Multi‐set factor analysis by means of Parafac2

We consider multi‐set data consisting of observations, k = 1,…, K (e.g., subject scores), on J variables in K different samples. We introduce a factor model for the J × J covariance matrices , k = 1,…, K, where the common part is modelled by Parafac2 and the unique variances , k = 1,…, K, are diagonal. The Parafac2 model implies a common loadings matrix that is rescaled for each k, and a common factor correlation matrix. We estimate the unique variances by minimum rank factor analysis on for each k. The factors can be chosen orthogonal or oblique. We present a novel algorithm to estimate the Parafac2 part and demonstrate its performance in a simulation study. Also, we fit our model to a data set in the literature. Our model is easy to estimate and interpret. The unique variances, the factor correlation matrix and the communalities are guaranteed to be proper, and a percentage of explained common variance can be computed for each k. Also, the Parafac2 part is rotationally unique under mild conditions.     

Moving in Parallel Toward a Modern Modeling Epistemology: Bayes Factors and Frequentist Modeling Methods

The Bayesian-frequentist debate typically portrays these statistical perspectives as opposing views. However, both Bayesian and frequentist statisticians have expanded their epistemological basis away from a singular focus on the null hypothesis, to a broader perspective involving the development and comparison of competing statistical/mathematical models. For frequentists, statistical developments such as structural equation modeling and multilevel modeling have facilitated this transition. For Bayesians, the Bayes factor has facilitated this transition. The Bayes factor is treated in articles within this issue of Multivariate Behavioral Research. The current presentation provides brief commentary on those articles and more extended discussion of the transition toward a modern modeling epistemology. In certain respects, Bayesians and frequentists share common goals.     

Nesselroade and Molenaar's Measurement Concerns and Proposals: An Introduction

In this special section Nesselroade and Molenaar (N & M) propose a provocative new approach to measurement invariance. When measures are collected repeatedly over time (e.g., daily diary studies), a potentially unique measurement model relating the items to the underlying construct can be created for each individual. If hypothesized causal paths specified between constructs (e.g., frustration → aggression) can be constrained to be equal across the individuals, a model with idiographic measurement of the constructs, but with nomothetic structural relationships can be specified. Three commentaries react to N & M's proposal. Revelle and Wilt challenge the priority given by N & M to unique individual measurement structures, arguing that between subjects differences in structural relationships are empirically important and meaningful. Markus's uses David Hume's framework to raise philosophy of science challenges for N & M's approach. Maydeu-Olivares challenges the incremental validity of N & M's approach, arguing that N & M's approach is unlikely to improve the prediction of between subjects criteria. Finally, N & M present a rejoinder to the three commentaries.     

Cross‐cultural Generalizability of the Alternative Five‐factor Model Using the Zuckerman–Kuhlman–Aluja Personality Questionnaire

Several personality models are known for being replicable across cultures, such as the Five‐Factor Model (FFM) or Eysenck's Psychoticism–Extraversion–Neuroticism (PEN) model, and are for this reason considered universal. The aim of the current study was to evaluate the cross‐cultural replicability of the recently revised Alternative FFM (AFFM). A total of 15 048 participants from 23 cultures completed the Zuckerman–Kuhlman–Aluja Personality Questionnaire (ZKA‐PQ) aimed at assessing personality according to this revised AFFM. Internal consistencies, gender differences and correlations with age were similar across cultures for all five factors and facet scales. The AFFM structure was very similar across samples and can be considered as highly replicable with total congruence coefficients ranging from .94 to .99. Measurement invariance across cultures was assessed using multi‐group confirmatory factor analyses, and each higher‐order personality factor did reach configural and metric invariance. Scalar invariance was never reached, which implies that culture‐specific norms should be considered. The underlying structure of the ZKA‐PQ replicates well across cultures, suggesting that this questionnaire can be used in a large diversity of cultures and that the AFFM might be as universal as the FFM or the PEN model. This suggests that more research is needed to identify and define an integrative framework underlying these personality models. Copyright © 2016 European Association of Personality Psychology     

结构需求:概念、测量及与相关变量的关系

结构需求是个体对简单结构、清晰有条理的事物与环境的偏爱和需要,其本质是一种动机,个体通常会以结构严密、有条理或简化复杂信息的认知加工方式将其表现出来。结构需求存在着个体差异性。高结构需求水平的个体能够简化复杂的信息和环境,以清晰和简单的表征与描述去理解、建构他们的世界,从而减少认知资源的支出和消耗,提高认知操作的效率,维持认知与行为倾向的内在稳定。研究者梳理了结构需求的概念内涵、理论基础,介绍了两种主要的结构需求测量工具(PNS-12量表,PNS-11量表),以及结构需求的相关研究,分别从结构需求的前因变量、结果变量的角度对其相关研究进行了阐述。未来研究应深入探究结构需求的概念与结构,拓展其研究方法,研发更加有效的测评工具,深入探讨其影响机制,开展结构需求的中国化研究。     

Health and Aging: A Perspective from the Far East

Singapore is an urban, highly industrialized country in South East Asia. By 2030, one-fifth of the population is projected to be composed of citizens aged above 65 years. Research on aging has largely focused on the effects of deteriorating physical ability on daily functioning capabilities (Iwarsson & Isacsson, 1997; Warr, 1995). More recently, the role of self-perceived usefulness, competence and control on well-being in the elderly have been investigated (Heberlein, Licht & Licht, 1999; Ranzjin, Keeves, Luszcz, & Feather, 1998). In other fields, activity and involvement have been identified as effective coping devices (Nair, 1989; Shalit, 1988). The present study compared the conceptual understanding of the esteem and well-being of the elderly on the dimensions of activity, involvement, and control, as viewed by an undergraduate sample (n = 60) and a cross-section of seniors (n = 71). Three separate factor analyses reflected interesting variations in the conceptual frameworks.     

Symptom Expression and Somatization Among Elderly Korean Immigrants

In a study of expression of symptoms of somatization, depression, and other biopsychological conditions, 70 elderly Korean immigrants in the greater Washington, D.C., metropolitan area (35 who met the criteria for major depression and 35 who did not meet those criteria) were administered a Korean version of the Brief Symptom Inventory (BSI). Subjects who met the criteria for depression had the highest mean score on the BSI somatization dimension compared with other normative samples including a sample of psychiatric inpatients. A factor analysis of data from the BSI showed that for elderly Korean immigrants, a factor of somatization was identified that included the items from the original BSI obsessive-compulsive, somatization, and anxiety dimensions. Items loading on the somatization factor suggest that elderly Korean subjects experience body and mind as a unitary system and tend to communicate the distress associated with old age, cultural adjustment, and family and social changes through somatic symptoms.     

初中生函数概念发展的特点

本研究通过测验法对北京市六所中学的８０２名初一至初三的学生进行考察,研究了初中生函数要领的发展水平及其特点,结果表明,初中三个年级学生函数要领的发展,从总体上看,随着看级的增高呈上升的发展趋势,但年级结学生函数概念发展的影响不显著,制约 初中学生函数的概念发展水平的关键是,学生所受教育的质量,学生主要以接受教育的方式来获得函数概念。     

Some relationships between factors and components

The asymptotic correlations between the estimates of factor and component loadings are obtained for the exploratory factor analysis model with the assumption of a multivariate normal distribution for manifest variables. The asymptotic correlations are derived for the cases of unstandardized and standardized manifest variables with orthogonal and oblique rotations. Based on the above results, the asymptotic standard errors for estimated correlations between factors and components are derived. Further, the asymptotic standard error of the mean squared canonical correlation for factors and components, which is an overall index for the closeness of factors and components, is derived. The results of a Monte Carlo simulation are presented to show the usefulness of the asymptotic results in the data with a finite sample size.The author is indebted to anonymous referees for their comments, corrections and suggestions which have led to the improvement of this article.