Nonparametric Estimation of Standard Errors in Covariance Analysis Using the Infinitesimal Jackknife

The infinitesimal jackknife provides a simple general method for estimating standard errors in covariance structure analysis. Beyond its simplicity and generality what makes the infinitesimal jackknife method attractive is that essentially no assumptions are required to produce consistent standard error estimates, not even the requirement that the population sampled has the covariance structure assumed. Commonly used covariance structure analysis software uses parametric methods for estimating parameters and standard errors. When the population sampled has the covariance structure assumed, but fails to have the distributional form assumed, the parameter estimates usually remain consistent, but the standard error estimates do not. This has motivated the introduction of a variety of nonparametric standard error estimates that are consistent when the population sampled fails to have the distributional form assumed. The only distributional assumption these require is that the covariance structure be correctly specified. As noted, even this assumption is not required for the infinitesimal jackknife. The relation between the infinitesimal jackknife and other nonparametric standard error estimators is discussed. An advantage of the infinitesimal jackknife over the jackknife and the bootstrap is that it requires only one analysis to produce standard error estimates rather than one for every jackknife or bootstrap sample.     

探索性因素分析因子抽取方法的比较

探索性因素分析决定因子抽取的方法主要有Bartlett法、K1原则、碎石检验法、Aaker原则、PA、MAP等六种,通过对样本1的395名大学生的学习过程问卷调查获得真实数据,运用这六种方法进行因素分析分别抽取7、4、2、4、3、2个因子;应用样本2的383名大学生的问卷调查数据进行验证性因素分析,结果显示,碎石检验方法与MAP方法抽取的二因素模型更理想。研究表明,因子抽取需兼顾“简约性原则”与“完备性原则”,同时要根据一定的理论建构、专业知识和经验来决定因子数。     

平行分析在探索性因素分析中的应用

平行分析是探索性因素分析中用来确定所保留的凶子个数的一种方法。探索性因素分析中常用的确定因子个数的方法有特征值大于1准则和碎石图,但这两种方法又各有不足。平行分析则为探索性因素分析中所保留因子个数的确定提供了另一种新思路。本文详细介绍了平行分析的步骤、潜在逻辑以及进行平行分析所用的软件,并通过实例来说明其在探索性因素分析中如何应用。     

Bootstrap探索性因素分析方法及其应用

传统的探索性因素分析方法需要满足正态分布等前提假设,且无法提供研究结果可重复性的证据.而Bootstrap探索性因素分析方法不必满足正态分布的前提假设,利用已有的测试数据,以评估探索性因素分析的可靠性.Bootstrap探索性因素分析方法作为传统的探索性因素分析方法的有力补充,克服了其未提供研究结果可重复性的不足,为心理学研究者特别是量表编制者提升研究结果的社会应用价值及可靠性提供了统计方法学上的支持.     

Estimating Standard Errors in Exploratory Factor Analysis

The article describes 6 issues influencing standard errors in exploratory factor analysis and reviews 7 methods of computing standard errors for rotated factor loadings and factor correlations. These 7 methods are the augmented information method, the nonparametric bootstrap method, the infinitesimal jackknife method, the method using the asymptotic distributions of unrotated factor loadings, the sandwich method, the parametric bootstrap method, and the jackknife method. Standard error estimates are illustrated using a personality study with 537 men and an intelligence study with 145 children.     

Exploratory Factor Analysis With Small Sample Sizes

Exploratory factor analysis (EFA) is generally regarded as a technique for large sample sizes (N), with N = 50 as a reasonable absolute minimum. This study offers a comprehensive overview of the conditions in which EFA can yield good quality results for N below 50. Simulations were carried out to estimate the minimum required N for different levels of loadings (λ), number of factors (f), and number of variables (p) and to examine the extent to which a small N solution can sustain the presence of small distortions such as interfactor correlations, model error, secondary loadings, unequal loadings, and unequal p/f. Factor recovery was assessed in terms of pattern congruence coefficients, factor score correlations, Heywood cases, and the gap size between eigenvalues. A subsampling study was also conducted on a psychological dataset of individuals who filled in a Big Five Inventory via the Internet. Results showed that when data are well conditioned (i.e., high λ, low f, high p), EFA can yield reliable results for N well below 50, even in the presence of small distortions. Such conditions may be uncommon but should certainly not be ruled out in behavioral research data.     

The Use of Exploratory Factor Analysis and Principal Components Analysis in Communication Research

Exploratory factor analysis is a popular statistical technique used in communication research. Although exploratory factor analysis (EFA) and principal components analysis (PCA) are different techniques, PCA is often employed incorrectly to reveal latent constructs (i.e., factors) of observed variables, which is the purpose of EFA. PCA is more appropriate for reducing measured variables into a smaller set of variables (i.e., components) by keeping as much variance as possible out of the total variance in the measured variables. Furthermore, the popular use of varimax rotation raises some concerns about the relationships among the factors that researchers claim to discover. This paper discusses the distinct purposes of PCA and EFA, using two data sets as examples to highlight the differences in results between these procedures, and also reviews the use of each technique in three major communication journals: Communication Monographs, Human Communication Research, and Communication Research.     

Multicultural Counseling Competencies: An Exploratory Factor Analysis

The author examined the underlying factors of the Association of Multicultural Counseling and Development's (AMCD) Multicultural Competencies. One hundred fifty‐one professional counselors who are members of the American Counseling Association responded to a survey that included items reflecting AMCD's multicultural competencies and Explanatory Statements. An exploratory factor analysis revealed 5 multicultural competencies factors: Awareness, Knowledge, Definitions of Terms, Racial Identity Development, and Skills.     

Exploratory Factor Analysis of the Pain Outcomes Profile

The Pain Outcomes Profile (POP) is a brief, multidimensional measure intended to assess pain intensity, functioning, and affect. It is presented as a practical measure with clinical utility. Results of studies support its concurrent, construct and predictive validity at the scale level. However, there have been no published studies of the measure at the item level. The present study was intended to assess the construct validity of the POP by way of factor analysis. A sample of 447 assessments of patients at a chronic non-cancer pain outpatient treatment center was employed. The 20 substantive items comprising the POP were entered into a factor analysis with oblique rotation. Five salient factors were obtained. Item-inclusion was generally consistent with factor loadings although noteworthy exceptions were observed in the Fear, Mobility and Vitality scales. Recommendations for further study and limitations of the current project are delineated.     

Analytic Standard Errors for Exploratory Process Factor Analysis

Exploratory process factor analysis (EPFA) is a data-driven latent variable model for multivariate time series. This article presents analytic standard errors for EPFA. Unlike standard errors for exploratory factor analysis with independent data, the analytic standard errors for EPFA take into account the time dependency in time series data. In addition, factor rotation is treated as the imposition of equality constraints on model parameters. Properties of the analytic standard errors are demonstrated using empirical and simulated data.     

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。     

Exploratory Factor Analysis: A Users’Guide

In 1978, Comrey wrote a guide to factor analysis in the Journal of Consulting and Clinical Psychology. This paper provides an update of the information given by Comrey in relation to exploratory factor analysis (EFA) for work and organizational psychologists, and particularly those involved with test development, interpretation and validation. In doing so, it offers a user's guide to contemporary methods and available techniques and introduces heuristics for dealing with problems of skew and kurtosis, social desirability response set, and factor naming.     

Exploratory Factor Analysis With Small Samples and Missing Data

Exploratory factor analysis (EFA) is an extremely popular method for determining the underlying factor structure for a set of variables. Due to its exploratory nature, EFA is notorious for being conducted with small sample sizes, and recent reviews of psychological research have reported that between 40% and 60% of applied studies have 200 or fewer observations. Recent methodological studies have addressed small size requirements for EFA models; however, these models have only considered complete data, which are the exception rather than the rule in psychology. Furthermore, the extant literature on missing data techniques with small samples is scant, and nearly all existing studies focus on topics that are not of primary interest to EFA models. Therefore, this article presents a simulation to assess the performance of various missing data techniques for EFA models with both small samples and missing data. Results show that deletion methods do not extract the proper number of factors and estimate the factor loadings with severe bias, even when data are missing completely at random. Predictive mean matching is the best method overall when considering extracting the correct number of factors and estimating factor loadings without bias, although 2-stage estimation was a close second.     

探索性因子分析及其在应用中存在的主要问题

探索性因子分析的发展非常迅速,已成为教育与社会心理学领域中最常用的统计方法之一。本文全面介绍了探索性因子分析的基本原理,阐述了其发生的机制及基本过程,对其在教育、心理领域应用中存在的问题进行了总结,并针对应用中样本容量和观测变量数目不够、因子求解方法的误用、因子数目的确定标准及因子旋转中存在的问题、因子值缺乏重复验证性、研究结果呈现形式不规范、过于依赖SPSS、缺乏主动性等问题提出了一些相应的建议。     

A Comparative Investigation of Rotation Criteria Within Exploratory Factor Analysis

Exploratory factor analysis (EFA) is a commonly used statistical technique for examining the relationships between variables (e.g., items) and the factors (e.g., latent traits) they depict. There are several decisions that must be made when using EFA, with one of the more important being choice of the rotation criterion. This selection can be arduous given the numerous rotation criteria available and the lack of research/literature that compares their function and utility. Historically, researchers have chosen rotation criteria based on whether or not factors are correlated and have failed to consider other important aspects of their data. This study reviews several rotation criteria, demonstrates how they may perform with different factor pattern structures, and highlights for researchers subtle but important differences between each rotation criterion. The choice of rotation criterion is critical to ensure researchers make informed decisions as to when different rotation criteria may or may not be appropriate. The results suggest that depending on the rotation criterion selected and the complexity of the factor pattern matrix, the interpretation of the interfactor correlations and factor pattern loadings can vary substantially. Implications and future directions are discussed.     

Developing Dyadic Evaluation for Supervision: An Exploratory Factor Analysis

This study addresses the need for empirically validated tools to support the training, supervision, and the discovery of best practices in Marital and Family Therapy (MFT). This project represents a first step in developing the Dyadic Supervision Evaluation (DSE), an assessment tool that is grounded in developmental and systemic theory and is psychometrically strong. An Exploratory Factor Analysis (EFA) approach was applied to data from 88 trainee-supervisor dyads across four time periods during the first year of clinical training, resulting in 20 factors, including 9 factors for trainees and 11 factors for supervisors with internal reliabilities ranging from α’s = .82–.98. Discussion addresses the utility of the DSE in documenting the developmental and dyadic progression of supervision during the first year of MFT training.     

A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis

Psychometrika - Marginal maximum likelihood (MML) estimation is the preferred approach to fitting item response theory models in psychometrics due to the MML estimator’s consistency,...     

Acquiescent Responding in Balanced Multidimensional Scales and Exploratory Factor Analysis

Personality tests often consist of a set of dichotomous or Likert items. These response formats are known to be susceptible to an agreeing-response bias called acquiescence. The common assumption in balanced scales is that the sum of appropriately reversed responses should be reasonably free of acquiescence. However, inter-item correlation (or covariance) matrices can still be affected by the presence of variance due to acquiescence. To analyse these correlation matrices, we propose a method that is based on an unrestricted factor analysis and can be applied to multidimensional scales. This method obtains a factor solution in which acquiescence response variance is isolated in an independent factor. It is therefore possible, without the potentially confounding effect of acquiescence, to: (a) examine the dominant factors related to content latent variables; and (b) estimate participants’ factor scores on content latent variables. This method, which is illustrated by two empirical data examples, has proved to be useful for improving the simplicity of the factor structure. This research was partially supported by a grant from the Spanish Ministry of Science and Technology (SEJ2005-09170-C04-04/PSIC), and a grant from the Catalan Ministry of Universities, the Research and Information Society (2005SGR00017). The authors are obliged to the team of reviewers for helpful comments on an earlier version of this paper.     

幼儿好奇心结构的探索性因素分析

幼儿好奇心结构的研究是幼儿好奇心发展研究的基础。根据已有的研究文献和对教师的开放式问卷调查,编制了幼儿好奇心发展教师问卷,对3-5岁幼儿的教师进行问卷调查,在此基础上进行探索性因素分析,结果表明,幼儿好奇心主要由敏感、观察、兴趣、探索、提问、解决问题、幻想、专注等8个因素构成。