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

Order statistics and their moments have been of great interest from the turn of this century since Sir Francis Galton (1902) and Karl Pearson (1902) studied the distribution of the difference of two successive order statistics. The moments of order statistics did, subsequently, assume considerable importance in the statistical literature and have been numerically tabulated extensively for several distributions. For example, one can refer to Harter (1970a,b) and David (1981) for a detailed list of these tables. Meanwhile, with the primary intention of reducing the amount of direct computation of these moments, many authors including Jones (1948), Godwin (1949), Cole (1951) and Sillitto (1951, 1964) carried out independent investigations and derived several recurrence relations and identities satisfied by these moments of order statistics. Many of these relations and identities are quite useful as they express the higher order moments in terms of the lower order moments thus making the evaluation of higher order moments easy and, in addition, provide some simple checks to test the accuracy of the computation of moments of order statistics. It was only 25 years ago, however, that Govindarajulu (1963a) nicely summarized all these results and established some more recurrence relations and identities satisfied by the single and the product moments of order statistics. He then systematically applied these results in order to determine the maximum number of single and double integrals to be evaluated for the calculation of means, variances and covariances of order statistics in a sample of size n, assuming these quantities for all sample sizes less than n to be known. By a simple generalization of one of the results of Govindarajulu (1963a), Joshi (1971) determined that for distributions symmetric about zero the number of double integrals to be evaluated for even values of n is in fact zero. Recently, Joshi and Balakrishnan (1982) established similar results for any arbitrary continuous distribution and applied them to improve over the bounds of Govindarajulu. Yet another interesting application of these recurrence relations and identities among order statistics is in establishing some combinatorial identities and this has been demonstrated by Joshi (1973) and Joshi and Balakrishnan (1981a).

Recurrence Relations and Identities for Order Statistics

The multivariate alpha-power model

A logistic process constructed using geometric minimization

This research is concerned with distribution estimation under RankedSet Sampling (RSS) and under a generalized version of RSS (i.e., in the ith sample, is observed instead of so that the data are . Distribution estimation under both balanced and generalized RSS is accomplished. Starting with a Dirichlet process prior for F, the common distribution of the X's, the missing X values are generated. The estimate of the distribution function F is updated (the posterior distribution is again a Dirichlet process) based on the complete pseudo data . These two steps are repeated until the estimate of F stabilizes.

Estimation of a distribution function under generalized ranked set sampling

In this paper we discuss various strategies for constructing bivariate Kumaraswamy distributions. As alternatives to the Nadarajah, Cordeiro and Ortega (2011) bivariate model, four different models are introduced utilizing a conditional specification approach, a conditional survival function approach, an Arnold-Ng bivariate beta distribution construction approach. Distributional properties for such bivariate distributions are investigated. Parameter estimation strategies for the models are discussed, as are the consequences of fitting two of the models to a particular data set involving the proportion of foggy days at two different airports in Colombia.

Barry C. Arnold

Papers

Recurrence Relations and Identities for Order Statistics

The multivariate alpha-power model

A logistic process constructed using geometric minimization

Estimation of a distribution function under generalized ranked set sampling

Some alternative bivariate Kumaraswamy models