Pooling multiple imputations when the sample happens to be the population

Current pooling rules for multiply imputed data assume infinite populations. In some situations this assumption is not feasible as every unit in the population has been observed, potentially leading to over-covered population estimates. We simplify the existing pooling rules for situations where the sampling variance is not of interest. We compare these rules to the conventional pooling rules and demonstrate their use in a situation where there is no sampling variance. Using the standard pooling rules in situations where sampling variance should not be considered, leads to overestimation of the variance of the estimates of interest, especially when the amount of missingness is not very large. As a result, populations estimates are over-covered, which may lead to a loss of statistical power. We conclude that the theory of multiple imputation can be extended to the situation where the sample happens to be the population. The simplified pooling rules can be easily implemented to obtain valid inference in cases where we have observed essentially all units and in simulation studies addressing the missingness mechanism only.Comment: 6 pages, 1 figure, 1 tabl

Broken Stick Model for Irregular Longitudinal Data

Many longitudinal studies collect data that have irregular observation times, often requiring the application of linear mixed models with time-varying outcomes. This paper presents an alternative that splits the quantitative analysis into two steps. The first step converts irregularly observed data into a set of repeated measures through the broken stick model. The second step estimates the parameters of scientific interest from the repeated measurements at the subject level. The broken stick model approximates each subject's trajectory by a series of connected straight lines. The breakpoints, specified by the user, divide the time axis into consecutive intervals common to all subjects. Specification of the model requires just three variables: time, measurement and subject. The model is a special case of the linear mixed model, with time as a linear B-spline and subject as the grouping factor. The main assumptions are: Subjects are exchangeable, trajectories between consecutive breakpoints are straight, random effects follow a multivariate normal distribution, and unobserved data are missing at random. The R package brokenstick v2.5.0 offers tools to calculate, predict, impute and visualize broken stick estimates. The package supports two optimization methods, including options to constrain the variance-covariance matrix of the random effects. We demonstrate six applications of the model: Detection of critical periods, estimation of the time-to-time correlations, profile analysis, curve interpolation, multiple imputation and personalized prediction of future outcomes by curve matching

Вклад интеллигенции в исследование социальной памяти

An important goal of growth monitoring is to identify genetic disorders, diseases or other conditions that manifest themselves through an abnormal growth. The two main conditions that can be detected by height monitoring are Turner's syndrome and growth hormone deficiency. Conditions or risk factors that can be detected by monitoring weight or body mass index include hypernatremic dehydration, celiac disease, cystic fibrosis and obesity. Monitoring infant head growth can be used to detect macrocephaly, developmental disorder and ill health in childhood. This paper describes statistical methods to obtain evidence-based referral criteria in growth monitoring. The referral criteria that we discuss are based on either anthropometric measurement(s) at a fixed age using (1) a Centile or a Standard Deviation Score, (2) a Standard Deviation corrected for parental height, (3) a Likelihood Ratio Statistic and (4) an ellipse, or on multiple measurements over time using (5) a growth rate and (6) a growth curve model. We review the potential uses of these methods, and outline their strengths and limitations

Мировой опыт создания и функционирования свободных экономических зон и возможности его использования в Украине

Сейчас в мире функционирует, по разным данным, от 400 до 2000 свободных экономических зон. Впервые СЭЗ были созданы в США по акту 1934 г. в виде зон внешней торговли. Целью их была активизация внешнеторговой деятельности посредством использования эффективных механизмов снижения таможенных издержек. При этом главным образом предполагалось сокращение импортных тарифов на детали и компоненты для производства автомобилей. В зоны внешней торговли были превращены склады, доки, аэропорты. Предприятия, действующие в указанных зонах, выводились из-под таможенного контроля в США, если импортируемые в зону товары затем направлялись в третью страну. Таможенные издержки снижались и тогда, когда в зоне осуществлялась "доводка" продукции фирм США для последующего экспорта. Если же товары из зоны шли в США, они в обязательном порядке проходили все таможенные процедуры, предусмотренные законодательством страны

mice: Multivariate Imputation by Chained Equations in R

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

Evaluation and prediction of individual growth trajectories

Background: Conventional growth charts offer limited guidance to track individual growth. Aim: To explore new approaches to improve the evaluation and prediction of individual growth trajectories. Subjects and methods: We generalise the conditional SDS gain to multiple historical measurements, using the Cole correlation model to find correlations at exact ages, the sweep operator to find regression weights and a specified longitudinal reference. We explain the various steps of the methodology and validate and demonstrate the method using empirical data from the SMOCC study with 1985 children measured during ten visits at ages 0–2years. Results: The method performs according to statistical theory. We apply the method to estimate the referral rates for a given screening policy. We visualise the child’s trajectory as an adaptive growth chart featuring two new graphical elements: amplitude (for evaluation) and flag (for prediction). The relevant calculations take about 1 millisecond per child. Conclusion: Longitudinal references capture the dynamic nature of child growth. The adaptive growth chart for individual monitoring works with exact ages, corrects for regression to the mean, has a known distribution at any pair of ages and is fast. We recommend the method for evaluating and predicting individual child growth

Looking back at the Gifi system of nonlinear multivariate analysis

Gifi was the nom de plume for a group of researchers led by Jan de Leeuw at the University of Leiden. Between 1970 and 1990 the group produced a stream of theoretical papers and computer programs in the area of nonlinear multivariate analysis that were very innovative. In an informal way this paper discusses the so-called Gifi system of nonlinear multivariate analysis, that entails homogeneity analysis (which is closely related to multiple correspondence analysis) and generalizations. The history is discussed, giving attention to the scientific philosophy of this group, and links to machine learning are indicated

Looking Back at the Gifi System of Nonlinear Multivariate Analysis

Gifi was the nom de plume for a group of researchers led by Jan de Leeuw at the University of Leiden. Between 1970 and 1990 the group produced a stream of theoretical papers and computer programs in the area of nonlinear multivariate analysis that were very innovative. In an informal way this paper discusses the so-called Gifi system of nonlinear multivariate analysis, that entails homogeneity analysis (which is closely related to multiple correspondence analysis) and generalizations. The history is discussed, giving attention to the scientific philosophy of this group, and links to machine learning are indicated