IRT-related factor analytic procedures for testing the equivalence of paper-and-pencil and Internet-administered questionnaires

This article describes a general item response theory-based factor analytic procedure that allows assessment of the equivalence between 2 administrative modes of a questionnaire: paper and pencil, and Internet based. The theoretical relations between the present procedure and other methods used in previous empirical research are shown, and the advantages of the procedure are discussed. An empirical application based on 2 personality questionnaires is given, and the results are compared with the results of using traditional procedures for assessing equivalence. The substantive implications of the results, as well as suggestions for further research and methodology, are discussed.     

Simultaneous optimization of factor assessibility and representativeness

P. M. Bentler has shown that Rao's canonical factor analysis is in effect a psychometric analysis, leading to factors that are maximally assessible from the data. He contrasts this with Kaiser and Caffrey's alpha factor analysis that leads to factors that maximally represent the true factors in the content domain. Noting the problems associated with factors that may be highly assessible, but not very representative, or vice versa, Bentler suggests the need for a technique that would, insofar as possible, be optimal with respect to both criteria. Such a technique is presented here, and is shown to resolve into a traditional scaling method, which in turn acquires a richer psychometric interpretation.The author would like to gratefully acknowledge support for this research from the Workshop in Political Theory and Policy Analysis (Indiana University) and Esco Research Associates. The paper benefitted substantially from the criticisms and suggestions of an anonymous referee.     

The psychopathology of anorexia nervosa: A factor analytic investigation

To examine the psychopathology of anorexia nervosa, behavioral assessment measures sampling a wide range of relevant constructs were collected on 150 women diagnosed as having anorexia nervosa. The data were subjected to an exploratory factor analysis using maximum-likelihood estimation and oblique rotation. Five factors were extracted, which were titled Fasting and Restrictive Eating, Depression, Anxiety, and Negative Self-image, Bulimic Behaviors, Fear of Fatness/Body Image Disturbance, and Impulsive Behavior/Post-Traumatic Response. Discriminate function analysis suggested that, other than the bulimic behaviors factor, the Impulsive Behavior/Post-Traumatic Response factor best discriminated between bulimic and restrictor subtypes of anorexics. These data suggest that the underlying dimensions of anorexia nervosa are very similar to those of bulimia nervosa. The findings also have implications for the multidimensional assessment and treatment of anorexia nervosa as well as conceptual models of the disorder.     

Motivation for orienteering An exploratory analysis using confirmatory factor analytic techniques

The aim of the present study was to investigate and identify different dimensions of motivation for the sport of orienteering, as well as to compare the strength of these dimensions by sex and age. Data for 512 subjects was analyzed with confirmatory factor analytic techniques in an extensive process where model generating was the primary matter of interest. There appear to be three broad main dimensions of motivation for orienteering. There is a main distinction between a social-recreational dimension and one reflecting a desire to achieve. Within the social-recreational dimension it is possible to identify more specific factors. In addition, there seems to be a relatively broad and distinct dimension, which is partly related to the other two, reflecting a search for internal stimulation. Comparisons of means of latent variables by sex and age indicate a number of clear and interesting differences.     

The factor structure of the Maslach Burnout Inventory in two Swedish human service organizations

The Maslach Burnout Inventory, MBI, is a well established measure of burnout. Its validity outside the USA is, however, uncertain. The aim of the present study was therefore to apply the MBI on personnel in two Swedish human service organizations, comparing factor solutions and scoring norms to the original results. The population consisted of 5730 employees in the Social Insurance Organization (SIO) and the Individual and Family Care section (IFC) of the social welfare agencies. Principal components analysis, principal axes and alpha factor analyses were performed, all with varimax rotation. The suggested three factor solution showed to be remarkably stable irrespective of type of analysis. Score levels were somewhat lower on two subscales in the Swedish population. The conclusion is that the psychometric properties of the MBI seem to be very satisfactory and stable, at least in comparison between Sweden and USA. It is suggested that the dimensionality of MBI is rather invariant, but that the score levels covary with national, cultural, or professional contexts within the human services.     

Anxiety sensitivity in traumatized Cambodian refugees: a discriminant function and factor analytic investigation

We examined the psychometric properties and factor structure of a Cambodian translation of the Anxiety Sensitivity Index (ASI) and an Augmented ASI (the ASI supplemented with a 9-item addendum that assesses additional Cambodian concerns about anxiety-related sensations). Both the ASI and the Augmented ASI distinguished among three diagnostic groups: highest score, PTSD with panic disorder (PP group); next, panic disorder without PTSD (P group); and then, other disorders than PTSD or panic disorder (O group). In the discriminant function analysis using the Augmented ASI, the best classificatory predictor (PP vs. P vs. O) was an Addendum item (“It scares me when I stand up and feel dizzy”). The principal component analysis (oblimin rotation) of the ASI yielded a 3-factor solution (I, Weak Heart Concerns; II, Control Concerns; III, Social Concerns) and of the Augmented ASI, a 4-factor solution (I, Weak Heart Concerns; II, Control Concerns; III, Wind Attack Concerns; IV, Social Concerns). The item clustering within the factor solution of both the ASI and Augmented ASI illustrates the role of cultural syndromes in generating fear of mental and bodily events.     

A factor analytic investigation of children's nighttime fear and coping responses

Checklists of children's nighttime fears and nighttime coping responses, completed by 178 8- to 13-year-old children and one of their parents, were factor analyzed. The resulting factors from each checklist were comparable for children and parents. The nighttime fear categories consisted of content around security either for one's personal life, loss, or safety or for others' safety and continued presence; imaginal-numinous concerns; and characteristics inherent in a nighttime situation. The coping categories consisted of responses related to internal self-control, social support, support from inanimate objects, prayer, and avoidance or escape either by controlling the inanimate environment or by controlling others.     

On the relations among regular, equal unique variances, and image factor analysis models

We investigate under what conditions the matrix of factor loadings from the factor analysis model with equal unique variances will give a good approximation to the matrix of factor loadings from the regular factor analysis model. We show that the two models will give similar matrices of factor loadings if Schneeweiss' condition, that the difference between the largest and the smallest value of unique variances is small relative to the sizes of the column sums of squared factor loadings, holds. Furthermore, we generalize our results and discus the conditions under which the matrix of factor loadings from the regular factor analysis model will be well approximated by the matrix of factor loadings from Jöreskog's image factor analysis model. Especially, we discuss Guttman's condition (i.e., the number of variables increases without limit) for the two models to agree, in relation with the condition we have shown, and conclude that Schneeweiss' condition is a generalization of Guttman's condition. Some implications for practice are discussed.Kentaro Hayashi is a visiting Assistant Professor, Department of Mathematics, Bucknell University, Lewisburg PA 17837, and Peter M. Bentler is Professor, Departments of Psychology and Statistics, University of California, Los Angeles CA 90095-1563. (Emails: Khayashi@bucknell.edu, bentler@ucla.edu) Parts of this paper were discussed in a session on Factor Analysis (J. ten Berge, Chair) at the IFCS-98 International Conference, Rome, July, 1998. This work was supported by National Institute on Drug Abuse grant DA 01070. The authors thank Professors Hans Schneeweiss and Ke-Hai Yuan, and four anonymous referees, for their invaluable comments which led to an improved version of this paper.     

Correlational and exploratory factor analyses (EFA) of commonly used empathy questionnaires: New insights

Empathy is a concept whose history has been marred by conceptual inconsistencies. Dispositional measures of empathy have varied in constituent subscales and have been suggested to conflate with other related constructs. The current investigation consists of correlational and exploratory factor analyses with self-report empathy measures to assess the commonalities between these measures. Four hundred ninety-seven university undergraduates completed a battery of self-report dispositional empathy measures, along with situational and dispositional sympathy measures. The novel findings include moderate correlations between scales purporting to measure empathy, an interpretable six-factor structure which represent subcomponents of these empathy scales, and the modest ability of existing questionnaires to contribute to these factor structures. The retained factor structure is not consistent with previous definitions of empathy, and it appears that self-report empathy measures do not adequately measure a uniform, consistent construct.     

A confirmatory factor analytic investigation of the TAS-20: corroboration of a five-factor model and suggestions for improvement

Alexithymia represents an individual difference dimension characterized by difficulties identifying emotions, difficulties describing emotions, and a utilitarian approach to thinking. The Toronto Alexithymia Scale-20 (TAS-20; Bagby, Parker, & Taylor, 1994) is a frequently used inventory to measure alexithymia, and although several studies have examined the factor structure of the TAS-20, a number of issues remain unresolved. Specifically, the severely unbalanced item-keyed nature of the TAS-20 has been suggested to limit the interpretation of the substantive Externally Oriented Thinking (EOT) factor. Further, it has also been suggested that the EOT factor may be better represented by 2 oblique factors. A review of the TAS-20 confirmatory factory analysis (CFA) literature has suggested that some improvement in CFA strategies could possibly be afforded by using a nested factors modeling approach. Based on a sample of 355 participants, we demonstrated that the TAS-20 was better represented by a nested factors model with 5 substantive factors. A novel, latent variable approach to estimating internal consistency reliability revealed that the subscales within the TAS-20 were associated with unacceptably low levels of reliability independently of the global alexithymia factor. Although there was some CFA evidence to suggest the plausibility of a negatively keyed factor, a thorough examination of the items in question offered an alternative interpretation. Further development of the TAS-20']s Externally Oriented Thinking subscale is encouraged.     

A case of extreme simplicity of the core matrix in three-mode principal components analysis

In three-mode Principal Components Analysis, theP ×Q ×R core matrixG can be transformed to simple structure before it is interpreted. It is well-known that, whenP=QR,G can be transformed to the identity matrix, which implies that all elements become equal to values specified a priori. In the present paper it is shown that, whenP=QR − 1,G can be transformed to have nearly all elements equal to values spectified a priori. A cllsed-form solution for this transformation is offered. Theoretical and practical implications of this simple structure transformation ofG are discussed. Constructive comments from anonymous reviewers are gratefully acknowledged.     

Religion and the five factor model of personality: An exploratory investigation using a Canadian university sample

The purpose of the present study was to examine the relation of religion, defined in terms of religious affiliation, religious involvement and religious orientation, to the five factor model of personality as measured by the NEO Personality Inventory-Revised using a religiously heterogeneous sample of 1129 Canadian university students. Results indicate that NEO-PI-R Agreeableness and Conscientiousness domains are significantly related to and affected by religion as measured across all three operationalizations of the construct used, though some sex differences were observed. Contrary to expectation, Neuroticism was found to differ as a function of religious affiliation with persons, particularly females, reporting No Religion obtaining significantly higher scores than those persons reporting a formal religious institution for their affiliation. Findings involving Extraversion were also inconsistent with hypotheses; Extraversion did not significantly relate to any form of religion measured. Openness was found to be largely unassociated with religion except for a significant negative correlation with a measure of extrinsic religious orientation. The article concludes with a discussion of the implications of the findings in relation to existing literature and Eysenck's hypothesis that religiousness is a function of conditionability and tender-minded attitudes. Limitations of the study and suggestions for future research are also overviewed.     

Should research experience be used for selection into graduate school: A discussion and meta‐analytic synthesis of the available evidence

Prior research experience is widely considered by graduate school admissions committees in the United States of America. Here, we use meta‐analytic methods and data from 18 unique samples and a total sample size of 3,525 students to shed light on the validity of prior research experience as a predictor of graduate school performance. Prior research experience was largely unrelated to academic performance (ρ = .01, k = 8, N = 1,419), degree attainment (ρ = .05, k = 3, N = 140), professional/practice performance (ρ = .06, k = 4, N = 1,120), and publication performance (ρ = .11, k = 7, N = 1,094). We also discuss whether consideration of prior research experience may unfairly disadvantage the students with lower levels of SES, students with childcare or eldercare responsibilities, and students from institutions at which research opportunities are limited.     

An empirical investigation of the factor structure of the AUDIT

This study investigated the Alcohol Use Disorders Identification Test's (AUDIT) factor structure and psychometric properties. The factor structure was derived from a sample of 7,035 men and women primary care patients. A principal components analysis identified 2 factors in the AUDIT data and was supported in a confirmatory factor analysis (CFA). The 2 factors were Dependence/Consequences and Alcohol Consumption. The CFA also provided support for a 3-factor model whose factors (Alcohol Consumption, Alcohol Dependence, and Related Consequences) matched those proposed by the AUDIT's developers. Psychometric indexes were determined by use of the baseline and 12-month follow-up data of 301 men and women who entered a clinical trial. The results showed that the 2 factors had good reliability. Validity tests supported the interpretation of what the 2 factors measure, its implications for relationships to other variables, and the comparability of the 2- and 3-factor models.     

On the optimality of the simultaneous redundancy transformations

The objective of this paper is to introduce and motivate additional properties and interpretations for the redundancy variables. It is shown that these variables can be derived by application of certain invariance arguments and without reference to the index of redundancy. In addition, an optimality property for the variables is presented which is important whenever one restricts attention in a study to a subset of the redundancy variables. This optimality property pertains to the subset rather than to the individual variables.This paper is based in part on the author's doctoral dissertation, Department of Statistics, Princeton, University. Research was conducted under the supervision of Lawrence S. Mayer.     

Maximization of sums of quotients of quadratic forms and some generalizations

Monotonically convergent algorithms are described for maximizing six (constrained) functions of vectors x, or matricesX with columns x₁, ..., x _r . These functions are h₁(x)= _k (xA _kx)(xC _kx)^–1, H₁(X)= _k tr (XA _k X)(XC _k X)^–1, h₁(X)= _{k l} (x _l A _kx _l ) (x _l C _kx _l )^–1 withX constrained to be columnwise orthonormal, h₂(x)= _k (xA _kx)²(xC _kx)^–1 subject to xx=1, H₂(X)= _k tr(XA _kX)(XA_kX)(XC_kX)^–1 subject toXX=I, and h₂(X)= _{k l} (x _l A _kx _l )² (x _l C _kX _l )^–1 subject toXX=I. In these functions the matricesC _k are assumed to be positive definite. The matricesA _k can be arbitrary square matrices. The general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis. Several applications of the general algorithms are given. Specifically, algorithms are given for reciprocal principal components analysis, binormamin rotation, generalized discriminant analysis, variants of generalized principal components analysis, simple structure rotation for one of the latter variants, and set component analysis. For most of these methods the algorithms appear to be new, for the others the existing algorithms turn out to be special cases of the newly derived general algorithms.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge for stimulating this research and for helpful comments on an earlier version of this paper.     

A factor analytic investigation of the BASC-2 Behavioral and Emotional Screening System Parent Form: psychometric properties, practical implications, and future directions

The Behavior Assessment System for Children, Second Edition (BASC-2) Behavioral and Emotional Screening System Parent Form (BESS Parent; Kamphaus & Reynolds, 2007) is a recently developed instrument designed to identify behavioral and emotional risk in students. To describe the underlying factor structure for this instrument, exploratory (EFA) and confirmatory factor analyses (CFA) were conducted utilizing two subsets of a large, nationally-representative sample. The results of the EFA suggested that the BESS Parent contained a four-factor latent structure (i.e., Externalizing, Internalizing, Adaptive Skills, and Inattention), which was supported by CFA. Results support further investigation into utilizing four subscales in addition to an overall risk score; distributional and reliability information for the BESS Parent subscales is provided. Practical implications for school psychologists interested in early identification and directions for future research are discussed.     

Riemannian Newton and trust-region algorithms for analytic rotation in exploratory factor analysis

In exploratory factor analysis, latent factors and factor loadings are seldom interpretable until analytic rotation is performed. Typically, the rotation problem is solved by numerically searching for an element in the manifold of orthogonal or oblique rotation matrices such that the rotated factor loadings minimize a pre-specified complexity function. The widely used gradient projection (GP) algorithm, although simple to program and able to deal with both orthogonal and oblique rotation, is found to suffer from slow convergence when the number of manifest variables and/or the number of latent factors is large. The present work examines the effectiveness of two Riemannian second-order algorithms, which respectively generalize the well-established truncated Newton and trust-region strategies for unconstrained optimization in Euclidean spaces, in solving the rotation problem. When approaching a local minimum, the second-order algorithms usually converge superlinearly or even quadratically, better than first-order algorithms that only converge linearly. It is further observed in Monte Carlo studies that, compared to the GP algorithm, the Riemannian truncated Newton and trust-region algorithms require not only much fewer iterations but also much less processing time to meet the same convergence criterion, especially in the case of oblique rotation.