Imputation of missing categorical data by maximizing internal consistency

This paper suggests a method to supplant missing categorical data by reasonable replacements. These replacements will maximize the consistency of the completed data as measured by Guttman's squared correlation ratio. The text outlines a solution of the optimization problem, describes relationships with the relevant psychometric theory, and studies some properties of the method in detail. The main result is that the average correlation should be at least 0.50 before the method becomes practical. At that point, the technique gives reasonable results up to 10–15% missing data.We thank Anneke Bloemhoff of NIPG-TNO for compiling and making the Dutch Life Style Survey data available to use, and Chantal Houée and Thérèse Bardaine, IUT, Vannes, France, exchange students under the COMETT program of the EC, for computational assistance. We also thank Donald Rubin, the Editors and several anonymous reviewers for constructive suggestions.     

Least-squares approximation of an improper correlation matrix by a proper one

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and sufficient condition is given for a solution to yield the unique global minimum of the least-squares function. Empirical verification of the condition indicates that the occurrence of non-optimal solutions with the proposed algorithm is very unlikely. A possible drawback of the optimal solution is that it is a singular matrix of necessity. In cases where singularity is undesirable, one may impose the additional nonsingularity constraint that the smallest eigenvalue of the solution be , where is an arbitrary small positive constant. Finally, it may be desirable to weight the squared errors of estimation differentially. A generalized solution is derived which satisfies the additional nonsingularity constraint and also allows for weighting. The generalized solution can readily be obtained from the standard unweighted singular solution by transforming the observed improper correlation matrix in a suitable way.     

The choice of constraints in correspondence analysis

A discussion of alternative constraint systems has been lacking in the literature on correspondence analysis and related techniques. This paper reiterates earlier results that an explicit choice of constraints has to be made which can have important effects on the resulting scores. The paper also presents new results on dealing with missing data and probabilistic category assignment.I am most grateful to the following for their helpful comments. Arto Demirjian, Michael Greenacre, Michael Healy, Shizuhiko Nishisato, Roderick Mcdonald, and several anonymous referees.     

Rasch's multiplicative poisson model with covariates

As a multivariate model of the number of events, Rasch's multiplicative Poisson model is extended such that the parameters for individuals in the prior gamma distribution have continuous covariates. The parameters for individuals are integrated out and the hyperparameters in the prior distribution are estimated by a numerical method separately from difficulty parameters that are treated as fixed parameters or random variables. In addition, a method is presented for estimating parameters in Rasch's model with missing values. The author is now affiliated with the Otara University of Commerce. The author is grateful to Yoshio Takane, Haruo Yanai, Eiji Muraki, the editor and referees for their careful readings and helpful suggestions on earlier versions of this paper. Part of this work was presented at the third European Congress of Psychology at Tampere, Finland in 1993.     

Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.     

社交媒体使用与错失焦虑的关系：一项元分析

社交媒体使用与错失焦虑均是当下生活中较为常见的现象, 诸多研究探讨了两者间的内在联系, 但研究结果却存在很大差异。为明确两者之间的整体关系, 以及产生分歧的原因, 对检索后获得的65项研究(70个独立样本)使用随机效应模型进行了元分析。结果发现：社交媒体使用与错失焦虑存在显著正相关(r = 0.38, 95% CI [0.34, 0.41]); 二者的相关强度受社交媒体使用测量指标和社交媒体类型的调节, 但不受性别、年龄、错失焦虑测量工具和个体主义指数的调节。结果一定程度上澄清了大众传播的社会认知理论和数字恰到好处假说的争论, 表明社交媒体使用程度越高的人往往也会伴随着较高水平的错失焦虑。防止社交媒体过度使用, 尤其是引导大众合理使用以图像为中心并且开放度较高的社交媒体有助于错失焦虑的缓解。     

错失恐惧对亲社会行为的影响

网络信息的纷繁复杂,让人们担忧因错失信息而导致自身的利益受损,本研究探讨这种现象的加剧对个体的亲社会行为的影响。本研究分别使用问卷法（研究1）和实验法（研究2）,探究错失恐惧对亲社会行为的影响以及在其过程中人际安全感的中介作用和基本心理需要满足的调节作用。结果发现：（1）个体的错失恐惧程度负向预测了其亲社会行为;（2）人际安全感在错失恐惧对亲社会行为的影响中起中介作用,高的错失恐惧水平会降低个体的人际安全感,从而减少个体的亲社会行为;（3）基本心理需要满足在错失恐惧对亲社会行为的负向预测作用中起调节作用,当个体的基本心理需要满足程度低的时候,错失恐惧对亲社会行为的消极影响显著增强。     

Maximizing data quality and shortening survey time: Three-form planned missing data survey design

Simulation studies have shown the three-form planned missing data design efficiently collects high quality data while reducing participant burden. This methodology is rarely used in sport and exercise psychology. Therefore, we conducted a re-sampling study with existing sport and exercise psychology survey data to test how three-form planned missing data survey design implemented with different item distribution approaches effect constructs’ internal measurement structure and validity. Results supported the efficacy of the three-form planned missing data survey design for cross-sectional data collection. Sample sizes of at least 300 (i.e., 100 per form) are recommended for having unbiased parameter estimates. It is also recommended items be distributed across survey forms to have representation of each facet of a construct on every form, and that a select few of these items be included across all survey forms. Further guidelines for three-form surveys based upon the results of this resampling study are provided.     

A unified approach to exploratory factor analysis with missing data,nonnormal data,and in the presence of outliers

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.     

Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms

In this paper, the constrained maximum likelihood estimation of a two-level covariance structure model with unbalanced designs is considered. The two-level model is reformulated as a single-level model by treating the group level latent random vectors as hypothetical missing-data. Then, the popular EM algorithm is extended to obtain the constrained maximum likelihood estimates. For general nonlinear constraints, the multiplier method is used at theM-step to find the constrained minimum of the conditional expectation. An accelerated EM gradient procedure is derived to handle linear constraints. The empirical performance of the proposed EM type algorithms is illustrated by some artifical and real examples.This research was supported by a Hong Kong UCG Earmarked Grant, CUHK 4026/97H. We are greatly indebted to D.E. Morisky and J.A. Stein for the use of their AIDS data in our example. We also thank the Editor, two anonymous reviewers, W.Y. Poon and H.T. Zhu for constructive suggestions and comments in improving the paper. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.