Evaluating Exploratory Factor Analysis Which Initial-Extraction Techniques Provide the Best Factor Fidelity?

Attacks by communication scholars on exploratory factor analysis (EFA) have cast doubt on prior findings based on the technique. The present study is one in a series of studies performed to test the ability of EFA to produce results that replicate known dimensions in a data set. It was designed to determine which of 7 initial extraction techniques produce the highest factor fidelity across 5 item distribution shapes and 3 sample sizes. Monte-Carlo-created data sets with known factors, known item distribution shapes, and a 30% error rate were submitted to EFA. Results from an analysis of variance (ANOH) indicate that image analysis reaches perfect factor fidelity with a smaller number of cases regardless of item distribution shape. This and other results reported in this study suggest that3ndings based on EFA should be viewed with cautious optimism and be evaluated according to the findings from this and similar studies.     

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.     

FACTOR: A computer program to fit the exploratory factor analysis model

Exploratory factor analysis (EFA) is one of the most widely used statistical procedures in psychological research. It is a classic technique, but statistical research into EFA is still quite active, and various new developments and methods have been presented in recent years. The authors of the most popular statistical packages, however, do not seem very interested in incorporating these new advances. We present the program FACTOR, which was designed as a general, user-friendly program for computing EFA. It implements traditional procedures and indices and incorporates the benefits of some more recent developments. Two of the traditional procedures implemented are polychoric correlations and parallel analysis, the latter of which is considered to be one of the best methods for determining the number of factors or components to be retained. Good examples of the most recent developments implemented in our program are (1) minimum rank factor analysis, which is the only factor method that allows one to compute the proportion of variance explained by each factor, and (2) the simplimax rotation method, which has proved to be the most powerful rotation method available. Of these methods, only polychoric correlations are available in some commercial programs. A copy of the software, a demo, and a short manual can be obtained free of charge from the first author.     

Semi-sparse PCA

It is well known that the classical exploratory factor analysis (EFA) of data with more observations than variables has several types of indeterminacy. We study the factor indeterminacy and show some new aspects of this problem by considering EFA as a specific data matrix decomposition. We adopt a new approach to the EFA estimation and achieve a new characterization of the factor indeterminacy problem. A new alternative model is proposed, which gives determinate factors and can be seen as a semi-sparse principal component analysis (PCA). An alternating algorithm is developed, where in each step a Procrustes problem is solved. It is demonstrated that the new model/algorithm can act as a specific sparse PCA and as a low-rank-plus-sparse matrix decomposition. Numerical examples with several large data sets illustrate the versatility of the new model, and the performance and behaviour of its algorithmic implementation.

     

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.     

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.     

Ordinary Least Squares Estimation of Parameters in Exploratory Factor Analysis With Ordinal Data

Exploratory factor analysis (EFA) is often conducted with ordinal data (e.g., items with 5-point responses) in the social and behavioral sciences. These ordinal variables are often treated as if they were continuous in practice. An alternative strategy is to assume that a normally distributed continuous variable underlies each ordinal variable. The EFA model is specified for these underlying continuous variables rather than the observed ordinal variables. Although these underlying continuous variables are not observed directly, their correlations can be estimated from the ordinal variables. These correlations are referred to as polychoric correlations. This article is concerned with ordinary least squares (OLS) estimation of parameters in EFA with polychoric correlations. Standard errors and confidence intervals for rotated factor loadings and factor correlations are presented. OLS estimates and the associated standard error estimates and confidence intervals are illustrated using personality trait ratings from 228 college students. Statistical properties of the proposed procedure are explored using a Monte Carlo study. The empirical illustration and the Monte Carlo study showed that (a) OLS estimation of EFA is feasible with large models, (b) point estimates of rotated factor loadings are unbiased, (c) point estimates of factor correlations are slightly negatively biased with small samples, and (d) standard error estimates and confidence intervals perform satisfactorily at moderately large samples.     

Factor analysis and scale revision

This article reviews methodological issues that arise in the application of exploratory factor analysis (EFA) to scale revision and refinement. The authors begin by discussing how the appropriate use of EFA in scale revision is influenced by both the hierarchical nature of psychological constructs and the motivations underlying the revision. Then they specifically address (a) important issues that arise prior to data collection (e.g., selecting an appropriate sample), (b) technical aspects of factor analysis (e.g., determining the number of factors to retain), and (c) procedures used to evaluate the outcome of the scale revision (e.g., determining whether the new measure functions equivalently for different populations).     

Enhancing Interpretability in Factor Analysis by Means of Mathematical Optimization

Abstract

Exploratory Factor Analysis (EFA) is a widely used statistical technique to discover the structure of latent unobserved variables, called factors, from a set of observed variables. EFA exploits the property of rotation invariance of the factor model to enhance factors’ interpretability by building a sparse loading matrix. In this paper, we propose an optimization-based procedure to give meaning to the factors arising in EFA by means of an additional set of variables, called explanatory variables, which may include in particular the set of observed variables. A goodness-of-fit criterion is introduced which quantifies the quality of the interpretation given this way. Our methodology also exploits the rotational invariance of EFA to obtain the best orthogonal rotation of the factors, in terms of the goodness-of-fit, but making them match to some of the explanatory variables, thus going beyond traditional rotation methods. Therefore, our approach allows the analyst to interpret the factors not only in terms of the observed variables, but in terms of a broader set of variables. Our experimental results demonstrate how our approach enhances interpretability in EFA, first in an empirical dataset, concerning volumes of reservoirs in California, and second in a synthetic data example.     

Generalized structured component analysis

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method avoids the principal limitation of partial least squares (i.e., the lack of a global optimization procedure) while fully retaining all the advantages of partial least squares (e.g., less restricted distributional assumptions and no improper solutions). The method is also versatile enough to capture complex relationships among variables, including higher-order components and multi-group comparisons. A straightforward estimation algorithm is developed to minimize the criterion.The work reported in this paper was supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the second author. We wish to thank Richard Bagozzi for permitting us to use his organizational identification data and Wynne Chin for providing PLS-Graph 3.0.     

Does the social concerns component of the anxiety sensitivity index belong to the domain of anxiety sensitivity or the domain of negative evaluation sensitivity?

The present study utilized an exploratory factor-analytic approach (i.e. principal-components analysis; PCA) to investigate whether the Social Concerns component of the Anxiety Sensitivity Index (ASI [Peterson, R. A., & Reiss, S. (1992). Anxiety Sensitivity Index manual (2nd ed.). Worthington, OH: International Diagnostic Systems.]) is best conceptualized as belonging to the domain of anxiety sensitivity (AS) and/or the domain of negative evaluation sensitivity (NES). A sample of university students (N = 216) was administered measures of both NES (i.e. Brief Fear of Negative Evaluation scale; Leary, 1983) and AS (i.e. ASI). Participants' responses to the items comprising these measures were subjected to a PCA with oblique rotation. Factors representing the NES construct and the three lower-order AS constructs (i.e. AS Physical, Psychological and Social Concerns) were obtained. Subscales derived from these four factors were positively and significantly correlated with one another and loaded on a single higher-order factor labeled Threat Sensitivity. Thus, the present findings suggest that the AS Social Concerns factor is distinct from NES and the other lower-order components of AS. However, correlational analyses and higher-order PCA indicated that the AS Social Concerns factor taps a blend of AS and NES as well as something unique and distinct from both global AS and NES.     

A Bibliometric Analysis of Communication Journals from 2002 to 2005

Journal impact ratings are often used by authors, promotion/hiring committees, and grant review teams as a proxy for scholarship quality. Journal citation data (2002–2005) from Social Sciences Citation Index were used to rank journals in the field of communication. A journal relatedness algorithm was applied to ascertain the 19 semantically related journals in communication. The mean journal impact index was 0.77 (SD= 0.28). Human Communication Research (HCR), Personal Relationships, Journal of Communication (JOC), and Communication Research (CR) were ranked the top four journals for the study years examined. Network analysis was conducted on in‐degree (i.e., citations to journals) and out‐degree (i.e., citations from journals) data for the 19 communication journals for 2003–2005. The purpose of the network analysis was to study the citation patterns among journals in the field of communication. Data using degree centrality indicate that Communication Monographs, CR, HCR, and JOC (in alphabetical order) are the four most central journals in the field.     

Factor Structure and Incremental Utility of the Multidimensional Cognitive Attentional Syndrome Scale (MCASS): A Bifactor Analysis

The Multidimensional Cognitive Attentional Syndrome Scale (MCASS) was developed to assess the seven maladaptive forms of self-regulation that make up the cognitive attentional syndrome (CAS). Both theory and empirical evidence highlight important distinctions among the seven forms of self-regulation underlying the CAS. The primary purpose of the present study was to determine whether the MCASS item scores are sufficiently multidimensional to warrant the use of subscale scores. A secondary aim was to examine the incremental utility of the MCASS domain-specific factors. A battery of self-report measures was administered to adults recruited through a crowd-sourcing website (N?=?359). Bifactor analysis was used to examine the multidimensionality of MCASS item scores. This analytic approach allowed for the quantification of variance captured by each domain-specific item score independent of the general factor. Results from the bifactor analysis suggest that the MCASS is a multidimensional measure, consisting of a strong general factor and domain-specific factors that are sufficiently distinct. Additionally, the majority of domain-specific factors provided incremental utility in predicting two criterion variables (i.e., general distress, happiness emotion goals) after accounting for the general factor. Taken together, results support continued use of the MCASS total scale and subscale scores and suggest that researchers may want to consider using a bifactor model when examining structural models that include the MCASS.

     

The High Cost of Complexity in Experimental Design and Data Analysis: Type I and Type II Error Rates in Multiway ANOVA

The availability of statistical software packages has led to a sharp increase in use of complex research designs and complex statistical analyses in communication research. An informal examination of studies from 2 leading communication journals suggests that the analysis of variance (ANOVA) is often the statistic of choice, and a substantial proportion of published research reports using ANOVA employ complex (k ≥ 3) factorial designs, often involving multiple dependent variables. This article reports a series of Monte Carlo simulations which demonstrate that this complexity may come at a heavier cost than many communication researchers realize. As frequently used, complex factorial ANOVA yield Type I and Type II error rates that many communication scholars would likely consider unacceptable. Consequently, quality of statistical inference in many studies is highly suspect. Communication researchers are warned about problems associated with design and statistical complexity and solutions are suggested.     

中国大学生面众恐惧的心理测量学再探

针对《心理科学》2011年第3期发表的《大学生面众交流恐惧的心理测量学初探》研究中存在的不足,通过理论与实践的深入反思,重新设计、研制了调查中国大学生面众恐惧的调研工具。在我国东、南、西、北、中各大地区随机抽取了17个省（市）共24所高校,用含有79个题项的预测量表进行预测,获得1057个有效预测样本,再将其划分为两组样本,分别进行探索性因素分析和验证性因素分析,研究结果表明：《中国大学生面众交流恐惧调查量表》（修订版）修订为新的四个维度和32个题项后,更能覆盖大学生面众恐惧现象的各个主要方面,量表具有更高的信效度,更好地达到了心理测量学的要求;四个维度分别是上台恐惧、面试恐惧、办事恐惧、团组与校外交流恐惧,可作为中国大学生面众交流恐惧的调研工具。     

The factor-gene basis of emotionality

This paper presents the empirical and theoretical evidence in support of the factor-gene model of emotionality. The theory views the expression of emotion as a product of the interaction between cognition and affect, where cognition and affect are each defined as complex systems whose wholistic functioning (cognition interprets inputs and affect controls arousal level) follows the principles of systems and information-processing theory and whose components are identified via factor analysis. On the basis of the empirical identification of factors at the 1st, 2nd, and 3rd strata, it has been hypothesized that the factors in each domain (33 cognitive factors and 31 affective factors) are hierarchically organized. The empirical research also indicates a significant hereditary effect for 31% of the factors in the cognitive domain and for 83% of the factors in the affective domain. The most pervasive experimental finding concerning the mode of inheritance is that each factor is polygenically determined. Furthermore, in the affective domain there is a range of dominance effects, depending on the class of factors. That is, factors related to escape and avoidance are governed by complete or overdominance, and some of them (e.g., escape) also manifest directional dominance, whereas factors related to undifferentiated arousal (e.g., autonomic balance) manifest either partial dominance or an intermediate form of inheritance. In brief, the factor-gene model is a multiple factor model at both the behavioral (i.e., the factors identified by factor analysis) and genetic (i.e., many genes accounting for each behavioral factor) levels. Futhermore, factors and genes are linked via a variety of unspecified, intervening (and to date unknown) psychobiological mechanisms.The experimental aspects of the author's research summarized in this review were supported by grants from the National Research Council of Canada, and the theoretical aspects were supported by grants from the Canada Council.     

In search of a measure to investigate mental performance among children: Development of the mental speed test

Processing speed is a component of general intelligence and an indicator of learning potential. There is a need for robust measures of mental speed based on contemporary theoretical developments. The current study addressed this need by proposing a mental speed test for children aged 60 to 96 months (5 to 8 years) and examining its psychometric properties. The test included indicators of perceptual speed, memory speed, reasoning speed, and fluency-flexibility speed presented through nonverbal items administered individually using touchscreen tablets. After establishing gender non-bias and concurrent validity with a contemporary intelligence test (i.e., ASIS, r = .59) with 107 children, the next administration included 373 children. Exploratory factor analysis (EFA) with subtest scores revealed a single-factor structure accounting for 45% of the total variance. Additional data from 212 children were used to assess structural validity and gender bias, which showed acceptable goodness of fit, providing evidence of the validity and reliability of the new measure for further use.     

Associations Among Body Mass Index,Depression, and Family Factors Across Two Generations

In this pilot study, we examined the relationship between health factors, sociodemographic factors, and body mass index (BMI) across two generations (n = 41 parent-child pairs). Generation 1 study variables included parent- and family-focused characteristics and health variables, the Generation 2 variables included child demographic factors, and the outcome variable was youths’ physical health (operationalized as BMI). Regression models revealed that Generation 1 variables, taken together, accounted for 26% of the variance in youth BMI. However, only the parent’s mental health symptoms (i.e., depression symptoms) made a unique contribution to the variance in youth BMI. Logistic regression analysis revealed that the youths’ race and age—but no other demographic factor—were significantly related to youth BMI-for-age. Our findings suggest that youth race, age, and parent mental health are each associated with youth physical health (i.e., BMI), confirming previous study findings that parental factors and demographic factors should be considered when exploring youth health outcomes.     

Affection and Abuse: Technology Use in Adolescent Romantic Relationships

Communication technologies benefit romantic relationships in terms of connection, but can also bring potential harm. Positive relational outcomes of adolescent technology use (i.e., increased emotional connection) have been examined separately from negative outcomes (i.e., unwanted monitoring of whereabouts) in previous research. However, the current study utilized hierarchical multiple regression to explore whether variance in both positive and negative relational outcomes could be explained by time spent online. Results suggest that time spent online predicts both positive relationship quality and cyber dating abuse after controlling age and gender. Implications include a greater understanding of the intersection between technology and adolescent relationships.