APPLIED MISSING DATA ANALYSIS

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1 APPLIED MISSING DATA ANALYSIS Craig K. Enders Series Editor's Note by Todd D. little THE GUILFORD PRESS New York London

2 Contents 1 An Introduction to Missing Data Introduction Chapter Overview Missing Data Patterns A Conceptual Overview of Missing Data Theory A More Formal Description of Missing Data Theory Why Is the Missing Data Mechanism Important? How Plausible Is the Missing at Random Mechanism? An Inclusive Analysis Strategy Testing the Missing Completely at Random Mechanism Planned Missing Data Designs The Three-Form Design Planned Missing Data for Longitudinal Designs Conducting Power Analyses for Planned Missing Data Designs Data Analysis Example Summary Recommended Readings 36 2 Traditional Methods for Dealing with Missing Data Chapter Overview An Overview of Deletion Methods Listwise Deletion Pairwise Deletion An Overview of Single Imputation Methods Arithmetic Mean Imputation Regression Imputation Stochastic Regression Imputation Hot-Deck Imputation Similar Response Pattern Imputation Averaging the Available Items Last Observation Carried Forward An Illustrative Computer Simulation Study 52

3 xü Contents 2.14 Summary Recommended Readings 55 3 An Introduction to Maximum Likelihood Estimation Chapter Overview The Univariate Normal Distribution The Sample Likelihood The Log-Likelihood Estimating Unknown Parameters The Role of First Derivatives Estimating Standard Errors Maximum Likelihood Estimation with Multivariate Normal Data A Bivariate Analysis Example Iterative Optimization Algorithms Significance Testing Using the Wald Statistic The Likelihood Ratio Test Statistic Should I Use the Wald Test or the Likelihood Ratio Statistic? Data Analysis Example Data Analysis Example Summary Recommended Readings 85 4 Maximum Likelihood Missing Data Handling Chapter Overview The Missing Data Log-Likelihood How Do the Incomplete Data Records Improve Estimation? An Illustrative Computer Simulation Study Estimating Standard Errors with Missing Data Observed versus Expected Information A Bivariate Analysis Example An Illustrative Computer Simulation Study An Overview of the EM Algorithm A Detailed Description of the EM Algorithm A Bivariate Analysis Example Extending EM to Multivariate Data Maximum Likelihood Estimation Software Options Data Analysis Example Data Analysis Example Data Analysis Example Data Analysis Example Data Analysis Example Summary Recommended Readings Improving the Accuracy of Maximum Likelihood Analyses Chapter Overview The Rationale for an Inclusive Analysis Strategy An Illustrative Computer Simulation Study 129 D. 5.4 Identifying a Set of Auxiliary Variables 131

4 Contents xiü 5.5 Incorporating Auxiliary Variables into a Maximum Likelihood Analysis The Saturated Correlates Model The Impact of Non-Normal Data Robust Standard Errors Bootstrap Standard Errors The Rescaled Likelihood Ratio Test Bootstrapping the Likelihood Ratio Statistic Data Analysis Example Data Analysis Example Data Analysis Example Summary Recommended Readings * An Introduction to Bayesian Estimation Chapter Overview What Makes Bayesian Statistics Different? A Conceptual Overview of Bayesian Estimation Bayes' Theorem An Analysis Example How Does Bayesian Estimation Apply to Multiple Imputation? The Posterior Distribution of the Mean The Posterior Distribution of the Variance The Posterior Distribution of a Covariance Matrix Summary Recommended Readings The Imputation Phase of Multiple Imputation Chapter Overview A Conceptual Description of the Imputation Phase A Bayesian Description of the Imputation Phase A Bivariate Analysis Example Data Augmentation with Multivariate Data Selecting Variables for Imputation The Meaning of Convergence Convergence Diagnostics Time-Series Plots Autocorrelation Function Plots Assessing Convergence from Alternate Starting Values Convergence Problems Generating the Final Set of Imputations How Many Data Sets Are Needed? Summary Recommended Readings The Analysis and Pooling Phases of Multiple Imputation Chapter Overview The Analysis Phase Combining Parameter Estimates in the Pooling Phase Transforming Parameter Estimates Pnor to Combining 220

5 xiv Contents 8.5 Pooling Standard Errors The Fraction of Missing Information and the Relative Increase in Variance When Is Multiple Imputation Comparable to Maximum Likelihood? An Illustrative Computer Simulation Study Significance Testing Using the í Statistic An Overview of Multiparameter Significance Tests Testing Multiple Parameters Using the Dj Statistic Testing Multiple Parameters by Combining Wald Tests Testing Multiple Parameters by Combining Likelihood Ratio Statistics Data Analysis Example Data Analysis Example Data Analysis Example Summary Recommended Readings Practical Issues in Multiple Imputation Chapter Overview Dealing with Convergence Problems Dealing with Non-Normal Data To Round or Not to Round? Preserving Interaction Effects Imputing Multiple-Item Questionnaires Alternate Imputation Algorithms Multiple-Imputation Software Options Data Analysis Example Data Analysis Example Summary Recommended Readings Models for Missing Not at Random Data Chapter Overview An Ad Hoc Approach to Dealing with MNAR Data The Theoretical Rationale for MNAR Models The Classic Selection Model Estimating the Selection Model Limitations of the Selection Model An Illustrative Analysis The Pattern Mixture Model Limitations of the Pattern Mixture Model An Overview of the Longitudinal Growth Model A Longitudinal Selection Model Random Coefficient Selection Models Pattern Mixture Models for Longitudinal Analyses Identification Strategies for Longitudinal Pattern Mixture Models Delta Method Standard Errors Overview of the Data Analysis Examples Data Analysis Example Data Analysis Example Data Analysis Example Data Analysis Example Summary Recommended Readings 328

6 Contents xv 11«Wrapping Things Up: Some Final Practical Considerations 11.1 Chapter Overview Maximum Likelihood Software Options Multiple-Imputation Software Options Choosing between Maximum Likelihood and Multiple Imputation 11.5 Reporting the Results from a Missing Data Analysis Final Thoughts Recommended Readings References Author Index Subject Index About the Author The companion website (yvww.appliedmissingdata.com) includes data files and syntax for the examples in the book, as well as up-to-date information on software.

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