Alternative factor models and factorial invariance of the GHQ-12: a large sample analysis using confirmatory factor analysis

This study tested alternative factor models of the General Health Questionnaire-12 (GHQ-12), based on previous research findings, with a large sample using confirmatory factor analysis. An alternative models framework was used to test 6 factor analytic models. A 3-factor model was the best explanation of the sample data. The 3 factors were labeled Anxiety-Depression, Social Dysfunction, and Loss of Confidence. The model was found to be factorially invariant between men and women. The utility of the 3 subscales, as opposed to the total GHQ-12 score, is questioned as they appear to provide little information beyond that of a general factor.     

Factorial invariance and significance

It is shown that invariance requirements remove the indeterminacy in factor determination and lead to an integration of factorial studies with promise of considerable reduction in computational labor. The selection of significant primary factors is discussed, with special reference to Thurstone's simple structure criterion.     

The state version of the recovery experience questionnaire: A multilevel confirmatory factor analysis

Although many studies in the field of recovery from work utilize a quantitative diary design, little is known about the validity of the daily measures used in such studies. The present study analyses the factor structure of the state version of the Recovery Experience Questionnaire (REQ) on the between-person (trait) and within-person (state) levels. A total of 127 employees participated in the study. Most of them filled out the questionnaire on three consecutive workdays (N = 375 observations). Results of multilevel confirmatory factor analyses (MCFA) showed that a four-factor model fit the data better than alternative models at both levels of analysis (between and within). In addition, some factor loadings of the four recovery experience dimensions (particularly for relaxation and control) were lower on the day level as compared to the general level. Nevertheless, we conclude that both state and trait versions of the REQ show good psychometric properties. Implications for future research on recovery are discussed.     

A confirmatory analysis of the factor structure and cross-age invariance of the Wechsler Adult Intelligence Scale-Third Edition

In the Wechsler Adult Intelligence Scale-Third Edition (WAIS-III; D. Wechsler, 1997), the manual reports several confirmatory factor analyses in support of the instrument's latent factor structure. In practice, examiners frequently compare an examinee's score from a current administration of the WAIS-III with the results from a previous test administration. Implicit in test-retest score comparisons is evidence that scores retain similar interpretive meaning across time. Establishing an instrument's factorial invariance provides the foundation for this practice. This study investigated the factorial invariance of the WAIS-III across the instrument's 13 age groups. The overall results from this study generally support both configural and factorial invariance of the WAIS-III when the 11 primary tests are administered.     

Measurement invariance,factor analysis and factorial invariance

Several concepts are introduced and defined: measurement invariance, structural bias, weak measurement invariance, strong factorial invariance, and strict factorial invariance. It is shown that factorial invariance has implications for (weak) measurement invariance. Definitions of fairness in employment/admissions testing and salary equity are provided and it is argued that strict factorial invariance is required for fairness/equity to exist. Implications for item and test bias are developed and it is argued that item or test bias probably depends on the existence of latent variables that are irrelevant to the primary goal of test constructers.Presidential address delivered at the Annual Meeting of the Psychometric Society in Berkeley, California, June 18–20, 1993.     

A bayesian approach to confirmatory factor analysis

Confirmatory factor analysis is considered from a Bayesian viewpoint, in which prior information on parameter is incorporated in the analysis. An iterative algorithm is developed to obtain the Bayes estimates. A numerical example based on longitudinal data is presented. A simulation study is designed to compare the Bayesian approach with the maximum likelihood method.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong.     

Analyzing multitrait-mulitmethod data with multilevel confirmatory factor analysis: An application to the validation of the State-Trait Cheerfulness Inventory

This article gives a didactic introduction to the analysis of multitrait-multimethod data with models of multilevel confirmatory factor analysis. In particular, the principles of the multilevel CT-C(M-1) model for interchangeable and structural different methods are explained in detail, and the first application of this model to more than two structurally different methods is presented. The model is illustrated by an application to the analysis of the convergent and discriminant validity of the trait subscales of the State-Trait Cheerfulness Inventory (STCI-T, Ruch, Köhler, & van Thriel, 1996). The results show that the STCI is a reliable and valid questionnaire for assessing the temperamental basis of sense of humor.     

Factorial invariance of the Rahim emotional quotient index

This study investigated the degree of factorial invariance of the 30-item Rahim Emotional Quotient Index (REQI) (Afzalur Rahim et al., 2002 Afzalur Rahim, M., Psenicka, C., Polychroniou, P., Zhao, J.-H., Yu, C.-S., Anita Chan, K., van Wyk, R. (2002). A model of emotional intelligence and conflict management strategies: A study in seven countries. The International Journal of Organizational Analysis, 10(4), 302–326. http://dx.doi.org/10.1108/eb028955[Crossref] , [Google Scholar]) across gender and language, using multiple group confirmatory factor analysis. Respondents were 341 full-time employed applicants to programmes in a South African Business School (females = 39.6%, African language group = 60.1%; non-African/Western language group = 39.9). With regard to age, the majority of the sample (25.5%) fell into the category 31–35 years. The Satorra-Bentler scaled chi-square difference tests showed no statistically significant differences between different gender and language groups, with regard to factor structure, factor loadings, variances and covariance. The findings support the original five-factor structure of the REQI for the two language groups, as well as the two gender groups.     

An illustration of multilevel factor analysis

The factor analysis of repeated measures psychiatric data presents interesting challenges for researchers in terms of identifying the latent structure of an assessment instrument. Specifically, repeated measures contain both within and between individual sources of variance. Although a number of techniques exist for separating out these 2 sources of variance, all are problematic. Recently, researchers have proposed that exploratory multilevel factor analysis (MFA) be used to appropriately analyze the latent structure of repeated measures data. The chief objective of this report is to provide a didactic step-by-step guide on how MFA may be applied to psychiatric data. In the discussion, we describe difficulties associated with MFA and consider challenges in factor analyzing life event appraisals in psychiatric samples.     

A note on invariance in three-mode factor analysis

Previous results of the application of Lawley's selection theorem to the common factor analysis model are extended to a revision of Tucker's three-mode principal components model. If the regression of the three-mode manifest variates on variates used to select subpopulations is both linear and homoscedastic, the two factor pattern matrices, the core matrix, and the residual variance-covariance matrix in the three-mode model can all be assumed to be invariant across subpopulations. The implication of this finding for simple structure is discussed.     

A confirmatory analysis of the factor stability hypothesis

The procedures recently developed by Jöreskog for studying similarities and differences in factor structures between different groups were applied to data from a study designed by Thurstone to investigate the sampling stability of a hypothesized isolated configuration. The hypothesis of an isolated configuration was rejected but not by much. The results represent a restricted and unique simple structure solution with the factor loadings and uniqueness values invariant over the two samples.     

Model‐related factor score predictors for confirmatory factor analysis

The present paper introduces model‐related (MR) factor score predictors, which reflect specific aspects of confirmatory factor models. The development is mainly based on Schönemann and Steiger's regression score components, but it can also be applied to the factor score coefficients. It is shown that the rotation of factor score predictors has no impact on the covariance matrix reproduced from the corresponding regression component patterns. Thus, regression score components or factor score coefficients can be rotated in order to obtain the required properties. This idea is the basis for MR factor score predictors, which are computed by means of a partial Procrustes rotation towards a target pattern representing the interesting properties of a confirmatory factor model. Two examples demonstrate the construction of MR factor score predictors reflecting specific constraints of a factor model.     

Measuring intention in language learning: a confirmatory factor analysis

Intention in language learning has not been studied effectively in research on second language (L2) learning. The goal is to fill this gap by designing and testing a measure of L2 learning intention. The scale was differentiated into two distinct but correlated components, goal intention and implementation intention, within the L2 context. The two intention scales were examined for reliability and validity using a series of standard psychometric procedures. A confirmatory factor model was then constructed and tested with a sample of 333 senior high school and college students. The results showed that a modified model had good psychometric characteristics and reasonable fit to the data.     

Factorial confirmatory models of Ryff's scales in a sample of elderly people

Several recent works have analysed the factorial structure of well-being measures. The aim of our study is to analyse the factorial structure of a widely used well-being scale, Ryff's Scales of Psychological Well-being, but in a specific subpopulation of the Spanish population, the elderly. For this particular subpopulation, the construct of well-being has been employed in most theoretical models that explain quality of life, and its role is therefore pivotal. The sample comprised 169 elderly people (65 years or more), sampled within the Valencian Community. The 54-item version of Ryff's scales was used. An item parcelling process was analytically employed before confirmatory factor analyses, allowing a total of 18 well-being indicators. Confirmatory factor analyses were specified and tested, including all theoretical and empirical solutions found in the literature, either in the general population or in specific populations of different cultural contexts. Goodness-of-fit results were similar to the ones found in the literature. Best solutions were a six-factor model with correlated factors, as defended by the authors, and a five-factor correlated solution, collapsing environmental mastery and self-acceptance into a single factor.     

A general approach to confirmatory maximum likelihood factor analysis

We describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method. The generality of the approach makes it possible to deal with all kinds of solutions: orthogonal, oblique and various mixtures of these. By choosing the fixed parameters appropriately, factors can be defined to have desired properties and make subsequent rotation unnecessary. The goodness of fit of the maximum likelihood solution under the hypothesis represented by the fixed parameters is tested by a large samplex ² test based on the likelihood ratio technique. A by-product of the procedure is an estimate of the variance-covariance matrix of the estimated parameters. From this, approximate confidence intervals for the parameters can be obtained. Several examples illustrating the usefulness of the procedure are given.This work was supported by a grant (NSF-GB 1985) from the National Science Foundation to Educational Testing Service.     

Bayesian factor analysis for multilevel binary observations

Multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs. We develop practical simulation based procedures for Bayesian inference of multilevel binary factor analysis models. We illustrate how Markov Chain Monte Carlo procedures such as Gibbs sampling and Metropolis-Hastings methods can be used to perform Bayesian inference, model checking and model comparison without the need for multidimensional numerical integration. We illustrate the proposed estimation methods using three simulation studies and an application involving student's achievement results in different areas of mathematics. The authors thank Ian Westbury, University of Illinois at Urbana Champaign for kindly providing the SIMS data for the application.     

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.     

A note on some equations of confirmatory factor analysis

The method of deriving the second derivatives of the goodness-of-fit functions of maximum likelihood and least-squares confirmatory factor analysis is discussed. The full set of second derivatives is reported.This research was supported by a PHS research grant No. M-10006 from the National Institutes of Mental Health, Public Health Service.     

Supervisors safety response: a multisample confirmatory factor analysis

Supervisors Safety Response (SSR) has been closely linked to workplace safety, and, as perceived by workers, it is considered to be one of the most influential issues with regard to employees compliance with safety behaviours. This study defines and tests a bifactorial and a monofactorial model of the SSR. Two facets of the SSR were measured: (a) supervisors response toward workers safe or unsafe behaviour and (b) supervisors safety attitudes and behaviours applied to their own work. In three samples of injured blue-collar workers ( N(1) = 110, N(2) = 123, N(3) = 104), multisample confirmatory factor analyses, using maximum likelihood estimation, were conducted to test both the bifactorial and the monofactorial model. Both models provide an overall good fit, but parsimony and the high correlation between factors in the bifactorial model support the monofactorial model. Attention is drawn to the measurement of the SSR as a diagnostic tool useful in selecting intervention goals, specifically integrating supervisors safety behaviour.