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.     

Preliminary analysis of the psychometric properties of Ryff's scales of psychological well-being in Portuguese adolescents

This article presents a set of research studies that aim to adapt Carol Ryff's scales of psychological wellbeing (SPWB) and to analyze its psychometric properties in adolescents. The first two studies focused on the reliability and factorial validity of different Portuguese short versions of SPWB, revealing measurement models inadequacies and low internal consistency. In the third study we developed a shortened version (30 items), taking into account the application of psychometric criteria suggested by van Dierendonck (2005). The scales of this version revealed better reliability and adequate goodness of fit indices for the six-factor model, as proposed by Carol Ryff's PWB theory. Although further research focused on the psychometrical properties reanalysis of this shortened version of SPWB is needed, this article provides a contribution to the research and intervention on positive mental health during adolescence.     

Finite mixtures in confirmatory factor-analysis models

In this paper, various types of finite mixtures of confirmatory factor-analysis models are proposed for handling data heterogeneity. Under the proposed mixture approach, observations are assumed to be drawn from mixtures of distinct confirmatory factor-analysis models. But each observation does not need to be identified to a particular model prior to model fitting. Several classes of mixture models are proposed. These models differ by their unique representations of data heterogeneity. Three different sampling schemes for these mixture models are distinguished. A mixed type of the these three sampling schemes is considered throughout this article. The proposed mixture approach reduces to regular multiple-group confirmatory factor-analysis under a restrictive sampling scheme, in which the structural equation model for each observation is assumed to be known. By assuming a mixture of multivariate normals for the data, maximum likelihood estimation using the EM (Expectation-Maximization) algorithm and the AS (Approximate-Scoring) method are developed, respectively. Some mixture models were fitted to a real data set for illustrating the application of the theory. Although the EM algorithm and the AS method gave similar sets of parameter estimates, the AS method was found computationally more efficient than the EM algorithm. Some comments on applying the mixture approach to structural equation modeling are made.Note: This paper is one of the Psychometric Society's 1995 Dissertation Award papers.—EditorThis article is based on the dissertation of the author. The author would like to thank Peter Bentler, who was the dissertation chair, for guidance and encouragement of this work. Eric Holman, Robert Jennrich, Bengt Muthén, and Thomas Wickens, who served as the committee members for the dissertation, had been very supportive and helpful. Michael Browne is appreciated for discussing some important points about the use of the approximate information in the dissertation. Thanks also go to an anonymous associate editor, whose comments were very useful for the revision of an earlier version of this article.     

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 structure of short scales measuring manic-depression in Kuwaiti undergraduates

A sample of 202 Kuwaiti college students (63 men and 139 women; Mage=21.6 yr., SD=2.4) responded to the Thalbourne, et al.'s Manic-Depressiveness Scale. In a factor analysis with a varimax rotation, 14 of 18 items had significant loadings (>.3) on the first factor, including 8 items of the original depression scale. 6 items significantly loaded on the second factor, including 3 items of the original mania scale. This did not match the hypothetical structure of the scale.     

Factorial validity of the Job Expectations Questionnaire in a sample of Mexican workers

The aim of this study was to examine the factorial validity of the Job Expectations Questionnaire (Cuestionario de Expectativas Laborales CEL) in a sample of Mexican workers. Following a cross validation approach, two samples were used in the study. The first sample consisted of 380 professionals who mainly performed administrative work in the Health Services in Puebla-Mexico. The second sample comprised 400 health professionals from the Hospital de la Mujer in Puebla-Mexico. Exploratory factor analysis yielded a three-factor solution, accounting for 51.8% of the variance. The results of confirmatory factorial analysis indicate that the three-factor model provided the best fit with the data (CFI = .96, GFI = .95, NNFI = .95, RMSEA = .04), maintaining the structure with 12 items. The reliability of the questionnaire and the diverse subscales showed high internal consistency. Significant correlations were found between job expectations and autonomy, vigor, dedication, and absorption, providing evidence of its construct validity. The evaluation of the psychometric qualities confirms this questionnaire as a valid and specific instrument to measure job expectations.     

A confirmatory factor analysis of the WISC-III in a clinical sample with cross-validation in the standardization sample.

Maximum likelihood confirmatory factor analysis was applied to the Wechsler Intelligence Scale for Children-Third Edition (WISC-III; Wechsler, 1991) data of a mixed clinical sample of 318 children. Analyses were designed to determine which of nine hypothesized oblique factor solutions could best explain intelligence as measured by the WISC-III in the clinical sample. Competing latent variable models were identified in previous studies, and results in the clinical sample were cross-validated by testing all models in the WISC-III standardization sample (n = 2200). Findings in both the clinical and standardization samples supported a five-factor model including Verbal Comprehension, Constructional Praxis, Visual Reasoning, Freedom from Distractibility, and Processing Speed factors. The Visual Reasoning factor was defined primarily by Picture Arrangement, whereas Mazes did not appear to improve model fit. Potential opportunities and pitfalls with regard to the interpretation of the proposed Visual Reasoning factor are discussed.     

Psychological needs associated with MMPI-2 scales in a nonclinical sample

The psychological needs derived from the Adjective Check List (ACL; Gough & Heilbrun, 1983b) that are associated with MMPI-2 scales were studied among 198 nonclinical participants. Both the Depression (D) and Psychasthenia (Pt) scales were negatively correlated with needs for achievement and dominance and positively correlated with needs for abasement and succorance (dependence). The Schizophrenia (Sc) scale was negatively associated with need for affiliation and positively associated with need for abasement. The Social Introversion (Si) scale was associated negatively with needs for achievement, dominance, affiliation, heterosexuality, exhibition, and autonomy and associated positively with needs for succorance, abasement, and deference, reflecting good construct validity for Scale Si. MMPI-2 Masculinity-Femininity (Mf) did not correlate with the ACL Masculinity and Femininity scales, suggesting poor concurrent validity for Mf.     

Assessing alternative models of individualism and collectivism: a confirmatory factor analysis

Six alternative structural models of individualism–collectivism are reviewed and empirically compared in a confirmatory factor analysis of questionnaire data from an Australian student sample (N = 340). Central to the debate about the structure of this broad social attitude are the issues of (1) polarity (are individualism and collectivism bipolar opposites, or orthogonal factors?) and (2) dimensionality (are individualism and collectivism themselves higher‐order constructs subsuming several more specific factors and, if so, what are they?). The data from this Australian sample support a model that represents individualism and collectivism as a higher‐order bipolar factor hierarchically subsuming several bipolar reference‐group‐specific individualisms and collectivisms. Copyright © 2001 John Wiley & Sons, Ltd.     

Exploratory and confirmatory factor analytic investigations of the Illness Attitudes Scale in a nonclinical sample.

The Illness Attitudes Scale (IAS) assesses fears, beliefs and attitudes associated with hypochondriasis [Kellner, R. (1986). Somatization and hypochondriasis. New York: Praeger Publishers.]. Recent factor analytic investigations of the IAS in non-clinical samples have suggested a number of different factor solutions. In study 1, we used principal components analysis with both orthogonal and oblique rotation to better explore the structure of this measure. Using a random selection of 390 participants from a larger pool of 780, a five-factor solution was identified: (1) fear of illness, death, disease and pain, (2) effects of symptoms, (3) treatment experiences, (4) disease conviction and (5) health habits. In study 2, confirmatory factor analysis (CFA) of responses from the remaining 390 students evaluated: (a) a single-factor model, (b) Kellner's original nine-factor model, (c) a four-factor model proposed by Ferguson and Daniel [Ferguson, E. & Daniel, E. (1995). The Illness Attitudes Scale (IAS): a psychometric evaluation on a nonclinical population. Personality and Individual Differences, 18, 463-469.], (d) a different four-factor model proposed by Stewart and Watt [Stewart, S. H. & Watt, M. C. (1998). A psychometric investigation of the Illness Attitudes Scale (IAS) in a nonclinical young adult sample. Submitted for publication.] and (e) the five-factor model derived in study 1. Of these models, greatest support was obtained for our five-factor model. However, it was also clear that this model could be improved. Based on the results of the CFA, as well as previous research and theoretical considerations, we tested a revised model in which the health habits factor was deleted. Analysis of the revised model showed that it received the greatest support and could be conceptualized as either four distinct factors or as hierarchical in nature, with four lower-order factors loading on a single higher-order factor. Future directions for research as well as suggestions for scoring and using the IAS with nonclinical samples are discussed.     

Factor analysis of MCMI-II and PACL basic personality scales in a college sample

This study examined factor dimensions common to the eight basic personality scales of the Millon Clinical Multiaxial Inventory-II (MCMI-II; Millon, 1987) and Personality Adjective Check List (PACL; Strack, 1987, 1990). Subjects were 140 college students (65 men and 75 women). MCMI-II weighted raw scores (WRS) and WRS corrected for number of items endorsed true by regression were employed for analysis along with PACL T-scores. Principal components analyses with varimax and direct oblimin rotations were carried out separately on the two sets of MCMI-II and PACL scores. MCMI-II and PACL scales measuring the same personalities were usually correlated most highly with each other, although some divergences were noted. WRS yielded three bipolar dimensions and a fourth unipolar method factor that loaded only the five MCMI-II scales that were strongly correlated with number of items endorsed true. Residual scores yielded a more meaningful set of three bipolar dimensions labeled Social Introversion-Extraversion, Emotionality-Restraint, and Social Dominance-Submissiveness, without the method factor, that were very similar to personality dimensions found separately in the two tests. More research is needed to clarify the response bias issue in the MCMI-II and to further explicate similarities and differences between the MCMI-II and the PACL.     

Factorial structure of the Kuwait University Anxiety Scale in a large sample of college students: rejoinder

Recently a study by Lester of American college students found a different factor structure for the Kuwait University Anxiety Scale than studies with students from Arab countries. Thus, a large sample of college students (N=3064) was recruited from 10 Arab countries to examine the replicability of the factors previously extracted from the Kuwait University Anxiety Scale. Three factors, identified in the present sample, were compatible with those in the prior larger sample (N=9031). These were labeled Cognitive/Affective Anxiety, Subjective Anxiety or Nervousness, and Somatic Anxiety. The factorial pattern of the scale has been verified by both large samples.     

The Male Body Attitudes Scale: A confirmatory factor analysis with a sample of gay men

The Male Body Attitudes Scale (MBAS; Tylka, Bergeron, & Schwartz, 2005) is a recently created instrument which assesses males’ attitudes regarding their muscularity, body fat, and height. Although the MBAS was created via exploratory and confirmatory factor analyses, its factor structure has yet to be replicated with more diverse samples. The aim of the current study was to conduct a confirmatory factor analysis of the MBAS with a sample of gay men. Results from an online sample of 207 self-identified gay men revealed that the original three-factor structure of the MBAS, as well as a two-factor structure, consisting of muscularity and body fat, displayed strong factorial validity. These findings suggest that either a two- or three-factor structure may be used when assessing body image concerns in gay men.     

Factorial dimensions of the Revised Behavior Problem Checklist: Replication and validation within a kindergarten sample

The factor structure of the Revised Behavior Problem Checklist (RBPC) was examined in a large sample of suburban kindergarten children. Teacher-rated dimensions of Conduct Disorder, Attention Problems-Immaturity, Anxiety-Withdrawal, and Psychotic Behavior were closely replicated, and a new factor labeled Unmotivated-Isolated was also revealed. These principal components were consistent across gender and across subsamples of children differing as to risk status for learning failure. Evidence was found for the divergent validity of the externalizing dimensions of Conduct Disorder and Attention Problems-Immaturity with respect to criterion measures of alternative behavior ratings, cognitive functioning, and academic achievement. Parent-rated components of Conduct Disorder, Attention Problems-Immaturity, Hyperactive-Impatient, Tense-Withdrawn, Anxiety, and Passive-Conforming were less clearly validated, and parent-teacher agreement was modest. It was concluded that the RBPC shows promise for the assessment of preschool-aged children and that narrow-band externalizing dimensions of inattentive versus conduct-disordered behavior are reasonably distinct at this age.We would like to express our deep appreciation to Winifred Setrakian, Judy Alien, and Elizabeth Stone of The CHILD Center for their invaluable administrative support.     

A multitrait-multisource confirmatory factor analytic approach to the construct validity of ADHD rating scales

Confirmatory factor analysis was used to model a multitrait-multisource design to evaluate the construct validity of attention-deficit/hyperactivity disorder (ADHD) rating scales. The 2 trait factors were the ADHD inattention and hyperactivity/impulsivity dimensions. The 2 source factors were parents and teachers. In Study 1, parents and teachers rated 1,475 Australian elementary school children on the ADHD symptoms. In Study 2, parents and teachers rated 285 Brazilian elementary school children on the ADHD symptoms. Similar results occurred in both studies with most of the ADHD symptoms containing more source than trait variance, thus providing weak evidence for the convergent and discriminant validity of the symptoms as measured by rating scales. The study outlines the implications of such strong source effects for understanding ADHD.     

Inventory of Interpersonal Problems Personality Disorder scales: operating characteristics and confirmatory factor analysis in nonclinical samples

Research involving clinical samples has demonstrated the utility of a 28-item personality disorder (PD) screening measure (Inventory of Interpersonal Problems--Personality Disorder scale [IIP-PD]) culled from the IIP in the prediction of the presence or absence of a PD (Pilkonis, Kim, Proietti, & Barkham, 1996). This article extends these diagnostic efficiency findings to nonclinical samples and presents additional data regarding the factor structure of the 28 IIP-PD items. Diagnostic efficiency statistics for the IIP-PD scale, calculated using both interview and self-report methods, support the utility of the IIP-PD scale as a screening tool for the presence or absence of a PD. High specificity estimates indicate that individuals who do not exceed Diagnostic and Statistical Manual of Mental Disorders (4th ed.; American Psychiatric Association, 1994) symptom thresholds rarely exceed the IIP-PD cutoff. Furthermore, a high negative predictive power (NPP) estimate derived using an interview-based diagnostic standard suggests that the IIP-PD scale accurately screens out individuals who do not have a PD. Finally, cross-validated confirmatory factor-analytic results involving items composing the 5 IIP PD subscales identified in previous research (Kim, Pilkonis, & Barkham, 1997) suggest that a measurement model with a single second-order factor (general PD) and 5 first-order factors (one representing each PD subscale) provided the best fit to the observed data compared to 2 other competing models.     

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.     

Content analysis scales measuring psychosocial maturity in the elderly

Content analysis scales measuring the constructs used to deal with the tasks of Erikson's eight stages of psychosocial development have been devised. The scoring categories for these 16 Content Analysis Scales of Psychosocial Maturity (CASPM) are summarized. Percentile norms are provided. Evidence for the reliability and validity of the scales is examined. The CASPM percentile profiles of two elderly people are considered, as are the practical advantages of employing the scales with elderly clients.