Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis

Joint maximum likelihood (JML) estimation is one of the earliest approaches to fitting item response theory (IRT) models. This procedure treats both the item and person parameters as unknown but fixed model parameters and estimates them simultaneously by solving an optimization problem. However, the JML estimator is known to be asymptotically inconsistent for many IRT models, when the sample size goes to infinity and the number of items keeps fixed. Consequently, in the psychometrics literature, this estimator is less preferred to the marginal maximum likelihood (MML) estimator. In this paper, we re-investigate the JML estimator for high-dimensional exploratory item factor analysis, from both statistical and computational perspectives. In particular, we establish a notion of statistical consistency for a constrained JML estimator, under an asymptotic setting that both the numbers of items and people grow to infinity and that many responses may be missing. A parallel computing algorithm is proposed for this estimator that can scale to very large datasets. Via simulation studies, we show that when the dimensionality is high, the proposed estimator yields similar or even better results than those from the MML estimator, but can be obtained computationally much more efficiently. An illustrative real data example is provided based on the revised version of Eysenck’s Personality Questionnaire (EPQ-R).

     

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.     

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.     

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.     

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 Infinitesimal Jackknife with Exploratory Factor Analysis

The infinitesimal jackknife, a nonparametric method for estimating standard errors, has been used to obtain standard error estimates in covariance structure analysis. In this article, we adapt it for obtaining standard errors for rotated factor loadings and factor correlations in exploratory factor analysis with sample correlation matrices. Both maximum likelihood estimation and ordinary least squares estimation are considered.     

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.     

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。     

A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis

Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show that these methods can be implemented in a flexible way which requires minimal technical sophistication on the part of the end user. After providing an overview of item factor analysis and MCMC, results from several examples (simulated and real) will be discussed. The bulk of these examples focus on models that are problematic for current “gold-standard” estimators. The results demonstrate that it is possible to obtain accurate parameter estimates using MCMC in a relatively user-friendly package.     

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.     

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。     

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.     

Bootstrap Confidence Intervals for Ordinary Least Squares Factor Loadings and Correlations in Exploratory Factor Analysis

This article is concerned with using the bootstrap to assign confidence intervals for rotated factor loadings and factor correlations in ordinary least squares exploratory factor analysis. Coverage performances of SE-based intervals, percentile intervals, bias-corrected percentile intervals, bias-corrected accelerated percentile intervals, and hybrid intervals are explored using simulation studies involving different sample sizes, perfect and imperfect models, and normal and elliptical data. The bootstrap confidence intervals are also illustrated using a personality data set of 537 Chinese men. The results suggest that the bootstrap is an effective method for assigning confidence intervals at moderately large sample sizes.     

Approximated Penalized Maximum Likelihood for Exploratory Factor Analysis: An Orthogonal Case

The problem of penalized maximum likelihood (PML) for an exploratory factor analysis (EFA) model is studied in this paper. An EFA model is typically estimated using maximum likelihood and then the estimated loading matrix is rotated to obtain a sparse representation. Penalized maximum likelihood simultaneously fits the EFA model and produces a sparse loading matrix. To overcome some of the computational drawbacks of PML, an approximation to PML is proposed in this paper. It is further applied to an empirical dataset for illustration. A simulation study shows that the approximation naturally produces a sparse loading matrix and more accurately estimates the factor loadings and the covariance matrix, in the sense of having a lower mean squared error than factor rotations, under various conditions.     

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。     

An Item Factor Analysis of the Revised Barrett-Lennard Relationship Inventory

The revised version of the Barrett-Lennard Relationship Inventory with an added advice-giving scale was given to 240 female and 95 male students, who completed it in terms of their current closest personal relationship. The correlations between the 80 items were factor-analysed using a principal-factor solution to determine whether the items represented the five postulated factors of advice-giving, empathy, congruence, and level of and unconditionally of regard. Eighteen factors were extracted and rotated by the Varimax method. The first five factors extracted accounted for 36.3% of the variance and reflected the five postulated factors, thus partially supporting the factorial validity of this questionnaire.     

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。     

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。     

企业中层管理者时间管理倾向量表的探索性因素分析

时间管理倾向是个体在运用时间方式上所表现出来的心理和行为特征,具有多维度多层次的心理结构。参照已有的研究文献和广泛的调查研究,编制出我国企业中层管理者时间管理倾向量表,通过对150名企业中层管理者的探索性因素分析,结果表明企业中层管理者时间管理倾向问卷由时间价值感(社会取向和个人取向的时间价值感)、时间监控能力(目标与控制、计划与安排、优先级、时间分配和反馈性)和时间效能感(时间管理效能和时间管理行为效能)三个维度构成。