Latent Factor Means Research Articles

The assessment of school engagement: Examining dimensionality and measurement invariance by gender and race/ethnicity

The construct of school engagement has attracted growing interest as a way to ameliorate the decline in academic achievement and increase in dropout rates. The current study tested the fit of a second-order multidimensional factor model of school engagement, using large-scale representative data on 1103 students in middle school. In order to make valid model comparisons by group, we evaluated the extent to which the measurement structure of this model was invariant by gender and by race/ethnicity (European-American vs. African-American students). Finally, we examined differences in latent factor means by these same groups. From our confirmatory factor analyses, we concluded that school engagement was a multidimensional construct, with evidence to support the hypothesized second-order engagement factor structure with behavioral, emotional, and cognitive dimensions. In this sample, boys and girls did not substantially differ, nor did European-American and African-American students, in terms of the underlying constructs of engagement and the composition of these constructs. Finally, there were substantial differences in behavioral and emotional engagement by gender and by racial/ethnic groups in terms of second-order factor mean differences.

Social influences, school motivation and gender differences: an application of the expectancy‐value theory

The present study examined the structural relations of social influences, task values, ability beliefs, educational expectation and academic engagement for both boys and girls. The structural equation modelling analyses provided nationally representative evidence of gender differences in: (1) the links from teacher–student relationship and peer friends’ academic value to student task values; and (2) the relations of student values and educational expectation with student academic engagement. Despite the detected gender differences, similar findings across gender groups were also noted. In addition, results from the Multiple Indicator Multiple Cause analyses demonstrated the existence of latent factor mean non‐invariance between boys and girls on multiple school motivational factors and social influences.

Measurement non-invariance of DSM-IV narcissistic personality disorder criteria across age and sex in a population-based sample of Norwegian twins.

We investigated measurement non-invariance of DSM-IV narcissistic personality disorder (NPD) criteria across age and sex in a population-based cohort sample of 2794 Norwegian twins. Age had a statistically significant effect on the factor mean for NPD. Sex had a statistically significant effect on the factor mean and variance. Controlling for these factor level effects, item-level analysis indicated that the criteria were functioning differently across age and sex. After correcting for measurement differences at the item level, the latent factor mean effect for age was no longer statistically significant. The mean difference for sex remained statistically significant after correcting for item threshold effects. The results indicate that DSM-IV NPD criteria perform differently in males and females and across age. Differences in diagnostic rates across groups may not be valid without correcting for measurement non-invariance.

Measurement Invariance and Latent Mean Differences of the Beck Depression Inventory II Across Gender Groups

This study examined measurement invariance (i.e., configural invariance, metric invariance, scalar invariance) of the Chinese version of Beck Depression Inventory II (BDI-II-C) across college males and females and compared gender differences on depression at the latent factor mean level. Two samples composed of 402 male college students and 595 female college students were analyzed. Results found the evidences of partial scalar invariance of the BDI-II-C with five noninvariant items (i.e., Items 2, 3, 4, 7, and 10), providing empirical evidences of construct validity of the BDI-II-C for the purpose of making gender latent mean comparisons. Additionally, the findings revealed significant latent mean differences favoring females on the Negative Attitude factor but not on the Performance Difficulty and Somatic Element factors. These results were discussed in light of the benefits of using latent mean analyses associated with specific factors when comparing gender differences on depression.

Confirmatory Factor Analysis of the Coping Strategies Questionnaire-Revised in Samples of Oncology Outpatients and Inpatients With Pain

The aims of this study of oncology outpatients with cancer pain were to perform an exploratory factor analysis (EFA) of the 48-item Coping Strategy Questionnaire (CSQ) and a confirmatory factor analysis of the 6-factor solution of the Coping Strategy Questionnaire-Revised (CSQ-R) suggested by Riley and Robinson in 1997. In addition, differences in latent factor means and in the CSQ-R subscale scores between inpatients and outpatients were evaluated. Data from oncology outpatients (n=217) and inpatients (n=225) with pain were used. The Mplus program was used to perform both the EFA and confirmatory factor analysis treating the items as ordinal, and using robust maximum likelihood estimation. Quartimin oblique rotation was used for the EFA. Model fit was evaluated with the chi test, the comparative fit index, the root mean square error of approximation, and the standardized root mean square residual, as well as by substantive evaluation of the solutions. The EFA of the original 48-item CSQ did not reproduce the factor structure defined by Rosentiel and Keefe. The 6-factor structure from the 27-item CSQ-R fit both the inpatient and outpatient data well with strong factorial invariance, as well as the combined data, allowing some correlated errors among items. Differences were found between the 2 samples for the ignoring, catastrophizing, and praying latent factor means, and for the catastrophizing and praying subscale means. The 27-item CSQ-R is recommended for use as a clinical instrument. However, further research of the 6-factor structure is recommended to identify reasons for the correlated errors.

A Cross-Cultural Validation of Perceived Locus of Causality Scale in Physical Education Context

We examined the validity of the factor structure and invariance of the Perceived Locus of Causality (PLOC) scale instrument scores across two nations endorsing collectivist (Singapore) and individualist (Great Britain) cultural values. Results indicated that confirmatory factor analytic models of the PLOC exhibited adequate ft according to multiple criteria within each sample and across samples. There was invariance in the item-intercepts across the two cultures. In addition, the simplex-like pattern of relations among the PLOC constructs was confirmed within cultures and in invariance analyses. Finally, latent factor means analysis revealed that the British participants tended to rate less self-determined forms of motivation lower than and more self-determined forms of motivation higher than the Singaporean participants.

Longitudinal invariance analysis of the satisfaction with life scale

This research examined longitudinal measurement invariance in the satisfaction with life scale using two studies. The first followed a sample of 236 university students (93 male and 143 female) who completed the SWLS twice over a two-month interval. The second used a sample of 242 adolescent athletes (133 male and 109 female) who completed the SWLS three times over a period of six months. Confirmatory factor analysis was used to examine longitudinal measurement invariance. For the university student sample, results showed that the SWLS is partial strict invariant (equality of factor patterns, loadings and intercepts across time for all items and equality of item uniqueness for Items 1, 2, 4 and 5 across time). For the adolescent athlete student sample, the SWLS is partial strong invariant (equality of factor patterns, loadings across time for all items and equality of intercepts for Items 2, 3, and 4 across time). For both samples, stability coefficients across time were moderately high and latent factor means were not significantly different across time. Generally, these results suggest that the SWLS has satisfactory psychometric properties for longitudinal measurement invariance.

Measurement invariance: Review of practice and implications

A review of efforts to assess the invariance of measurement instruments across different respondent groups using confirmatory factor analysis (CFA) is provided for the years since the Vandenberg and Lance [Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3, 4–69.] review. Investigators are more frequently reporting tests of scalar invariance and tests for differences in latent factor means and partial invariance. Efforts have been made to assess, the impact of the choice of a referent indicator in multi-group studies, the appropriateness of forming partials as indicators of a latent construct, the degree of convergence of item response theory and CFA analyses of measurement differences across groups, and the implications of findings of invariance. In this context, a demonstration of the impact of partial invariance on estimated group differences in reliability and means is provided and discussed.

The Beck Depression Inventory-II: Testing for Measurement Equivalence and Factor Mean Differences Across Hong Kong and American Adolescents

Working within the framework of a confirmatory factor analytic (CFA) model, this study adds another dimension to construct validation of both the Beck Depression Inventory-II (BDI-II; Beck, Steer, & Brown, 1996) and a Chinese version of the BDI-II (C-BDI-II; Chinese Behavioral Sciences Society, 2000). Specifically, we tested for measurement equivalence of the C-BDI-II with the original BDI-II across Hong Kong (N = 1771) and American (N = 501) adolescents, respectively. Provided with evidence of measurement equivalence, we then tested for differences in the latent factor means (i.e., subscale levels) of three first-order factors of negative attitude, performance difficulty, and somatic elements and one second-order factor of general depression. All procedures were based on analyses of mean and covariance structures (MACS) that took into account both the incompleteness and non-normality of the data. Findings revealed sound evidence of measurement equivalence of the C-BDI-II and BDI-II factorial structures, and latent factor means that pointed to higher levels of depressive symptoms for Hong Kong adolescents than for their American counterparts.

Factorial Invariance of the 13-item Sense of Coherence Scale across Gender

This study examined the gender invariance of the 13-item Sense of Coherence (SOC) scale. Confirmatory factor analyses indicated that a single factor model with one pair of correlated errors fit the data well. Invariance testing indicated that the scale is both congeneric and tau equivalent, meaning that a single latent SOC construct holds equally well for males and females, and that both genders demonstrate an equivalent pattern of factor loadings. There was little evidence in support of latent factor mean equivalence across gender. Explanations for the lack of factor mean equivalence were discussed and recommendations for future research were suggested.

Evidence for the Factorial Validity of the Dispositional Hope Scale

Confirmatory factor analyses were employed to test the factorial validity and structure of the Dispositional Hope Scale (DHS; Snyder et al., 1991 ). In a large multiethnic sample (n = 1031), a two-factor representation of the DHS fit the data significantly better than a one-factor model. These findings suggest that the DHS is better conceptualized as being composed of Agency and Pathways components and not as a unidimensional representation of general hope. Multigroup analyses revealed that the factor pattern coefficients were invariant across gender and ethnic groups, respectively, thus establishing metric invariance of the DHS. However, item intercepts, item uniqueness terms, the factor variance for the Agency factor, and both the Agency and Pathways latent factor means statistically differed as a function of gender (but not ethnicity). These findings suggest that while the two-factor structure of the DHS is relatively stable and robust, both measurement and substantive differences as a function of gender must be accounted for.

Teacher's Corner: Testing Measurement Invariance of Second-Order Factor Models

We illustrate testing measurement invariance in a second-order factor model using a quality of life dataset (n = 924). Measurement invariance was tested across 2 groups at a set of hierarchically structured levels: (a) configural invariance, (b) first-order factor loadings, (c) second-order factor loadings, (d) intercepts of measured variables, (e) intercepts of first-order factors, (f) disturbances of first-order factors, and (g) residual variances of observed variables. Given that measurement invariance at the factor loading and intercept levels was achieved, the latent factor mean difference on the higher order factor between the groups was also estimated. The analyses were performed on the mean and covariance structures within the framework of the confirmatory factor analysis using the LISREL 8.51 program. Implications of second-order factor models and measurement invariance in psychological research were discussed.

Testing the Dimensionality of Place Attachment in Recreational Settings

The purpose of this investigation was to examine the psychometric properties of a place-attachment scale using data collected from visitors to the Appalachian Trail in the United States. These data supported a correlated three-factor model consisting of place identity, place dependence, and social bonding. Multigroup confirmatory factor analysis was used to cross-validate the model using two sub-samples of the data. Latent factor means were also compared. Although these analyses provided mixed evidence indicating the scale to be a valid and reliable measure of place attachment, there remains some concern about the performance of several indicators (i.e., low factor loadings, low reliability). Latent mean differences were also observed between the two groups on the place identity dimension. The analyses presented in this investigation provide an example of the utility of covariance structure analysis for testing the psychometric properties of scales and for comparing latent mean differences among groups within populations.

Universal Nonverbal Intelligence Test Factor Invariance Across Deaf and Standardization Samples

The Universal Nonverbal Intelligence Test (UNIT) is an individually administered, nonverbal intelligence test designed for use with non-English-speaking, limited English proficient, or deaf children. The aim of this study was to assess the factor structure invariance of the UNIT across deaf and standardization samples through the use of multisample confirmatory factor an alysis. Two theoretical models were evaluated: a primary two-factor (Memory and Reasoning) model and a secondary two-factor (Symbolic and Nonsymbolic) model. The general forms of both models were invariant across groups, thus supporting both theoretical models. For the primary model, partial measurement invariance was found. A follow-up analysis found that the analogic reasoning measurement intercept was not invariant, indicating that the expected subtest scores for deaf examinees were lower than those for examinees in the standardization sample. In addition, the standardization sample had a higher Memory latent factor mean than the deaf sample did. The secondary model was not invariant, with three pattern coefficients differing across groups.

Are intelligence and personality changeable? Generality of Chinese students' beliefs across various personal attributes and age groups

Students' subjective beliefs on whether intelligence and other personal attributes (personality, creativity, emotional intelligence, morality) can be changed will affect their learning and motivational behavior. In two related studies, we examined the generality of such beliefs across different personal attributes and age groups. The first study investigated whether students who believed intelligence was inborn also believed that personality and other personal attributes were inherited and were difficult to change. The comparison of the factorial structures using confirmatory factor analyses of Chinese senior high school students' ( N=574) responses to a self-constructed questionnaire suggested a high degree of generality among beliefs of various personal attributes. The second study examined the differences in these beliefs between elementary and high school students (total N=1650). A comparison of the latent factor means showed that elementary and high school students' beliefs on the changeability of different personal attributes were very similar. Older students, in comparison to younger ones, had only a slight tendency of believing more that personality, intelligence and creativity could not be changed. The results are discussed in terms of cognitive maturity and socialization processes.

Self-Report Methods of Assessing Health Status and Health Service Utilization: A Hierarchical Confirmatory Analysis.

Self reports are often used to determine health status and extent of health service utilization. These assessments are frequently used as indicators of health quality. Using a sample of 739 young adults, this study examines gender differences and the factor structure of 15 self-reported measures of health and health seeking behavior. Women consistently reported more physical problems, less physical hardiness, more physical symptoms, and more utilization of medical services than men. These mean differences were apparent both on the individual variables and on the latent-factor means. However, the factor structure of the 15 variables was found to vary only slightly between men and women. Four primary-order factors were confirmed using latent-variable models. These factors included Physical Hardiness, Subjective Health Problems, Physical Symptomatology, and Health Service Utilization. The three health status factors were highly intercorrelated and were found to be generated by a second-order factor of Poor Physical Health. This general factor was correlated moderately with the Health Service Utilization construct, suggesting that seeking medical services is not an excellent indicator of health status: It probably grossly underestimates the extent of illness in a given population and measures attitudes toward help seeking and availability of medical services.