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 cautionary note on the use of probability values to evaluate interobserver agreement

Proposed methods of assessing the statistical significance of interobserver agreements provide erroneous probability values when conducted on serially correlated data. Investigators who wish to evaluate interobserver agreements by means of statistical significance can do so by limiting the analysis to every k(th) interval of data, or by using Markovian techniques which accommodate serial correlations.     

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.     

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.     

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.     

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.     

Measuring Latinos' perceptions of depression: a confirmatory factor analysis of the Illness Perception Questionnaire

This study examined the psychometric properties of the Revised Illness Perception Questionnaire adapted for a clinical sample of low-income Latinos suffering from depression. Participants (N = 339) were recruited from public primary care centers. Their average age was 49.73 years and the majority was foreign born females of either Mexican or Central American descent. Confirmatory factor analysis was used to test the factor structure of this measure. Construct and discriminant validity and internal consistency were evaluated. After the elimination of three items because of low factor loadings (< .40) and the specification of seven error covariances, a revised model composed of 24 items had adequate goodness-of-fit indices and factor loadings, supporting construct validity. Each of the subscales reported satisfactory internal consistency. Intercorrelations between the 5 illness perception factors provided initial support for the discriminant validity of these factors in the context of depression. The establishment of the psychometric properties of this adapted measure will pave the way for future studies examining the role illness perceptions play in the help seeking and management of depression among Latinos.     

A note on factor analysis by the method of principal axes

The resolution of a set of variables into principal components may be performed upon variables having arbitrary variances, or upon variables obtained from these by reduction of all variances to unity. The two procedures do not yield the same results even if the principal components are reduced to unit variance in both cases, except when the original variances are all equal.This article was written while the author was on a W.P.A. project at Teacher's College, Columbia University.     

The effect of sampling error on convergence,improper solutions,and goodness-of-fit indices for maximum likelihood confirmatory factor analysis

A Monte Carlo study assessed the effect of sampling error and model characteristics on the occurrence of nonconvergent solutions, improper solutions and the distribution of goodness-of-fit indices in maximum likelihood confirmatory factor analysis. Nonconvergent and improper solutions occurred more frequently for smaller sample sizes and for models with fewer indicators of each factor. Effects of practical significance due to sample size, the number of indicators per factor and the number of factors were found for GFI, AGFI, and RMR, whereas no practical effects were found for the probability values associated with the chi-square likelihood ratio test.James Anderson is now at the J. L. Kellogg Graduate School of Management, Northwestern University. The authors gratefully acknowledge the comments and suggestions of Kenneth Land and the reviewers, and the assistance of A. Narayanan with the analysis. Support for this research was provided by the Graduate School of Business and the University Research Institute of the University of Texas at Austin.     

Measurement equivalence: a comparison of methods based on confirmatory factor analysis and item response theory

Current interest in the assessment of measurement equivalence emphasizes 2 major methods of analysis. The authors offer a comparison of a linear method (confirmatory factor analysis) and a nonlinear method (differential item and test functioning using item response theory) with an emphasis on their methodological similarities and differences. The 2 approaches test for the equality of true scores (or expected raw scores) across 2 populations when the latent (or factor) score is held constant. Both approaches can provide information about when measurement nonequivalence exists and the extent to which it is a problem. An empirical example is used to illustrate the 2 approaches.     

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.     

Exploratory and confirmatory factor analysis of a short-form of the EMBU among Chinese adolescents

The present study used a sample of Chinese adolescents and validated a short-form of the Egna Minnen Betr?ffande Uppfostran: One's Memories of Upbringing (s-EMBU) assessing perceived parental rearing styles. A Chinese revision of the s-EMBU by the authors was administered to a total of 779 high school students, ages 11 to 19 years. Exploratory factor analysis with half of the sample yielded a three-factor solution of Rejection, Emotional Warmth, and Overprotection, accounting for 47.1% of the total variance onthe father form and 48.8% of the total variance on the mother form. Then, confirmatory factor analysis indicated a good fit of the three-factor model to the data in the other half of the sample. The three subscales consisted of 6, 6, and 7 items, respectively. Scores on these subscales had Cronbach alphas ranging from .71 to .81, indicating adequate internal consistency. These psychometric properties suggest its applicability for research with Chinese adolescents.     

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.     

Measuring motivations for intercollegiate athlete alcohol use: a confirmatory factor analysis of the drinking motives measure

This study examined the psychometric properties of the Drinking Motives Measure (DMM) on a sample of 227 collegiate athletes. Confirmatory factor analyses indicated that the 4-factor structure of the DMM provided a better fit than either 2- or 1-factor models, but the overall fit of the 4-factor model was moderate at best. A revised 3-factor model consistent with prior research (M. L. Cooper, M. Russell, J. B. Skinner, & M. Windle, 1992) provided the best fit. Hierarchical multiple regression analyses indicated that the 3 DMM factors included in the revised model accounted for 17%-21% of the unique variance on alcohol consumption variables. Results provide preliminary evidence supporting the internal consistency, construct validity, and convergent validity of the revised 3-factor DMM with collegiate athletes.     

Coping patterns of African American adolescents: a confirmatory factor analysis and cluster analysis of the Children's Coping Strategies Checklist

The current study examined patterns of coping strategies in a sample of 497 low-income urban African American adolescents (mean age = 12.61 years). Results of confirmatory factor analysis indicated that the 4-factor structure of the Children's Coping Strategies Checklist (T. S. Ayers, I. N. Sandler, S. G. West, & M. W. Roosa, 1996) was not replicated in the current sample. The final model was a 3-factor model that was invariant across gender. The Active Coping factor and Revised Avoidant Coping factor were highly correlated in the present sample. Results of cluster analyses identified 2 coping groups differing on the frequency of coping use and preferred coping methods. The 1st group was more likely to use avoidant coping and less likely to use social support-seeking coping than the 2nd group, which showed more consistent use across coping strategies. There were no significant differences in the association between stressors and symptoms across the 2 groups. The results highlight the importance of examining factor structures of coping measures with underrepresented groups.     

Cross-cultural confirmatory factor analysis of the CES-D in Spanish and Mexican dementia caregivers

The Center for Epidemiologic Studies-Depression Scale (CES-D) is the most frequently used scale for measuring depressive symptomatology in caregiving research. The aim of this study is to test its construct structure and measurement equivalence between caregivers from two Spanish-speaking countries. Face-to-face interviews were carried out with 595 female dementia caregivers from Madrid, Spain, and from Coahuila, Mexico. The structure of the CES-D was analyzed using exploratory and confirmatory factor analysis (EFA and CFA, respectively). Measurement invariance across samples was analyzed comparing a baseline model with a more restrictive model. Significant differences between means were found for 7 items. The results of the EFA clearly supported a four-factor solution. The CFA for the whole sample with the four factors revealed high and statistically significant loading coefficients for all items (except item number 4). When equality constraints were imposed to test for the invariance between countries, the change in chi-square was significant, indicating that complete invariance could not be assumed. Significant between-countries differences were found for three of the four latent factor mean scores. Although the results provide general support for the original four-factor structure, caution should be exercised on reporting comparisons of depression scores between Spanish-speaking countries.