Flexible Imputation of Missing Data
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1 Chapman & Hall/CRC Interdisciplinary Statistics Series Flexible Imputation of Missing Data Stef van Buuren TNO Leiden, The Netherlands University of Utrecht The Netherlands crc pness Taylor &l Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis an Group, Informa business A CHAPMAN St HALL BOOK
2 Contents Foreword xvii Preface xix About the Author xxi Symbol Description xxiii List of Algorithms xxv I Basics 1 1 Introduction The problem of missing data Current practice Changing perspective on missing data Concepts of MCAR, MAR and MNAR Simple solutions that do not (always) work Listwise deletion Pairwise deletion Mean imputation Regression imputation Stochastic regression imputation LOCF and BOFC Indicator method Summary Multiple imputation in a nutshell Procedure Reasons to use multiple imputation Example of multiple imputation Goal of the book What the book does not cover Prevention Weighting procedures Likelihood-based approaches Structure of the book Exercises 23 ix
3 .. ' X Contents 2 Multiple imputation 2.1 Historic overview Imputation Multiple imputation V The expanding literature on multiple imputation 2.2 Concepts in incomplete data Incomplete data perspective Causes of missing data Notation 2.2,1 MCAR. MAR and MNAR again Ignorable and nonignorable * Implications of ignorability 2.3 Why and when multiple imputation works Goal of multiple imputation Three sources of variation * Proper imputation Scope of the imputation model Variance ratios * 2.3.G * Degrees of freedom Numerical example 2.4 Statistical intervals and tests Scalar or multi-parameter inference? Scalar inference 2.5 Evaluation criteria Imputation is not prediction Simulation designs and performance measures 2.G When to use multiple imputation 2.7 How many imputations? 2.8 Ext rcises 3 Univariate missing data 3.1 How to generate multiple imputations Predict method Predict + noise method Predict + noise + parameter uncertainty A second predictor Drawing from the observed data 3.1.G Conclusion 3.2 Imputation under the normal linear normal Overview Algorithms * Performance Generating MAR missing data Conclusion 3.3 Imputation under non-normal distributions
4 Contents xi Overview Imputation from the t-distribution * Example * Predictive mean matching Overview Computational details * Algorithm * Conclusion Categorical data Overview Perfect prediction * Other data types Count data Semi-continuous data Censored, truncated and rounded data Classification and regression trees Overview Imputation using CART models Multilevel data Overview Two formulations of the linear multilevel model * Computation * Conclusion Nonignorable missing data Overview Selection model Pattern-mixture model Converting selection and pattern-mixture models Sensitivity analysis Role of sensitivity analysis Exercises 93 4 Multivariate missing data Missing data pattern Overview Summary statistics Influx and outflux Issues in multivariate imputation Monotone data imputation Overview Algorithm Joint modeling Overview Continuous data * Categorical data 107
5 xii Contents 4.5 Fully conditional specification Overview The MICE algorithm Performance Ill Compatibility * Ill Number of iterations Example of slow convergence FCS and,1m Relations between FCS and JM Comparison Illustration Conclusion Exercises Imputation in practice Overview of modeling choices lgnorable or nonignorable? Model form and predictors Model form Predictors Derived variables Ratio of two variables Sum scores Interaction terms Conditional imputation Compositional data * Quadratic relations * Algorithmic options Visit sequence Convergence Diagnostics Model fit versus distributional discrepancy Diagnostic graphs Conclusion Exercises Analysis of imputed data What to do with the imputed data? Averaging and stacking the data Repeated analyses Parameter pooling Scalar inference of normal quantities Scalar inference of non-normal quantities Statistical tests for multiple imputation Wald test * 157
6 Contents xiii Likelihood ratio test * x2-test * Custom hypothesis tests of model parameters * Computation Stepwise model selection Variable selection techniques Computation Model optimism Conclusion Exercises 166 II Case studies Measurement issues Too many columns Scientific question Leiden 85+Cohort Data exploration Outflux Logged events Quick predictor selection for wide data Generating the imputations A further improvement: Survival as predictor variable Some guidance Sensitivity analysis Causes and consequences of missing data Scenarios Generating imputations under the ^-adjustment Complete data analysis Conclusion Correct prevalence estimates from self-reported data Description of the problem Don't count on predictions The main idea Data Application Conclusion Enhancing comparability Description of the problem Pull dependence: Simple equating Independence: Imputation without 196 a bridge study Fully dependent or independent? Imputation using a bridge study Interpretation Conclusion 203
7 xiv Contents 7.5 Exercises Selection issues Correcting for selective drop-out POPS study; 19 years follow-up Characterization of the drop-out Imputation model A degenerate solution A better solution Results Conclusion Correcting for nonresponse Fifth Dutch Growth Study Nonresponse Comparison to known population totals Augmenting the sample Imputation model Influence of nonresponse on final height Discussion Exercises 219 ( Longitudinal data Long and wide format SE Fireworks Disaster Study Intention to treat Imputation model Inspecting imputations Complete data analysis Results from the complete data analysis Time raster imputation Change score Scientific question: Critical periods Broken stick model * Terneuzen Birth Cohort Shrinkage and the change score * Imputation Complete data analysis Conclusion Exercises 244 III Extensions 247
8 Contents *v 10 Conclusion Some dangers, some do's and some don'ts Some dangers Some do's Some don'ts Reporting Reporting guidelines Template Other applications Synthetic datasets for data protection Imputation of potential outcomes Analysis of coarsened data File matching of multiple datasets Planned missing data for efficient designs Adjusting for verification bias Correcting for measurement error Future developments Derived variables Convergence of MICE algorithm Algorithms for blocks and batches Parallel computation Nested imputation Machine learning for imputation Incorporating expert knowledge Distribution-free pooling rules Improved diagnostic techniques Building block in modular statistics Exercises 260 A Software 263 A.J H 263 A.2 S-PLUS 265 A.3 Stata 265 A.4 SAS 266 A.5 SPSS 266 A.6 Other software 266 References 269 Author Index 299 Subject Index 307
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