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

This article gives a comprehensive introduction into one of the main branches of evolutionary computation – the evolution strategies (ES) the history of which dates back to the 1960s in Germany Starting from a survey of history the philosophical background is explained in order to make understandable why ES are realized in the way they are Basic ES algorithms and design principles for variation and selection operators as well as theoretical issues are presented, and future branches of ES research are discussed

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Evolution strategies –A comprehensive introduction

Basics Introduction The problem of missing data Concepts of MCAR, MAR and MNAR Simple solutions that do not (always) work Multiple imputation in a nutshell Goal of the book What the book does not cover Structure of the book Exercises Multiple imputation Historic overview Incomplete data concepts Why and when multiple imputation works Statistical intervals and tests Evaluation criteria When to use multiple imputation How many imputations? Exercises Univariate missing data How to generate multiple imputations Imputation under the normal linear normal Imputation under non-normal distributions Predictive mean matching Categorical data Other data types Classification and regression trees Multilevel data Non-ignorable methods Exercises Multivariate missing data Missing data pattern Issues in multivariate imputation Monotone data imputation Joint Modeling Fully Conditional Specification FCS and JM Conclusion Exercises Imputation in practice Overview of modeling choices Ignorable or non-ignorable? Model form and predictors Derived variables Algorithmic options Diagnostics Conclusion Exercises Analysis of imputed data What to do with the imputed data? Parameter pooling Statistical tests for multiple imputation Stepwise model selection Conclusion Exercises Case studies Measurement issues Too many columns Sensitivity analysis Correct prevalence estimates from self-reported data Enhancing comparability Exercises Selection issues Correcting for selective drop-out Correcting for non-response Exercises Longitudinal data Long and wide format SE Fireworks Disaster Study Time raster imputation Conclusion Exercises Extensions Conclusion Some dangers, some do's and some don'ts Reporting Other applications Future developments Exercises Appendices: Software R S-Plus Stata SAS SPSS Other software References Author Index Subject Index

Flexible Imputation of Missing Data

The goal of multiple imputation is to provide valid inferences for statistical estimates from incomplete data. To achieve that goal, imputed values should preserve the structure in the data, as well as the uncertainty about this structure, and include any knowledge about the process that generated the missing data. Two approaches for imputing multivariate data exist: joint modeling (JM) and fully conditional specification (FCS). JM is based on parametric statistical theory, and leads to imputation procedures whose statistical properties are known. JM is theoretically sound, but the joint model may lack flexibility needed to represent typical data features, potentially leading to bias. FCS is a semi-parametric and flexible alternative that specifies the multivariate model by a series of conditional models, one for each incomplete variable. FCS provides tremendous flexibility and is easy to apply, but its statistical properties are difficult to establish. Simulation work shows that FCS behaves very well in ...

Multiple imputation of discrete and continuous data by fully conditional specification

SUMMARY The paper extends earlier work on the so-called skew-normal distribution, a family of distributions including the normal, but with an extra parameter to regulate skewness. The present work introduces a multivariate parametric family such that the marginal densities are scalar skew-normal, and studies its properties, with special emphasis on the bivariate case.

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The multivariate skew-normal distribution

It is frequently easier to visualize conditional distributions of experimental variables rather than joint distributions. In this article we consider the most general class of bivariate distributions such that both sets of conditional densities are exponential. The class proves to be remarkably simple to describe: The joint density must be proportional to exp(- λx - μy - νxy), where the constant of proportionality depends on the classical exponential integral. The joint distribution has marginals that are not exponential and a negative correlation coefficient, except in the special case of independence. After deriving some distributional results, we develop methods for parameter estimation and simulation. A simple method-of-moments estimator appears to give reasonable results. We also briefly discuss generalizations to higher dimensions and to distributions with conditionals in a general exponential family.

Bivariate Distributions with Exponential Conditionals

The skew-Cauchy distribution

Data from a classical Pareto distribution are to be used to make inferences about the inequality and precision parameters. In addition, it is desired to predict the behavior of further observations from the distribution. Three typical data configurations are considered (iid and two types of censoring). Dependent conjugate prior analyses are reviewed and are compared with an analysis involving independent priors for the inequality and precision parameters. It is argued that mathematical tractability should be, perhaps, a minor consideration in the choice of priors. A comparative example is included.

Bayesian Estimation and Prediction for Pareto Data

A bivariate distribution can sometimes be characterized completely by properties of its conditional distributions. The present article surveys available research in this area. Questions of compatibility of conditional specifications are addressed as are characterizations of distributions based on their having conditional distributions that are members of prescribed parametric families of distributions. The topics of compatibility and near compatibility of conditional distributions are discussed. Estimation strategies for conditionally specified distributions are summarized. Additionally, certain conditionally specified densities are shown to provide convenient flexible conjugate prior families in certain multi- parameter Bayesian settings.

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Conditionally Specified Distributions: An Introduction (with comments and a rejoinder by the authors)

https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118445112.stat01100.pub2

Barry C. Arnold

Papers

Bivariate Distributions with Exponential Conditionals

The skew-Cauchy distribution

Bayesian Estimation and Prediction for Pareto Data

Conditionally Specified Distributions: An Introduction (with comments and a rejoinder by the authors)

Pareto Distribution