Table of Contents

1. An Introduction to Missing Data
1.1 Introduction
1.2 Chapter Overview
1.3 Missing Data Patterns
1.4 A Conceptual Overview of Missing Data Theory
1.5 A More Formal Description of Missing Data Theory
1.6 Why Is the Missing Data Mechanism Important?
1.7 How Plausible Is the Missing at Random Mechanism?
1.8 An Inclusive Analysis Strategy
1.9 Testing the Missing Completely at Random Mechanism
1.10 Planned Missing Data Designs
1.11 The Three-Form Design
1.12 Planned Missing Data for Longitudinal Designs
1.13 Conducting Power Analyses for Planned Missing Data Designs
1.14 Data Analysis Example
1.15 Summary
1.16 Recommended Readings
2. Traditional Methods for Dealing with Missing Data
2.1 Chapter Overview
2.2 An Overview of Deletion Methods
2.3 Listwise Deletion
2.4 Pairwise Deletion
2.5 An Overview of Single Imputation Techniques
2.6 Arithmetic Mean Imputation
2.7 Regression Imputation
2.8 Stochastic Regression Imputation
2.9 Hot-Deck Imputation
2.10 Similar Response Pattern Imputation
2.11 Averaging the Available Items
2.12 Last Observation Carried Forward
2.13 An Illustrative Simulation Study
2.14 Summary
2.15 Recommended Readings
3. An Introduction to Maximum Likelihood Estimation
3.1 Chapter Overview
3.2 The Univariate Normal Distribution
3.3 The Sample Likelihood
3.4 The Log-Likelihood
3.5 Estimating Unknown Parameters
3.6 The Role of First Derivatives
3.7 Estimating Standard Errors
3.8 Maximum Likelihood Estimation with Multivariate Normal Data
3.9 A Bivariate Analysis Example
3.10 Iterative Optimization Algorithms
3.11 Significance Testing Using the Wald Statistic
3.12 The Likelihood Ratio Test Statistic
3.13 Should I Use the Wald Test or the Likelihood Ratio Statistic?
3.14 Data Analysis Example 1
3.15 Data Analysis Example 2
3.16 Summary
3.17 Recommended Readings
4. Maximum Likelihood Missing Data Handling
4.1 Chapter Overview
4.2 The Missing Data Log-Likelihood
4.3 How Do the Incomplete Data Records Improve Estimation?
4.4 An Illustrative Computer Simulation Study
4.5 Estimating Standard Errors with Missing Data
4.6 Observed Versus Expected Information
4.7 A Bivariate Analysis Example
4.8 An Illustrative Computer Simulation Study
4.9 An Overview of the EM Algorithm
4.10 A Detailed Description of the EM Algorithm
4.11 A Bivariate Analysis Example
4.12 Extending EM to Multivariate Data
4.13 Maximum Likelihood Software Options
4.14 Data Analysis Example 1
4.15 Data Analysis Example 2
4.16 Data Analysis Example 3
4.17 Data Analysis Example 4
4.18 Data Analysis Example 5
4.19 Summary
4.20 Recommended Readings
5. Improving the Accuracy of Maximum Likelihood Analyses
5.1 Chapter Overview
5.2 The Rationale for an Inclusive Analysis Strategy
5.3 An Illustrative Computer Simulation Study
5.4 Identifying a Set of Auxiliary Variables
5.5 Incorporating Auxiliary Variables Into a Maximum Likelihood Analysis
5.6 The Saturated Correlates Model
5.7 The Impact of Non-Normal Data
5.8 Robust Standard Errors
5.9 Bootstrap Standard Errors
5.10 The Rescaled Likelihood Ratio Test
5.11 Bootstrapping the Likelihood Ratio Statistic
5.12 Data Analysis Example 1
5.13 Data Analysis Example 2
5.14 Data Analysis Example 3
5.15 Summary
5.16 Recommended Readings
6. An Introduction to Bayesian Estimation
6.1 Chapter Overview
6.2 What Makes Bayesian Statistics Different?
6.3 A Conceptual Overview of Bayesian Estimation
6.4 Bayes’ Theorem
6.5 An Analysis Example
6.6 How Does Bayesian Estimation Apply to Multiple Imputation?
6.7 The Posterior Distribution of the Mean
6.8 The Posterior Distribution of the Variance
6.9 The Posterior Distribution of a Covariance Matrix
6.10 Summary
6.11 Recommended Readings
7. The Imputation Phase of Multiple Imputation
7.1 Chapter Overview
7.2 A Conceptual Description of the Imputation Phase
7.3 A Bayesian Description of the Imputation Phase
7.4 A Bivariate Analysis Example
7.5 Data Augmentation with Multivariate Data
7.6 Selecting Variables for Imputation
7.7 The Meaning of Convergence
7.8 Convergence Diagnostics
7.9 Time-Series Plots
7.10 Autocorrelation Function Plots
7.11 Assessing Convergence from Alternate Starting Values
7.12 Convergence Problems
7.13 Generating the Final Set of Imputations
7.14 How Many Data Sets Are Needed?
7.15 Summary
7.16 Recommended Readings
8. The Analysis and Pooling Phases of Multiple Imputation
8.1 Chapter Overview
8.2 The Analysis Phase
8.3 Combining Parameter Estimates in the Pooling Phase
8.4 Transforming Parameter Estimates Prior to Combining
8.5 Pooling Standard Errors
8.6 The Fraction of Missing Information and the Relative Increase in Variance
8.7 When Is Multiple Imputation Comparable to Maximum Likelihood?
8.8 An Illustrative Computer Simulation Study
8.9 Significance Testing Using the t Statistic
8.10 An Overview of Multiparameter Significance Tests
8.11 Testing Multiple Parameters Using the D1 Statistic
8.12 Testing Multiple Parameters by Combining Wald Tests
8.13 Testing Multiple Parameters by Combining Likelihood Ratio Statistics
8.14 Data Analysis Example 1
8.15 Data Analysis Example 2
8.16 Data Analysis Example 3
8.17 Summary
8.18 Recommended Readings
9. Practical Issues in Multiple Imputation
9.1 Chapter Overview
9.2 Dealing with Convergence Problems
9.3 Dealing with Non-Normal Data
9.4 To Round or Not to Round?
9.5 Preserving Interaction Effects
9.6 Imputing Multiple-Item Questionnaires
9.7 Alternate Imputation Algorithms
9.8 Multiple Imputation Software Options
9.9 Data Analysis Example 1
9.10 Data Analysis Example 2
9.11 Summary
9.12 Recommended Readings
10. Models for Missing Not at Random Data
10.1 Chapter Overview
10.2 An Ad Hoc Approach to Dealing with MNAR Data
10.3 The Theoretical Rationale for MNAR Models
10.4 The Classic Selection Model
10.5 Estimating the Selection Model
10.6 Limitations of the Selection Model
10.7 An Illustrative Analysis
10.8 The Pattern Mixture Model
10.9 Limitations of the Pattern Mixture Model
10.10 An Overview of the Longitudinal Growth Model
10.11 A Longitudinal Selection Model
10.12 Random Coefficient Selection Models
10.13 Pattern Mixture Models for Longitudinal Analyses
10.14 Identification Strategies for Longitudinal Pattern Mixture Models
10.15 Delta Method Standard Errors
10.16 Overview of the Data Analysis Examples
10.17 Data Analysis Example 1
10.18 Data Analysis Example 2
10.19 Data Analysis Example 3
10.20 Data Analysis Example 4
10.21 Summary
10.22 Recommended Readings
11. Wrapping Things Up: Some Final Practical Considerations
11.1 Chapter Overview
11.2 Maximum Likelihood Software Options
11.3 Multiple Imputation Software Options
11.4 Choosing between Maximum Likelihood and Multiple Imputation
11.5 Reporting the Results from a Missing Data Analysis
11.6 Final Thoughts
11.7 Recommended Readings

About the Author

Craig K. Enders, Department of Psychology, Arizona State University, Tempe, USA

Reviews

"This is a well-written book that will be particularly useful for analysts who are not PhD statisticians. Enders provides a much-needed overview and explication of the current technical literature on missing data. The book should become a popular text for applied methodologists." - Bengt Muthen, Professor Emeritus, University of California, Los Angeles, USA "A needed and valuable addition to the literature on missing data. The simulations are excellent and are a clear strength of the book." - Alan C. Acock, Distinguished Professor and Knudson Chair in Family Research, Department of Human Development and Family Sciences, Oregon State University, USA "The book contains very accessible material on missing data. I would recommend it to colleagues and students, especially those who do not have formal training in mathematical statistics." - Ke-Hai Yuan, Department of Psychology, University of Notre Dame, USA "Many applied researchers are not trained in statistics to the level that would make the classic sources on missing data accessible. Enders makes a concerted - and successful - attempt to convey the statistical concepts and models that define missing data methods in a way that does not assume high statistical literacy. He writes in a conceptually clear manner, often using a simple example or simulation to show how an equation or procedure works. This book is a refreshing addition to the literature for applied social researchers and graduate students doing quantitative data analysis. It covers the full range of state-of-the-art methods of handling missing data in a clear and accessible manner, making it an excellent supplement or text for a graduate course on advanced, but widely used, statistical methods." - David R. Johnson, Department of Sociology, The Pennsylvania State University, USA "A useful overview of missing data issues, with practical guidelines for making decisions about real-world data. This book is all about an issue that is usually ignored in work on OLS regression - but that most of us spend significant time dealing with. The writing is clear and accessible, a great success for a challenging topic. Enders provides useful reminders of what we need to know and why. I appreciated the interpretation of formulas, terms, and output. This book provides comprehensive and vital information in an easy-to-consume style. I learned a great deal reading it." - Julia McQuillan, Director, Bureau of Sociological Research, and Department of Sociology, University of Nebraska--Lincoln, USA