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

We introduce two families of continuous distribution functions with not-necessarily symmetric densities, which contain a parent distribution as a special case. The two families proposed depend on two parameters and are presented as an alternative to the skew normal distribution and other proposals in the statistical literature. The density functions of these new families are given by a closed expression which allows us to easily compute probabilities, moments and related quantities. The second family can exhibit bimodality and its standardized fourth central moment (kurtosis) can be lower than that of the Azzalini skew normal distribution. Since the second proposed family can be bimodal we fit two well-known data set with this feature as applications. We concentrate attention on the case in which the normal distribution is the parent distribution but some consideration is given to other parent distributions, such as the logistic distribution.

https://www.mdpi.com/2227-7390/9/1/87/pdf

Properties and Applications of a New Family of Skew Distributions

We introduce a uniform generalized order statistic process. It is a simple Markov process whose initial segment can be identified with a set of uniform generalized order statistics. A standard marginal transformation leads to a generalized order statistic process related to non-uniform generalized order statistics. It is then demonstrated that the nth variable in such a process has the same distribution as an nth Pfeifer record value. This process representation of Pfeifer records facilitates discussion of the possible limit laws for Pfeifer records and, in some cases, of sums thereof. Because of the close relationship between Pfeifer records and generalized order statistics, the results shed some light on the problem of determining the nature of the possible limiting distributions of the largest generalized order statistic.

Generalized order statistic processes and Pfeifer records

We introduce a bivariate distribution with Cauchy conditionals that is centered at the origin. The construction is patterned after the functional equation methods employed by Castillo and Galambos(1987), Arnold(1987), Castillo and Galambos(1989), and Arnold and Strauss( 1988a) in the development of various bivariate densities with conditionally specified distributions. An application of the Cauchy conditionals density as a model for body mass index(BMI) and cholesterol ratios is presented.

Centered distributions with cauchy conditionals

As an alternative to available bivariate Birnbaum–Saunders (BS) models, a conditionally specified distribution with BS conditionals is considered. The behavior of conditional or pseudo-likelihood parameter estimates of the model parameters is investigated via simulation. A comparison using a mineralogy data set suggests that the conditionally specified model outperforms competing models (with BS marginals). An analogous comparison using a well-known data set of Australian athletes also suggests the superiority of the conditionally specified model. Further investigation of its possible general superiority is suggested.

https://www.mdpi.com/2073-8994/13/5/762/pdf

A Note on the Birnbaum–Saunders Conditionals Model

The graphical measure of inequality proposed by Lorenz (1905) in an income inequality context is intimately related to the concept of majorization. The Lorenz curve, however, can be meaningfully used to compare arbitrary distributions rather than distributions concentrated on n points, as is the case with the majorization partial order. The Lorenz order can, thus, be thought of as a useful generalization of the majorization order. While extending our domain of definitions in one direction, to general rather than discrete distributions, we find it convenient to add a restriction which was not assumed in Chapter 2, a restriction that our distributions be supported on the non-negative reals and have finite expectation. In an income or wealth distribution context the restriction to non-negative incomes is often acceptable. The restriction to distributions with finite means is potentially more troublesome. Any real world (finite) population will have a (sample) distribution with finite mean. However, a commonly used approximation to real world income distributions, the Pareto distribution, only has a finite mean if the relevant shape parameter is suitably restricted. See Arnold (1983) for a detailed discussion of Pareto distributions in the income modelling context. To avoid distorted Lorenz curves (as alluded to in exercise 1 and illustrated in Wold (1935)), we will hold fast to our restriction that all distributions to be discussed will be supported on IR+ and will have finite means. In terms of random variables our restriction is that they be non-negative with finite expectations. We will speak interchangeably of our Lorenz (partial) order as being defined on the class of distributions (supported on IR+ with finite means) or as being defined on the class of integrable non-negative random variables.

Barry C. Arnold

Papers

Properties and Applications of a New Family of Skew Distributions

Generalized order statistic processes and Pfeifer records

Centered distributions with cauchy conditionals

A Note on the Birnbaum–Saunders Conditionals Model

The Lorenz Order in the Space of Distribution Functions