Structural Equation Modeling With AMOS,EQS, and LISREL: Comparative Approaches to Testing for the Factorial Validity of a Measuring Instrument

Using a confirmatory factor analytic (CFA) model as a paradigmatic basis for all comparisons, this article reviews and contrasts important features related to 3 of the most widely-used structural equation modeling (SEM) computer programs: AMOS 4.0 (Arbuckle, 1999), EQS 6 (Bentler, 2000), and LISREL 8 (Joreskog & Sorbom, 1996b). Comparisons focus on (a) key aspects of the programs that bear on the specification and testing of CFA models-preliminary analysis of data, and model specification, estimation, assessment, and misspecification; and (b) other important issues that include treatment of incomplete, nonnormally-distributed, or categorically-scaled data. It is expected that this comparative review will provide readers with at least a flavor of the approach taken by each program with respect to both the application of SEM within the framework of a CFA model, and the critically important issues, previously noted, related to data under study.     

The structure of feared social situations among individuals with a lifetime diagnosis of social anxiety disorder in two independent nationally representative mental health surveys

The present study employed both exploratory and confirmatory factor analytic approaches with nationally representative samples of individuals with a lifetime diagnosis of social anxiety disorder (n=1123; n=3091, respectively) using split-halves of the National Comorbidity Replication Survey (n=9282) and cross-validated with the Canadian Community Health Survey on Mental Health and Wellbeing (n=36,984). Strong support was found for a three-factor solution. This model was obtained from exploratory factor analysis and was further evaluated using two confirmatory factor analytic investigations in the two national samples. The three social situational domains reflected (1) Social Interaction Fears, (2) Observation Fears, and (3) Public Speaking Fears. Individuals with generalized social anxiety disorder (i.e., those who endorsed 7 or more of 13 feared social situations assessed in the survey) were significantly more likely to report Social Interaction Fears and Observation Fears compared to individuals with non-generalized social anxiety disorder (i.e., those who endorsed only 6 or fewer of 13 feared social situations). Individuals with generalized social anxiety were particularly characterized by combinations of Public Speaking Fears plus Social Interaction Fears and Observation Fears. The clinical and classification implications of our study for DSM-V are discussed.     

Two Studies Examining the Error Theory Underlying the Measurement Model of the Verbal Aggressiveness Scale

Meta‐analysis indicates moderate correlations between the Verbal Aggressiveness Scale (VAS) and other self‐report measures but near‐zero correlations with behavioral measures. Accurately interpreting correlations between the VAS and other variables, however, requires an examination of the untested error theory underlying the measurement model for the VAS. In two separate studies, the results of single‐factor correlated uniqueness confirmatory factor analytic models revealed a pattern of significant error covariances indicating that VAS item scores are confounded by systematic error attributable to multiple unspecified latent effects. After pruning the item sets, we identified 4 items that were free of latent variable influences other than trait verbal aggressiveness. Implications for interpreting the verbal aggressiveness literature are discussed along with recommendations for revising the VAS.     

A comparison of the LISREL and EQS programs for obtaining parameter estimates in confirmatory factor analysis studies

Recently, researchers in psychology have been provided with the techniques for confirming factor analytic structures. Many software packages are now available that provide the researcher with the ability to test factor structures and measurement models with some precision. However, the literature fails to provide the researcher with any comparison of the available software. This paper reviews the basic premise of confirmatory factor analysis and describes the use of two of the more popular software packages (e.g., LISREL and EQS) for obtaining parameter estimates. The two programs are then compared for similarity in estimates and ease of use.     

A further examination of the constructs underlying assessment center ratings

Previous factor analytic work (Sackett and Dreher, 1982) has found exercise factors, rather than the expected dimension factors, underlying ratings made in managerial assessment centers. The present paper responds to criticisms that inappropriate analyses were conducted and that unrepresentative assessment centers were studied. Exercise factors were found to predominate in two new sets of assessment data which we obtained and in three studies published by other authors, thus indicating that the results were not idiosyncratic to the three centers studied by Sackett and Dreher. Analyses using confirmatory, rather than exploratory, factor analysis also support the dominance of exercise factors. Although dimension factors were found in three of four data sets studied, variables loading on a dimension factor consistently loaded more highly on an exercise factor as well.     

Structural equation modeling with interchangeable dyads

Structural equation modeling (SEM) can be adapted in a relatively straightforward fashion to analyze data from interchangeable dyads (i.e., dyads in which the 2 members cannot be differentiated). The authors describe a general strategy for SEM model estimation, comparison, and fit assessment that can be used with either dyad-level or pairwise (double-entered) dyadic data. They present applications illustrating this approach with the actor-partner interdependence model, confirmatory factor analysis, and latent growth curve analysis.     

Dimensionality of posttraumatic stress symptoms: a confirmatory factor analysis of DSM-IV symptom clusters and other symptom models

Recent exploratory [Taylor, S., Kuch, K., Koch, W. J., Crockett, D. J., & Passey, G. (1998). The structure of posttraumatic stress symptoms. Journal of Abnormal Psychology, 107, 154-160.] and confirmatory [Buckley, T. C., Blanchard, E. B., & Hickling, E. J. (1998). A confirmatory factor analysis of posttraumatic stress symptoms. Behaviour Research and Therapy, 36, 1091-1099; King, D. W., Leskin, G. A., King, L. A., & Weathers, F. W. (1998). Confirmatory factor analysis of the clinician-administered PTSD scale: evidence for the dimensionality of posttraumatic stress disorder. Psychological Assessment, 10, 90-96.] factor analytic investigations suggest that the three symptom clusters of posttraumatic stress disorder (PTSD) as defined in the Diagnostic and Statistical Manual [4th ed.; DSM-IV; American Psychiatric Association (1994). Diagnostic and statistical manual of mental disorders (4th ed.). Washington, DC: Author.] may not provide the best conceptualization of symptom dimensionality. However, the alternative models have not been in agreement, nor have they been compared against each other or models based on the DSM-IV. The purpose of the present investigation was to test a series of dimensional models suggested by these recent factor analytic investigations and the DSM-IV. Using data collected with the PTSD Checklist--Civilian Version [Weathers, F. W., Litz, B. T., Huska, J. A., & Keane, T. M. (1994). PCL-C for DSM-IV. Boston: National Center for PTSD--Behavioral Science Division.] from 349 referrals to a primary care medical clinic, we used confirmatory factor analysis to evaluate a: (1) hierarchical four-factor model, (2) four-factor intercorrelated model, (3) hierarchical three-factor model, (4) three-factor intercorrelated model, and (5) hierarchical two-factor model. The hierarchical four-factor model (comprising four first-order factors corresponding to reexperiencing, avoidance, numbing, and hyperarousal all subsumed by a higher-order general factor) provided the best overall fit to the data; although, all models met some standards specified for good model fit. More research is needed to establish the dimensional nature of PTSD symptoms and to assess whether identified dimensions differ as a function of the trauma experience. Implications for assessment, diagnosis, and treatment are also discussed.     

Structural equation modeling: reviewing the basics and moving forward

This tutorial begins with an overview of structural equation modeling (SEM) that includes the purpose and goals of the statistical analysis as well as terminology unique to this technique. I will focus on confirmatory factor analysis (CFA), a special type of SEM. After a general introduction, CFA is differentiated from exploratory factor analysis (EFA), and the advantages of CFA techniques are discussed. Following a brief overview, the process of modeling will be discussed and illustrated with an example using data from a HIV risk behavior evaluation of homeless adults (Stein & Nyamathi, 2000). Techniques for analysis of nonnormally distributed data as well as strategies for model modification are shown. The empirical example examines the structure of drug and alcohol use problem scales. Although these scales are not specific personality constructs, the concepts illustrated in this article directly correspond to those found when analyzing personality scales and inventories. Computer program syntax and output for the empirical example from a popular SEM program (EQS 6.1; Bentler, 2001) are included.     

Factor analytic models: viewing the structure of an assessment instrument from three perspectives

The overarching purpose of this article is to present a nonmathematical introduction to the application of confirmatory factor analysis (CFA) within the framework of structural equation modeling as it applies to psychological assessment instruments. In the interest of clarity and ease of understanding, I model exploratory factor analysis (EFA) structure in addition to first- and second-order CFA structures. All factor analytic structures are based on the same measuring instrument, the Beck Depression Inventory-II (BDI-II; Beck, Steer, & Brown, 1996). Following a "walk" through the general process of CFA modeling, I identify several common misconceptions and improper application practices with respect to both EFA and CFA and tender caveats with a view to preventing further proliferation of these pervasive practices.     

A confirmatory factor analysis of the structure of schizotypy

Recent research into schizotypal traits has been concerned with the number and nature of these personality dimensions. Earlier exploratory factor analytic work using a wide variety of scales (the CSTQ) has generated a four-factor solution but other solutions have been provided by other investigators. This study uses confirmatory factor analysis on a large sample to compare several plausible models of the relationships between scales. These models include a two-factor model separating ‘positive’ from ‘negative’ schizotypal features, a three-factor model including features of cognitive disorganization, and the four-factor model generated previously by exploratory factor analysis. Results offer support for the four-factor solution as the only structure meeting multiple criteria for goodness of fit. The relevance of Eysenck's dimensions, and the P scale in particular, to the results is discussed. Attention is drawn to the possibility that the factors describe predispositions of risk of psychotic disorders beyond that of schizophrenia.     

The facets of anxiety sensitivity represented in the childhood anxiety sensitivity index: confirmatory analyses of factor models from past studies

Results of past factor analytic studies of the Childhood Anxiety Sensitivity Index and Anxiety Sensitivity Index were used to formulate hypotheses about factor models of anxiety sensitivity. Using a nonclinical sample of 767 children and adolescents and confirmatory factor analysis, hypothesized models with 2, 3, and 4 lower order factors (facets) were tested. Goodness-of-fit criteria indicated that a model with 4 facets fits these data well. Support was found for factorial invariance of the 4 facets across age and gender, using nonclinical and clinical samples. Results support a hierarchical factor model in that there was a strong general factor, explaining 71% of the variance. Findings are discussed in the context of anxiety sensitivity theory and research with children and adolescents.     

Rethinking psychological approaches towards health promotion

The purpose of the present study was to test the factorial and discriminant validity of the Revised Illness Perception Questionnaire (IPQ-R), a measure of illness representations based on Leventhal, Meyer and Nerenz's Self-Regulation Theory, in a cervical screening context using confirmatory factor analysis. Six hundred and sixty women, who had attended a colposcopy clinic and were invited to re-attend, completed the IPQ-R. Data were analysed using covariance structure analysis. The adequacy of an a priori confirmatory factor analytic model that included seven dimensions of the cognitive illness representation: identity, timeline-acute/chronic, serious consequences, personal control, treatment control, illness coherence, and causal attributions, and one emotional representation factor was tested against the observed data. After the elimination of two items responsible for large standardised residuals and with low factor loadings, the model adequately accounted for covariances among the IPQ-R items according to multiple criteria for goodness-of-fit. Factor inter-correlations supported the discriminant validity of the constructs and the factors exhibited satisfactory composite reliability. A theoretically predictable pattern of relationships among the representation dimensions was evident. In particular, the control-related constructs and the illness coherence dimension were negatively related to other illness representation constructs. The present study provided confirmatory evidence using a robust hypothesis-testing framework to support the proposed structure of the illness representation dimensions in a cervical screening context.     

Confirmatory Factor Analysis and Multidimensional Scaling for Construct Validation of Cognitive Abilities

Although factor analysis is the most commonly-used method for examining the structure of cognitive variable interrelations, multidimensional scaling (MDS) can provide visual representations highlighting the continuous nature of interrelations among variables. Using data (N = 8,813; ages 17-97 years) aggregated across 38 separate studies, MDS was applied to 16 cognitive variables representative of five well-established cognitive abilities. Parallel to confirmatory factor analytic solutions, and consistent with past MDS applications, the results for young (18-39 years), middle (40-65 years), and old (66-97 years) adult age groups consistently revealed a two-dimensional radex disk, with variables from fluid reasoning tests located at the center. Using a new method, target measures hypothesized to reflect three aspects of cognitive control (updating, storage-plus-processing, and executive functioning) were projected onto the radex disk. Parallel to factor analytic results, these variables were also found to be centrally located in the cognitive ability space. The advantages and limitations of the radex representation are discussed.     

GENERAL SAFETY PERFORMANCE: A TEST OF A GROUNDED THEORETICAL MODEL

In this investigation, we report the results of 2 studies designed to (a) conduct confirmatory factor analytic tests of a model of general safety performance with performance ratings from 550 coworker appraisals (Study 1), and (b) examine hypothesized relationships between indicators of breadth and depth of knowledge constructs and confirmed safety performance factors (from Study 1) with training history data and supervisory appraisals for 133 hazardous waste workers in 23 jobs and 4 organizations (Study 2). Confirmatory factor analytic results from Study 1 provided support for a 4-factor model of general safety performance with performance factors labeled Using Personal Protective Equipment, Engaging in Work Practices to Reduce Risk, Communicating Health and Safety Information, and Exercising Employee Rights and Responsibilities. In general, the results from Study 2 supported the hypothesized dominance of depth of knowledge over breadth of knowledge in the prediction of performance with respect to more routine, consistent safety tasks. Issues concerning the general-izability of these factors to other types of work and the human resource management implications of these results are discussed.     

Investigation of the factor structure of spirituality and religiosity in Iranian Shiite university students

One of the important challenges facing psychologists of religion pertains to the definition of religiosity and spirituality. One way of understanding the connection between these two concepts is to suppose that one of them is a subset of the other. Another useful and sensitive way, however, is to view spirituality and religiosity as overlapping constructs, sharing some characteristics but also retaining nonshared features. Empirical studies examining the factor structure of spirituality and religiosity are scant and almost all of them come from Western culture. These factor analytic studies generally confirm that religiosity and spirituality can best be described in terms of two distinct yet correlated factors. To date, no study has investigated the relationship between these two constructs in Islamic cultures. To redress this imbalance, confirmatory factor analysis was used to examine the factor structure of religiosity and spirituality in two Iranian Shiite samples using an extensive set of scales (including Santa Clara Strength of Religious Faith, Spiritual Involvement and Beliefs Scale - Revised, Spiritual Meaning Scale, and Spiritual Transcendence Scale). Two hypothetical models were tested: a model that viewed spirituality and religiosity as correlated but separate constructs and a model that combined the indicators of religiosity and spirituality into a single construct. In keeping with the results obtained in Western cultures, results of confirmatory factor analyses, conducted in Study 1 (N=225) and Study 2 (N=288), revealed that a two-factor model fitted the data better than a single-factor model. Implications of the results are discussed, as are study limitations and directions for further research.     

Confirmatory factor analysis of eating disorder symptoms in college women

Recent studies have found that the eating disorders can best be conceptualized as multidimensional. Four factors have consistently emerged from factor analytic studies of eating disorder symptoms: dietary restraint, bulimic behaviors, neurotic personality characteristics, and body image/body dysphoria. Confirmatory factor analysis was utilized to determine if this four-factor structure of eating disorder symptoms would be found in a sample of college women. Principal components analysis extracted four factors which were supported with a confirmatory factor analysis procedure. These four factors were negative affect and body dysphoria, bulimic behaviors, restrictive eating, and body image. The negative affect and body dysphoria factor was positively correlated with the other factors (i.e., bulimic behaviors, restrictive eating, and body image). This factor structure was similar to the factor structure found in samples of patients with bulimia and anorexia nervosa, except that the factors were more highly intercorrelated in the nonclinical sample. Results suggest that the measures of eating disorder symptoms used in this investigation are measuring the same multidimensional constructs in clinical and nonclinical subjects.This paper is partially based upon the master's thesis of the first author.     

Second-order confirmatory factor analysis of the WAIS-III. Wechsler Adult Intelligence Scale

According to Vernon's structure-of-intellect paradigm, abilities can be conceptualized as a hierarchy, with a factor of general intelligence at the top of the hierarchy, and successively more specific abilities toward the bottom. This paradigm has proven useful for interpreting a number of Wechsler intelligence scales. However, most of the research with this paradigm has used exploratory factor analysis, and the validity of the paradigm for the newest Wechsler Adult Intelligence Scale (WAIS-III) has yet to be evaluated. The present study examined the WAIS-III using second-order confirmatory factor analysis, which is a more appropriate analytic tool when specific hypotheses are tested. Using the standardization sample for the WAIS-III (N = 2,450), support was found for the hierarchical factor structure with a second-order factor of general intelligence and four first-order factors of Verbal Comprehension, Perceptual Organization, Working Memory, and Processing Speed.     

Reflections on reflections … on the nature of intuition,analysis and the construct validity of the Cognitive Style Index

Hayes, Allinson, Hudson, and Keasey (2003) maintain that the theoretical arguments and empirical evidence presented by Hodgkinson and Sadler‐Smith (2003) in support of an alternative two‐dimensional conception of the Allinson‐Hayes Cognitive Style Index (CSI) are insufficiently robust to challenge the original unidimensional formulation and that, accordingly, users of the CSI should continue to score the instrument as a single bipolar scale. In reply, we show that their reasoning is flawed, being based on a series of misinterpretations of the nature and purpose both of the item parcelling procedure and the exploratory factor analysis technique we employed. Furthermore, their defence fails to take account of the extensive confirmatory factor analytic evidence we presented in support of our conclusions.     

A Reexamination of the Structure of the Inward Outward Upward Prayer Scale

The dimensional structure of the Inward Outward Upward Prayer Scale was examined using exploratory factor analytic and confirmatory factor analytic (CFA) methods. A total of 703 adult Jewish pray-ers participated in the study. CFA indicated a satisfactory fit for the first-order eight-factor structure after excluding two cross-loaded items. The eight prayer subscales demonstrated acceptable levels of reliability, and the correlations between the subscales were similar to those reported in past research. CFA on second-order models indicated that a two-dimensional modality model (cognitive prayer/emotional prayer) had the best fit and was clearly superior to the directionality and intentionality models presented in past research. The implications of these findings for future research on the psychology of prayer are discussed.