作者j.l.schafer

Contents
Preface
1 Introduction
1.1 Purpose
1.2 Background
1.2.1 The EM algorithm
1.2.2 Markov chain Monte Carlo
1.3 Why analysis by simulation?
1.4 Looking ahead
1.4.1 Scope of the rest of this book
1.4.2 Knowledge assumed on the part of the reader
1.4.3 Software and computational details
1.5 Bibliographic notes
2 Assumptions
2.1 The complete-data model
2.2 Ignorability
2.2.1 Missing at random
2.2.2 Distinctness of parameters
2.3 The observed-data likelihood and posterior
2.3.1 Observed-data likelihood
2.3.2 Examples
2.3.3 Observed-data posterior
2.4 Examining the ignorability assumption
2.4.1 Examples where ignorability is known to hold
2.4.2 Examples where ignorability is not known to hold
2.4.3 Ignorability is relative
2.5 General ignorable procedures
2.5.1 A simulated example
2.5.2 Departures from ignorability
2.5.3 Notes on nonignorable alternatives
©1997 CRC Press LLC
2.6 The role of the complete-data model
2.6.1 Departures from the data model
2.6.2 Inference treating certain variables as fixed
3 EM and data augmentation
3.1 Introduction
3.2 The EM algorithm
3.2.1 Definition
3.2.2 Examples
3.2.3 EM for posterior modes
3.2.4 Restrictions on the parameter space
3.2.5 The ECM algorithm
3.3 Properties of EM
3.3.1 Stationary values
3.3.2 Rate of convergence
3.3.3 Example
3.3.4 Further comments on convergence
3.4 Markov chain Monte Carlo
3.4.1 Gibbs sampling
3.4.2 Data augmentation
3.4.3 Examples of data augmentation
3.4.4 The Metropolis-Hastings algorithm
3.4.5 Generalizations and hybrid algorithms
3.5 Properties of Markov chain Monte Carlo
3.5.1 The meaning of convergence
3.5.2 Examples of nonconvergence
3.5.3 Rates of convergence
4 Inference by data augmentation
4.1 Introduction
4.2 Parameter simulation
4.2.1 Dependent samples
4.2.2 Summarizing a dependent sample
4.2.3 Rao-Blackwellized estimates
4.3 Multiple imputation
4.3.1 Bayesianly proper multiple imputations
4.3.2 Inference for a scalar quantity
4.3.3 Inference for multidimensional estimands
4.4 Assessing convergence
4.4.1 Monitoring convergence in a single chain
©1997 CRC Press LLC
4.4.2 Monitoring convergence with parallel chains
4.4.3 Choosing scalar functions of the parameter
4.4.4 Convergence of posterior summaries
4.5 Practical guidelines
4.5.1 Choosing a method of inference
4.5.2 Implementing a parameter-simulation experiment
4.5.3 Generating multiple imputations
4.5.4 Choosing an imputation model
4.5.5 Further comments on imputation modeling
5 Methods for normal data
5.1 Introduction
5.2 Relevant properties of the complete-data model
5.2.1 Basic notation
5.2.2 Bayesian inference under a conjugate prior
5.2.3 Choosing the prior hyperparameters
5.2.4 Alternative parameterizations and sweep
5.3 The EM algorithm
5.3.1 Preliminary manipulations
5.3.2 The E-step
5.3.3 Implementation of the algorithm
5.3.4 EM for posterior modes
5.3.5 Calculating the observed-data loglikelihood
5.3.6 Example: serum-cholesterol levels of heart attack
patients
5.3.7 Example: changes in heart rate due to marijuana use
5.4 Data augmentation
5.4.1 The I-step
5.4.2 The P-step
5.4.3 Example: cholesterol levels of heart-Attack patients
5.4.4 Example: changes in heart rate due to marijuana use
6 More on the normal model
6.1 Introduction
6.2 Multiple imputation: example
6.2.1 Cholesterol levels of heart-attack patients
6.2.2 Generating the imputations
6.2.3 Complete-data point and variance estimates
6.2.4 Combining the estimates
6.2.5 Alternative choices for the number of imputations
©1997 CRC Press LLC
6.3 Multiple imputation: example 2
6.3.1 Predicting achievement in foreign language study
6.3.2 Applying the normal model
6.3.3 Exploring the observed-data likelihood and posterior
6.3.4 Overcoming the problem of inestimability
6.3.5 Analysis by multiple imputation
6.4 A simulation study
6.4.1 Simulation procedures
6.4.2 Complete-data inferences
6.4.3 Results
6.5 Fast algorithms based on factored likelihoods
6.5.1 Monotone missingness patterns
6.5.2 Computing alternative parameterizations
6.5.3 Noniterative inference for monotone data
6.5.4 Monotone data augmentation
6.5.5 Implementation of the algorithm
6.5.6 Uses and extensions
6.5.7 Example
7 Methods for categorical data
7.1 Introduction
7.2 The multinomial model and Dirichlet prior
7.2.1 The multinomial distribution
7.2.2 Collapsing and partitioning the multinomial
7.2.3 The Dirichlet distribution
7.2.4 Bayesian inference
7.2.5 Choosing the prior hyperparameters
7.2.6 Collapsing and partitioning the Dirichlet
7.3 Basic algorithms for the saturated model
7.3.1 Characterizing an incomplete categorical dataset
7.3.2 The EM algorithm
7.3.3 Data augmentation
7.3.4 Example: victimization status from the National
Crime Survey
7.3.5 Example: Protective Services Project for Older
Persons
7.4 Fast algorithms for near-monotone patterns
7.4.1 Factoring the likelihood and prior density
7.4.2 Monotone data augmentation
7.4.3 Example: driver injury and seatbelt use
©1997 CRC Press LLC
8 Loglinear models
8.1 Introduction
8.2 Overview of loglinear models
8.2.1 Definition
8.2.2 Eliminating associations
8.2.3 Sufficient statistics
8.2.4 Model interpretation
8.3 Likelihood-based inference with complete data
8.3.1 Maximum-likelihood estimation
8.3.2 Iterative proportional fitting
8.3.3 Hypothesis testing and goodness of fit
8.3.4 Example: misclassification of seatbelt use and injury
8.4 Bayesian inference with complete data
8.4.1 Prior distributions for loglinear models
8.4.2 Inference using posterior modes
8.4.3 Inference by Bayesian IPF
8.4.4 Why Bayesian IPF works
8.4.5 Example: misclassification of seatbelt use and injury
8.5 Loglinear modeling with incomplete data
8.5.1 ML estimates and posterior modes
8.5.2 Goodness-of-fit statistics
8.5.3 Data augmentation and Bayesian IPF
8.6 Examples
8.6.1 Protective Services Project for Older Persons
8.6.2 Driver injury and seatbelt use
9 Methods for mixed data
9.1 Introduction
9.2 The general location model
9.2.1 Definition
9.2.2 Complete-data likelihood
9.2.3 Example
9.2.4 Complete-data Bayesian inference
9.3 Restricted models
9.3.1 Reducing the number of parameters
9.3.2 Likelihood inference for restricted models
9.3.3 Bayesian inference
9.4 Algorithms for incomplete mixed data
9.4.1 Predictive distributions
©1997 CRC Press LLC
9.4.2 EM for the unrestricted model
9.4.3 Data augmentation
9.4.4 Algorithms for restricted models
9.5 Data examples
9.5.1 St. Louis Risk Research Project
9.5.2 Foreign Language Attitude Scale
9.5.3 National Health and Nutrition Examination Survey
10 Further topics
10.1 Introduction
10.2 Extensions of the normal model
10.2.1 Restricted covariance structures
10.2.2 Heavy-tailed distributions
10.2.3 Interactions
10.2.4 Semicontinuous variables
10.3 Random-effects models
10.4 Models for complex survey data
10.5 Nonignorable methods
10.6 Mixture models and latent variables
10.7 Coarsened data and outlier models
10.8 Diagnostics
Appendices
A Data examples
B Storage of categorical data
C Software
References