference for the t Model
			12.2.6 Further Extensions of the t Model
		12.3 Penalized Spline of Propensity Prediction
		Problems
		Note
	13 Models for Partially Classified Contingency Tables, Ignoring the Missingness Mechanism
		13.1 Introduction
		13.2 Factored Likelihoods for Monotone Multinomial Data
			13.2.1 Introduction
			13.2.2 ML and Bayes for Monotone Patterns
			13.2.3 Precision of Estimation
		13.3 ML and Bayes Estimation for Multinomial Samples with General Patterns of Missingness
		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
		Problems
	14 Mixed Normal and Nonnormal Data with Missing Values, Ignoring the Missingness 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 Computation 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 Previous Sections to Accommodate Parameter Restrictions
			14.3.5 Simplifications When Categorical Variables are More Observed than 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
		Problems
	15 Missing Not at Random Models
		15.1 Introduction
		15.2 Models with Known MNAR Missingness Mechanisms: Grouped and Rounded Data
		15.3 Normal Models for MNAR Missing Data
			15.3.1 Normal Selection and Pattern-Mixture Models for Univariate Missingness
			15.3.2 Following up a Subsample of Nonrespondents
			15.3.3 The Bayesian Approach
			15.3.4 Imposing Restrictions on Model Parameters
			15.3.5 Sensitivity Analysis
			15.3.6 Subsample Ignorable Likelihood for Regression with Missing Data
		15.4 Other Models and Methods for MNAR Missing Data
			15.4.1 MNAR Models for Repeated-Measures Data
			15.4.2 MNAR Models for Categorical Data
			15.4.3 Sensitivity Analyses for Chained-Equation Multiple Imputations
			15.4.4 Sensitivity Analyses in Pharmaceutical Applications
		Problems
References
Author Index
Subject Index
EULA