The R package mice imputes incomplete multivariate data by chained equations. The software mice 1.0 appeared in the year 2000 as an S-PLUS library, and in 2001 as an R package. mice 1.0 introduced predictor selection, passive imputation and automatic pooling. This article documents mice, which extends the functionality of mice 1.0 in several ways. In mice, the analysis of imputed data is made completely general, whereas the range of models under which pooling works is substantially extended. mice adds new functionality for imputing multilevel data, automatic predictor selection, data handling, post-processing imputed values, specialized pooling routines, model selection tools, and diagnostic graphs. Imputation of categorical data is improved in order to bypass problems caused by perfect prediction. Special attention is paid to transformations, sum scores, indices and interactions using passive imputation, and to the proper setup of the predictor matrix. mice can be downloaded from the Comprehensive R Archive Network. This article provides a hands-on, stepwise approach to solve applied incomplete data problems.

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mice: Multivariate Imputation by Chained Equations in R

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Two classes of modern missing data procedures, maximum likelihood (ML) and multiple imputation (MI), tend to yield similar results when implemented in comparable ways. In either approach, it is possible to include auxiliary variables solely for the purpose of improving the missing data procedure. A simulation was presented to assess the potential costs and benefits of a restrictive strategy, which makes minimal use of auxiliary variables, versus an inclusive strategy, which makes liberal use of such variables. The simulation showed that the inclusive strategy is to be greatly preferred. With an inclusive strategy not only is there a reduced chance of inadvertently omitting an important cause of missingness, there is also the possibility of noticeable gains in terms of increased efficiency and reduced bias, with only minor costs. As implemented in currently available software, the ML approach tends to encourage the use of a restrictive strategy, whereas the MI approach makes it relatively simple to use an inclusive strategy.

A comparison of inclusive and restrictive strategies in modern missing data procedures.

Two major reasons for the popularity of the EM algorithm are that its maximum step involves only complete-data maximum likelihood estimation, which is often computationally simple, and that its convergence is stable, with each iteration increasing the likelihood. When the associated complete-data maximum likelihood estimation itself is complicated, EM is less attractive because the M-step is computationally unattractive. In many cases, however, complete-data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

Maximum likelihood estimation via the ECM algorithm: A general framework

Statistical Analysis with Missing Data

Beyond Anova: Basics of Applied Statistics

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Why Understand Statistics? Probability in Engineering Decisions: Introduction. Defining Probability. The Addition Rule of Probability. Conditional Probability. Arrangements and Choices. Decision Trees. Summary. Justifying Engineering Decisions: Presenting Data. Summarising Data. Fatigue Damage. Shape of Distributions. Summary. Modelling Variability: Discrete Probability Distributions. Continuous Probability Distributions. Modelling Rainfall. Summary. Combining Variables: Introductions. Sample Covariance and Correlation. Joint Probability Distributions. Population Covariance and Correlation. Linear Combination of Random Variables. Distribution of the Sample Mean. Statistical Process Control Charts. Nonlinear Functions of Random Variables. Summary. Precision of Estimates: Precision of Means. Precision of Standard Deviations. Comparing Standard Deviations. Comparing Means. Sample Size. Proportions. Random Breath Tests? Summary. Asset Management Plan: Background. Statistical Issues. Sampling Scheme. Unit Cost Formulae. Zone Costs. Stratum Costs. Total Costs of Local Distribution Networks. Discussion. Summary. Making Predictions from One Variable: Linear Regression. Intrinsically Linear Models. Conditional Distributions. Relationship Between Correlation and Regression. Fitting Straight Lines When Both Variables Subject to Error. Calibration Lines. Summary. Making Predictions from Several Explanatory Variables: Regression on Two Explanatory Variables. Multiple Regression Model. Categorical Variables. Chrome Plating of Rods for Hydraulic Machinery. Summary. Design of Experiments: Evolutionary Operation. More Than Two Factors. Comparing Several Means. Experimental Design for Welded Joints. Summary. Modelling Variability in Time and Space: Evaluation of Mini-Roundabouts as a Road Safety Measure. Predicting Short Term Flood Risk. Spectral Analysis for Design of Offshore Structures. Endnote. Appendices: Appendix A: Mathematical Explanations of Key Results: Derivation of Poisson Distribution. Central Limit Theorem. Derivation of EVGI Distribution. Estimated Variance of Ratio Estimator. Multiple Regression Model. Du Mouchel's Algorithm. Appendix B: Reference Guide: Notation. Glossary. Problem Solving Guide. Suggested Short Course. Appendix C: Summary of Minitab Commands Used in Text. Appendix D: Data Sets. Tables. Appendix E: Statistical Tables. Appendix F: Answers to Selected Exercises.

Martin G. Gibson

Papers

Statistical Analysis with Missing Data

Beyond Anova: Basics of Applied Statistics

The Design and Analysis of Clinical Experiments

Statistics in engineering : a practical approach