探索性因素分析、目标旋转与因素结构的一致性

在因素结构水平上评估跨群体的一致性是在心理学研究中常常遇见的一个问题,对此问题的解答,可以选择探索性因素分析→目标旋转→一致性评估这一途径。本文首先介绍正交目标旋转的简单原理,然后介绍其在心理研究中的应用以及相关软件和程序。目标旋转之后,结构一致性的量化可以采用一致性系数等指标,这些指标可采用一定的实证分布、近似处理或经验标准进行统计检验。之后采用一项实证数据,演示探索性因素分析、目标旋转以及结构一致性的评估方法。     

探索性因素分析——最近10年的评述

目的：(1)介绍国外心理统计学界对探索性因素分析中几个重大问题的基本观点;(2)系统地评述过去10年里(1991～2000年)我国心理学研究对这一技术的使用情况;(3)强调运用这一技术时值得注意的一些事项,以期这一技术对我国心理学研究发挥更大的作用。方法：作检索了《心理学报》和《心理科学》在1991～2000年间与探索性因素分析有关的章,对其中以探索性因素分析为主要研究方法的重点章(feature article)进行了编码,统计了频数及百分比分布。结果：我国心理学研究在积极使用探索性因素分析这一先进统计技术时还存在一些问题,主要表现在：(1)在确定因素个数时,倾向于机械地依靠桌个单一方法来作决定,(2)大量使用正交旋转,(3)过于依赖SPSS,(4)对因素分析过程中的重要信息／结果报告不够。结论：探索性因素分析在过去十年得到了广泛的应用,如能吸收国外同行的一些观点,探索性因素分析这一技术在我国心理学研究中必将获得更广泛有效的应用。     

Exploratory second-order analyses for components and factors

Abstract: Exploratory methods using second‐order components and second‐order common factors were proposed. The second‐order components were obtained from the resolution of the correlation matrix of obliquely rotated first‐order principal components. The standard errors of the estimates of the second‐order component loadings were derived from an augmented information matrix with restrictions for the loadings and associated parameters. The second‐order factor analysis proposed was similar to the classical method in that the factor correlations among the first‐order factors were further resolved by the exploratory method of factor analysis. However, in this paper the second‐order factor loadings were estimated by the generalized least squares using the asymptotic variance‐covariance matrix for the first‐order factor correlations. The asymptotic standard errors for the estimates of the second‐order factor loadings were also derived. A numerical example was presented with simulated results.     

探索性因素分析在测验编制中局限性的模拟实验

本文主要用模拟研究的方法,通过生成拟合优度验证性因素分析的数据,来考察探索性因素分析在测验编制中的局限性。结果表明探索性因素分析作为纯数据基础上的一种统计方法,在因素问相关程度较大时．得到与理论假设不一致的结论。本文还就测验中会聚效度的一些限制作了初步探讨,结合具体情况介绍了中等相关限定条件的实质。     

Newton Algorithms for Analytic Rotation: an Implicit Function Approach

In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to m factors and p variables. The speed of the new algorithms is compared to that of existing algorithms and to that of Newton algorithms based on alternative parameterizations. Several rotation criteria were examined and the algorithms were evaluated over a range of values for m. Initial guesses for Newton algorithms were improved by subconvergence iterations of the gradient projection algorithm. Simulation results suggest that no one algorithm is fastest for minimizing all criteria for all values of m. Among competing algorithms, the gradient projection algorithm alone was faster than the implicit function algorithm for minimizing a quartic criterion over oblique rotation matrices when m is large. In all other conditions, however, the implicit function algorithms were competitive with or faster than the fastest existing algorithms. The new algorithms showed the greatest advantage over other algorithms when minimizing a nonquartic component loss criterion.     

A note on identification in the oblique and orthogonal factor analysis models

Conditions for removing the indeterminancy due to rotation are given for both the oblique and orthogonal factor analysis models. The conditions indicate why published counterexamples to conditions discussed by Jöreskog are not identifiable.The author would like to thank Gordon Bechtel and the reviewers for their comments and suggestions.     

3～6岁幼儿好奇心结构探索与验证性因子分析

以幼儿园3～6岁幼儿为对象,通过80名幼儿教师对480名幼儿好奇心行为特征描述的开放式问卷调查,编制出60个项目的初始问卷,对500名幼儿的初测结果进行探索性因子分析后,形成了33个项目的正式问卷,对1000名幼儿的评价结果进行验证性因子分析,结果表明:教师评价的3～6岁幼儿好奇心结构包括敏感、对未知事物的关注、好问、喜欢摆弄、探索持久和好奇体验6个因子。     

Exploratory structural equation modeling,bifactor models,and standard confirmatory factor analysis models: Application to the BASC-2 Behavioral and Emotional Screening System Teacher Form

Several psychological assessment instruments are based on the assumption of a general construct that is composed of multiple interrelated domains. Standard confirmatory factor analysis is often not well suited for examining the factor structure of such scales. This study used data from 1885 elementary school students (mean age = 8.77 years, SD = 1.47 years) to examine the factor structure of the Behavioral Assessment System for Children, Second Edition (BASC-2) Behavioral and Emotional Screening System (BESS) Teacher Form that was designed to assess general risk for emotional/behavioral difficulty among children. The modeling sequence included the relatively new exploratory structural equation modeling (ESEM) approach and bifactor models in addition to more standard techniques. Findings revealed that the factor structure of the BASC-2 BESS Teacher Form is multidimensional. Both ESEM and bifactor models showed good fit to the data. Bifactor models were preferred on conceptual grounds. Findings illuminate the hypothesis-generating power of ESEM and suggest that it might not be optimal for instruments designed to assess a predominant general factor underlying the data.     

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects

Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay &; Silverman, 2005 Ramsay, J. O., &; Silverman, B. W. (2005). Functional data analysis (2nd ed.). New York, NY: Springer-Verlag. [Google Scholar]), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, &; Peel, 2010 Boker, S. M., Deboeck, P. R., Edler, C., &; Peel, P. K. (2010). Generalized local linear approximation of derivatives from time series. In S. Chow, E. Ferrer, &; F. Hsieh (Eds.), Statistical methods for modeling human dynamics: An interdisciplinary dialogue (pp. 161–178). New York, NY: Taylor &; Francis. [Google Scholar]), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 Deboeck, P. R. (2010). Estimating dynamical systms: Derivative estimation hints from Sir Ronald A. Fisher. Multivariate Behavioral Research, 45, 725–745. doi:10.1080/00273171.2010.498294[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children’s self-regulation.     

A simple general method for oblique rotation

A simple and very general algorithm for oblique rotation is identified. While motivated by the rotation problem in factor analysis, it may be used to minimize almost any function of a not necessarily square matrix whose columns are restricted to have unit length. The algorithm has two steps. The first is to compute the gradient of the rotation criterion and the second is to project this onto a manifold of matrices with unit length columns. For this reason it is called a gradient projection algorithm. Because the projection step is very simple, implementation of the algorithm involves little more than computing the gradient of the rotation criterion which for many applications is very simple. It is proven that the algorithm is strictly monotone, that is as long as it is not already at a stationary point, each step will decrease the value of the criterion. Examples from a variety of areas are used to demonstrate the algorithm, including oblimin rotation, target rotation, simplimax rotation, and rotation to similarity and simplicity simultaneously. While it may be, the algorithm is not intended for use as a standard algorithm for well established problems, but rather as a tool for investigating new methods where its generality and simplicity may save an investigator substantial effort.The author would like to thank the review team for their insights and recommendations.     

Estimating Optimal Weights for Compound Scores: A Multidimensional IRT Approach

A method is proposed for constructing indices as linear functions of variables such that the reliability of the compound score is maximized. Reliability is defined in the framework of latent variable modeling [i.e., item response theory (IRT)] and optimal weights of the components of the index are found by maximizing the posterior variance relative to the total latent variable variance. Three methods for estimating the weights are proposed. The first is a likelihood-based approach, that is, marginal maximum likelihood (MML). The other two are Bayesian approaches based on Markov chain Monte Carlo (MCMC) computational methods. One is based on an augmented Gibbs sampler specifically targeted at IRT, and the other is based on a general purpose Gibbs sampler such as implemented in OpenBugs and Jags. Simulation studies are presented to demonstrate the procedure and to compare the three methods. Results are very similar, so practitioners may be suggested the use of the easily accessible latter method. A real-data set pertaining to the 28-joint Disease Activity Score is used to show how the methods can be applied in a complex measurement situation with multiple time points and mixed data formats.     

中国人格量表编制的本土化研究

为了深入探究中国人人格特质与结构,并编制本土化人格量表; 本文综合QZPS、CPAI-2及CPFFI的因素命名特征,编制出包含116个项目的人格词汇评定表。通过对1455名被试人格词汇评定结果的探索性分析,最终确定7个维度的人格词汇评定量表。该该量表7个因素对总变异的贡献率为51.63%,内部一致性信度在0.663-0.912之间,总量表的内部一致性信度为0.800; 7个因素的重测信度在0.700～0.874(p<0.001)之间。研究结果显示情绪性与外向性两个人格特质是人们共有的人格特质内容,该人格量表中的其他人格因素既有与西方人格因素趋同的方面,也有中国文化背景下本土化内容。同QZPS、CPAI-2及CPFFI相比,该人格因素结构几乎可以包含以上3个模型的绝大多数人格因素内容,且结构清晰全面。     

A Polychoric Instrumental Variable (PIV) Estimator for Structural Equation Models with Categorical Variables

This paper presents a new polychoric instrumental variable (PIV) estimator to use in structural equation models (SEMs) with categorical observed variables. The PIV estimator is a generalization of Bollen’s (Psychometrika 61:109–121, 1996) 2SLS/IV estimator for continuous variables to categorical endogenous variables. We derive the PIV estimator and its asymptotic standard errors for the regression coefficients in the latent variable and measurement models. We also provide an estimator of the variance and covariance parameters of the model, asymptotic standard errors for these, and test statistics of overall model fit. We examine this estimator via an empirical study and also via a small simulation study. Our results illustrate the greater robustness of the PIV estimator to structural misspecifications than the system-wide estimators that are commonly applied in SEMs. Kenneth Bollen gratefully acknowledges support from NSF SES 0617276, NIDA 1-RO1-DA13148-01, and DA013148-05A2. Albert Maydeu-Olivares was supported by the Department of Universities, Research and Information Society (DURSI) of the Catalan Government, and by grant BSO2003-08507 from the Spanish Ministry of Science and Technology. We thank Sharon Christ, John Hipp, and Shawn Bauldry for research assistance. The comments of the members of the Carolina Structural Equation Modeling (CSEM) group are greatly appreciated. An earlier version of this paper under a different title was presented by K. Bollen at the Psychometric Society Meetings, June, 2002, Chapel Hill, North Carolina.     

The Child Behavior Checklist for Group Care Workers: A Study Regarding the Factor Structure

In this study we examined the factor structure of the Child Behavior Checklist (CBCL) filled out by group care workers. Group care workers' judgements were collected on 846 children and adolescents treated in various residential settings in The Netherlands. Using confirmatory factor analysis, we were able to show that the original CBCL factor model based on parental judgments of child behavior also fits for the judgments of group care workers. This means that the well known 8 narrow-band syndromes (Withdrawn, Somatic Complaints, etc.) as well as the 2 broad-band syndromes (Internalizing and Externalizing) can be used to interpret the CBCL scores of group care workers. This confirmation of the CBCL factor structure is a first step to add a group care worker version to the CBCL family. However, as a second step, normative data need to be gathered to further enhance the use of the CBCL for group care workers.     

How to separate coordinate and categorical spatial relation components in integrated spatial representations: A new methodology for analysing sketch maps

Spatial relations between landmarks can be represented by means of categories and coordinates. In the present research, this paradigm was applied to sketch maps based on information acquired in goal-directed behaviour of exploration of a university campus area. The first aim was to investigate whether categorical and coordinate information can be considered conceptually independent in sketch maps. The second aim was to assess which kind of distance measure served better to represent coordinate information in the present case study, and finally to assess the factorial structure of coordinate and categorical data. Analytic methodology as well as statistical analysis were found to confirm that separating coordinate and categorical components was formally as well as empirically appropriate. A series of confirmatory factor analyses showed the best fit for the model with two correlated components, as well as an acceptable reliability of measures emerged. The two components were moderately correlated. Moreover, the adoption of Manhattan distance seemed to be the most effective method to represent coordinate spatial relations in spatial sketch maps of areas acquired through navigation.