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.     

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.     

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.     

Sex differences in the structure of intelligence: A confirmatory factor analysis

The LISREL model of Jöreskog and Sörbom was used to perform a comparative factor analysis on intelligence data from four sex by generation groups. The covariance matrices for 10 psychometric ability measures were used to isolate Spatial and Verbal Intelligence factors. Results from a series of factor analysis models indicated substantial invariance in the factor pattern and factor covariance matrices, although the hypothesis of complete invariance in factor pattern was rejected. The groups did differ in observed and unique variances. The results were basically consistent with the hypothesis that males and females have similar intellectual structure, which would have been obscured had standardized factor analysis been employed. There were also sex and generation differences in the Spatial and Verbal factor means.     

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.     

State vs trait anxiety: A case study in confirmatory factor analysis

The State-Trait Anxiety Inventory (STAI; Spielberger et al., 1970) originally divided anxiety into two factors: state anxiety, reflecting how an individual currently feels, and trait anxiety, reflecting how an individual generally feels. Recently, however, Spielberger revised his position to separate the presence and absence of anxiety symptoms within state and trait factors, yielding a hypothetical correlated 4-factor structure (Spielberger et al., 1980). Endler and Magnusson (1965) and Endler et al. (1976) have challenged the state vs trait distinction based upon their own factor analytical results. Since both sets of investigations used exploratory approaches, which do not postulate a particular factor structure, these studies do not provide an explicit test of the state vs trait distinction. A confirmatory factor analytic approach was used in the present study to evaluate Spielberger's 4-factor hypothesis. The subjects were large samples of male air force trainees and high school students for whom STAI data were available. The results of these confirmatory analyses indicated that the factors identified in exploratory analysis by Spielberger and his colleagues accounted for the data quite well.     

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.     

Loneliness and solitude in adolescence: A confirmatory factor analysis of alternative models

The present study tested a four-factor model of adolescent loneliness and solitude that comprises peer-related loneliness, family loneliness, negative attitude toward solitude, and positive attitude toward solitude. Nine different instruments for a total of 14 scales and derivative subscales were completed by a sample of mid-adolescents (N = 534) from Grades 10 through 12 (aged 15–18 years) in the Dutch-speaking part of Belgium. As expected, the four-factor solution provided a better fit to the data than did alternative models that comprised just a single factor, or two and three factors. Use of the Loneliness and Aloneness Scale for Children and Adolescents (LACA) is recommended, because the instrument measures all four aspects of the model. Implications for current theories on adolescent loneliness and associated phenomena, such as adolescents’ attitude toward being on their own, are briefly discussed.     

Loneliness and solitude in adolescence: A confirmatory factor analysis of alternative models

The present study tested a four-factor model of adolescent loneliness and solitude that comprises peer-related loneliness, family loneliness, negative attitude toward solitude, and positive attitude toward solitude. Nine different instruments for a total of 14 scales and derivative subscales were completed by a sample of mid-adolescents (N = 534) from Grades 10 through 12 (aged 15–18 years) in the Dutch-speaking part of Belgium. As expected, the four-factor solution provided a better fit to the data than did alternative models that comprised just a single factor, or two and three factors. Use of the Loneliness and Aloneness Scale for Children and Adolescents (LACA) is recommended, because the instrument measures all four aspects of the model. Implications for current theories on adolescent loneliness and associated phenomena, such as adolescents’ attitude toward being on their own, are briefly discussed.     

Factorial invariance in multilevel confirmatory factor analysis

This paper presents a procedure to test factorial invariance in multilevel confirmatory factor analysis. When the group membership is at level 2, multilevel factorial invariance can be tested by a simple extension of the standard procedure. However level‐1 group membership raises problems which cannot be appropriately handled by the standard procedure, because the dependency between members of different level‐1 groups is not appropriately taken into account. The procedure presented in this article provides a solution to this problem. This paper also shows Muthén's maximum likelihood (MUML) estimation for testing multilevel factorial invariance across level‐1 groups as a viable alternative to maximum likelihood estimation. Testing multilevel factorial invariance across level‐2 groups and testing multilevel factorial invariance across level‐1 groups are illustrated using empirical examples. SAS macro and Mplus syntax are provided.     

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.     

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.     

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.     

Adherence in childhood diabetes: results of a confirmatory factor analysis

In an earlier study (Johnson, Silverstein, Rosenbloom, Carter, & Cunningham, 1986), an exploratory factor analysis identified five components of adherence in childhood diabetes. In this investigation, a simultaneous confirmatory analysis was used to test the equality of this factor pattern across two independent samples. Factors 1 through 4--Exercise, Injection, Diet Type, and Eating/Testing Frequency-were confirmed. Factor 5--Diet Amount--proved to be too complex; the adherence measures comprising this factor (total calories and concentrated sweets consumed) are best treated as separate, single-indicator constructs. The results support a multivariate conceptualization of adherence, offer insight into the nature of the components underlying diabetes adherence, and provide measurement information for reliable component estimation.     

The four dimensions of sensation seeking: a confirmatory factor analysis

The factor structure of the Sensation Seeking Scale, Form V was obtained for a large Canadian sample consisting of 299 males and 439 females. Constrained maximum likelihood confirmatory factor analyses demonstrated that both male and female factors correspond to the four-dimensional model of sensation seeking postulated by Zuckerman (1979). These findings are in close agreement with previous reports of the factor structure and psychometric indices obtained with other cultural and national groups. However, the four factors accounted for only 21% of the variation for males and 20% for females. This finding is consistent with the modest KR-20 values obtained for the test subscales. Items displaying undesirable psychometric characteristics common to the present study and the extant literature are identified.     

Theoretical structure of adolescent alienation: a multigroup confirmatory factor analysis

This study examined the construct validity of adolescent alienation using second-order confirmatory factor analysis of the five dimensions conceptualized by Seeman (1959). Analysis was based on data from 275 high school students aged 14 to 18. The hypothesized multidimensionality of the construct was confirmed for both boys and girls using a second-order factor labeled alienation. Central dimensions of alienation as a latent construct were self-estrangement and powerlessness. Social isolation, meaninglessness, and especially normlessness were poorly explained by the second-order factor, suggesting that these dimensions entail enough specificity to be considered separately. A different theoretical model relating these dimensions is suggested and discussed.     

The structure of the Beck Hopelessness Scale: A confirmatory factor analysis in UK students

The aim of this paper was to confirm the factor structure of the 20-item Beck Hopelessness Scale in a non-clinical population. Previous research has highlighted a lack of clarity in its construct validity with regards to this population.Based on previous factor analytic findings from both clinical and non-clinical studies, 13 separate confirmatory factor models were specified and estimated using LISREL 8.72 to test the one, two and three-factor models.Psychology and medical students at Queen’s University, Belfast (n = 581) completed both the BHS and the Beck Depression Inventory (BDI).All models showed reasonable fit, but only one, a four-item single-factor model demonstrated a non-significant chi-squared statistic. These four items can be used to derive a Short-Form BHS (SBHS) in which increasing scores (0-4) corresponded with increasing scores in the BDI. The four items were also drawn from all three of Beck’s proposed triad, and included both positively and negatively scored items.This study in a UK undergraduate non-clinical population suggests that the BHS best measures a one-factor model of hopelessness. It appears that a shorter four-item scale can also measure this one-factor model.