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.     

Test anxiety and the validity of cognitive tests: A confirmatory factor analysis perspective and some empirical findings

The validity of cognitive ability tests is often interpreted solely as a function of the cognitive abilities that these tests are supposed to measure, but other factors may be at play. The effects of test anxiety on the criterion related validity (CRV) of tests was the topic of a recent study by Reeve, Heggestad, and Lievens (2009) (Reeve, C. L., Heggestad, E. D., & Lievens, F. (2009). Modeling the impact of test anxiety and test familiarity on the criterion-related validity of cognitive ability tests. Intelligence, 37, 34?41.). They proposed a model on the basis of classical test theory, and concluded on the basis of data simulations that test anxiety typically decreases the CRV. In this paper, we view the effects of test anxiety on cognitive ability test scores and its implications for validity coefficients from the perspective of confirmatory factor analysis. We argue that CRV will be increased above the effect of targeted constructs if test anxiety affects both predictor and criterion performance. This prediction is tested empirically by considering convergent validity of subtests in five experimental studies of the effect of stereotype threat on test performance. Results show that the effects of test anxiety on cognitive test performance may actually enhance the validity of tests.     

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.     

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.     

State and trait anxiety: A cross-cultural comparison of Chinese and Caucasian students in Canada

Chinese people immigrating to North America are subject to specific Stressors in moving to a new country, and, furthermore, these factors interact with their cultural background to produce higher levels of anxiety than are commonly believed to exist. The present study compared the responses of 60 Chinese and 60 Caucasian Canadian students to questionnaires measuring multidimensional trait and state anxiety. As predicted, the Chinese students endorsed significantly higher levels of trait anxiety for ambiguous situations and daily routines than did the Caucasians. Moreover, they were also significantly more likely than the Caucasians to rate the research situation as being ambiguous and threatening. Of all the possible background variables tested, English fluency was the single most powerful covariate that was predictive of the results, with those students who indicated a lowered English proficiency tending to score higher across all four facets of trait anxiety. As the Chinese students were also significantly more likely than the Caucasians to indicate a lower level of English fluency, the present results are supportive of the likelihood that lack of familiarity with the adopted culture and language may contribute to adjustment difficulties in Chinese immigrants.     

State and trait anxiety: A cross-cultural comparison of Chinese and Caucasian students in Canada

Chinese people immigrating to North America are subject to specific Stressors in moving to a new country, and, furthermore, these factors interact with their cultural background to produce higher levels of anxiety than are commonly believed to exist. The present study compared the responses of 60 Chinese and 60 Caucasian Canadian students to questionnaires measuring multidimensional trait and state anxiety. As predicted, the Chinese students endorsed significantly higher levels of trait anxiety for ambiguous situations and daily routines than did the Caucasians. Moreover, they were also significantly more likely than the Caucasians to rate the research situation as being ambiguous and threatening. Of all the possible background variables tested, English fluency was the single most powerful covariate that was predictive of the results, with those students who indicated a lowered English proficiency tending to score higher across all four facets of trait anxiety. As the Chinese students were also significantly more likely than the Caucasians to indicate a lower level of English fluency, the present results are supportive of the likelihood that lack of familiarity with the adopted culture and language may contribute to adjustment difficulties in Chinese immigrants. This paper is based in part on an M.A. thesis in psychology at York University by the first author under the supervision of the second author. This research was supported in part by a research grant from the Social Sciences and Humanities Research Council of Canada (SSHRC) to the second author (Grant No. 410-94-1473).     

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.     

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.     

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.     

Cross-sectional and longitudinal confirmatory factor models for the german test anxiety inventory: A construct validation

Construct validity of the German Test Anxiety Inventory (TAI-G) was tested in two respects. Firstly, the purported four-dimensional structure of the TAI-G (comprising subscales Emotionality, Worry, Interference, and Lack of Confidence) as well as relations of the test anxiety dimensions to self-efficacy were tested. Secondly, the trait conception of the TAI-G was tested within the framework of Latent State-Trait theory. The TAI-G was given to a student sample (N=302) on three occasions with a time interval of 2 weeks along with a study-specific self-efficacy scale on occasion 1. Dimensionality assumptions as well as relations with self-efficacy were tested using cross-sectional second-order confirmatory factor analysis. The trait conception was tested separately for TAI-G subscales by specifying longitudinal confirmatory factor models (Latent State-Trait models) and by calculating variance proportions of manifest variables (Latent State-Trait coefficients) referring to different sources of systematic variance (person, situation, and method) based on parameter estimates of the models. Results were supportive of both the purported four-dimensional structure and hypothesized relationships to self-efficacy (i.e., acceptable model fit) as well as of the trait conception of test anxiety (i.e., acceptable model fit and high proportion of variance due to person component). Implications for further validation studies were 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.     

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.     

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.     

Cognitive-affective stress propensity: A confirmatory factor analysis of stress propensity measures

A cognitive-affective stress propensity (CASP) construct is used to integrate previous findings regarding individual differences in experienced stress and resultant strain. A confirmatory factor analysis determined the structure of the CASP construct using a one factor model. This model and alternative models of factor structure contain two additional new constructs, psychological magnification and cognitive-affective connectivity. These two variables, and five trait variables previously identified as moderators in stress propensity research, were used in the analysis. Results show the one factor model to fit the data better than alternative models, thus supporting the notion of a latent construct (CASP).     

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.     

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.