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1.
We present a test for cluster bias, which can be used to detect violations of measurement invariance across clusters in 2-level data. We show how measurement invariance assumptions across clusters imply measurement invariance across levels in a 2-level factor model. Cluster bias is investigated by testing whether the within-level factor loadings are equal to the between-level factor loadings, and whether the between-level residual variances are zero. The test is illustrated with an example from school research. In a simulation study, we show that the cluster bias test has sufficient power, and the proportions of false positives are close to the chosen levels of significance.  相似文献   

2.
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.  相似文献   

3.
As a prerequisite for meaningful comparison of latent variables across multiple populations, measurement invariance or specifically factorial invariance has often been evaluated in social science research. Alongside with the changes in the model chi-square values, the comparative fit index (CFI; Bentler, 1990) is a widely used fit index for evaluating different stages of factorial invariance, including metric invariance (equal factor loadings), scalar invariance (equal intercepts), and strict invariance (equal unique factor variances). Although previous literature generally showed that the CFI performed well for single-group structural equation modeling analyses, its applicability to multiple group analyses such as factorial invariance studies has not been examined. In this study we argue that the commonly used default baseline model for the CFI might not be suitable for factorial invariance studies because (a) it is not nested within the scalar invariance model, and thus (b) the resulting CFI values might not be sensitive to the group differences in the measurement model. We therefore proposed a modified version of the CFI with an alternative (and less restrictive) baseline model that allows observed variables to be correlated. Monte Carlo simulation studies were conducted to evaluate the utility of this modified CFI across various conditions including varying degree of noninvariance and different factorial invariance models. Results showed that the modified CFI outperformed both the conventional CFI and the ΔCFI (Cheung & Rensvold, 2002) in terms of sensitivity to small and medium noninvariance.  相似文献   

4.
Two Monte Carlo studies were conducted to examine the sensitivity of goodness of fit indexes to lack of measurement invariance at 3 commonly tested levels: factor loadings, intercepts, and residual variances. Standardized root mean square residual (SRMR) appears to be more sensitive to lack of invariance in factor loadings than in intercepts or residual variances. Comparative fit index (CFI) and root mean square error of approximation (RMSEA) appear to be equally sensitive to all 3 types of lack of invariance. The most intriguing finding is that changes in fit statistics are affected by the interaction between the pattern of invariance and the proportion of invariant items: when the pattern of lack of invariance is uniform, the relation is nonmonotonic, whereas when the pattern of lack of invariance is mixed, the relation is monotonic. Unequal sample sizes affect changes across all 3 levels of invariance: Changes are bigger when sample sizes are equal rather than when they are unequal. Cutoff points for testing invariance at different levels are recommended.  相似文献   

5.
Exploratory structural equation modeling (ESEM) is an approach for analysis of latent variables using exploratory factor analysis to evaluate the measurement model. This study compared ESEM with two dominant approaches for multiple regression with latent variables, structural equation modeling (SEM) and manifest regression analysis (MRA). Main findings included: (1) ESEM in general provided the least biased estimation of the regression coefficients; SEM was more biased than MRA given large cross-factor loadings. (2) MRA produced the most precise estimation, followed by ESEM and then SEM. (3) SEM was the least powerful in the significance tests; statistical power was lower for ESEM than MRA with relatively small target-factor loadings, but higher for ESEM than MRA with relatively large target-factor loadings. (4) ESEM showed difficulties in convergence and occasionally created an inflated type I error rate under some conditions. ESEM is recommended when non-ignorable cross-factor loadings exist.  相似文献   

6.
When developing self-report instruments, researchers often have included both positively and negatively worded items to negate the possibility of response bias. Unfortunately, this strategy may interfere with examinations of the latent structure of self-report instruments by introducing method effects, particularly among negatively worded items. The substantive nature of the method effects remains unclear and requires examination. Building on recommendations from previous researchers (Tomás& Oliver, 1999), this study examined the longitudinal invariance of method effects associated with negatively worded items using a self-report measure of global self-esteem. Data were obtained from the National Educational Longitudinal Study (NELS; Ingels et al., 1992) across 3 waves, each separated by 2 years, and the longitudinal invariance of the method effects was tested using LISREL 8.20 with weighted least squares estimation on polychoric correlations and an asymptotic variance/covariance matrix. Our results indicated that method effects associated with negatively worded items exhibited longitudinal invariance of the factor structure, factor loadings, item uniquenesses, factor variances, and factor covariances. Therefore, method effects associated with negatively worded items demonstrated invariance across time, similar to measures of personality traits, and should be considered of potential substantive importance. One possible substantive interpretation is a response style.  相似文献   

7.
Chinese University of Hong Kong students (N = 844) selected a “good” and a “poor” teacher, and rated each using a Chinese translation of the Students' Evaluations of Educational Quality (SEEQ) instrument. Multigroup confirmatory factor analysis (CFA) models, based on a 3 × 2 design, were constructed to test the invariance of the SEEQ factor structure across 3 discipline groups (a between‐group comparison of ratings by students in arts, social sciences, and education; in business administration; and in engineering, medicine, and science) and across ratings of good and poor teachers (via within‐subjects comparison). The selected model imposed between‐group invariance constraints on factor loadings, factor correlations, and factor variances across the 3 discipline groups and within‐subjects invariance constraints on factor loadings across ratings of good and poor teachers. The results support the use of SEEQ in this Chinese setting, demonstrating the generality of North American research findings and the usefulness of CFA in this research area.  相似文献   

8.
In exploratory or unrestricted factor analysis, all factor loadings are free to be estimated. In oblique solutions, the correlations between common factors are free to be estimated as well. The purpose of this article is to show how likelihood-based confidence intervals can be obtained for rotated factor loadings and factor correlations, by applying maximum likelihood factor analysis subject to scaling and rotation constraints. As an illustrative example, an oblique 5-factor model will be fitted to the variance-covariance matrix of the 30 personality facets measured by the Revised NEO Personality Inventory, and confidence intervals will be estimated for all factor loadings and factor correlations, as well as for the associated reliability and validity coefficients.  相似文献   

9.
Multigroup exploratory factor analysis (EFA) has gained popularity to address measurement invariance for two reasons. Firstly, repeatedly respecifying confirmatory factor analysis (CFA) models strongly capitalizes on chance and using EFA as a precursor works better. Secondly, the fixed zero loadings of CFA are often too restrictive. In multigroup EFA, factor loading invariance is rejected if the fit decreases significantly when fixing the loadings to be equal across groups. To locate the precise factor loading non-invariances by means of hypothesis testing, the factors’ rotational freedom needs to be resolved per group. In the literature, a solution exists for identifying optimal rotations for one group or invariant loadings across groups. Building on this, we present multigroup factor rotation (MGFR) for identifying loading non-invariances. Specifically, MGFR rotates group-specific loadings both to simple structure and between-group agreement, while disentangling loading differences from differences in the structural model (i.e., factor (co)variances).  相似文献   

10.
Maximum likelihood is commonly used for estimation of model parameters in analysis of two-level structural equation models. Constraints on model parameters could be encountered in some situations such as equal factor loadings for different factors. Linear constraints are the most common ones and they are relatively easy to handle in maximum likelihood analysis. Nonlinear constraints could be encountered in complicated applications. In this paper we develop an EM-type algorithm for estimating model parameters with both linear and nonlinear constraints. The empirical performance of the algorithm is demonstrated by a Monte Carlo study. Application of the algorithm for linear constraints is illustrated by setting up a two-level mean and covariance structure model for a real two-level data set and running an EQS program.  相似文献   

11.
If the factor structure of a test does not hold over time (i.e., is not invariant), then longitudinal comparisons of standing on the test are not meaningful. In the case of the Wechsler Intelligence Scale for Children‐Third Edition (WISC‐III), it is crucial that it exhibit longitudinal factorial invariance because it is widely used in high‐stakes special education eligibility decisions. Accordingly, the present study analyzed the longitudinal factor structure of the WISC‐III for both configural and metric invariance with a group of 177 students with disabilities tested, on average, 2.8 years apart. Equivalent factor loadings, factor variances, and factor covariances across the retest interval provided evidence of configural and metric invariance. It was concluded that the WISC‐III was measuring the same constructs with equal fidelity across time which allows unequivocal interpretation of score differences as reflecting changes in underlying latent constructs rather than variations in the measurement operation itself. © 2001 John Wiley & Sons, Inc.  相似文献   

12.
Latent class analysis is an analytic technique often used in educational and psychological research to identify meaningful groups of individuals within a larger heterogeneous population based on a set of variables. This technique is flexible, encompassing not only a static set of variables but also longitudinal data in the form of growth mixture modeling, as well as the application to complex multilevel sampling designs. The goal of this study was to investigate—through a Monte Carlo simulation study—the performance of several methods for parameterizing multilevel latent class analysis. Of particular interest was the comparison of several such models to adequately fit Level 1 (individual) data, given a correct specification of the number of latent classes at both levels (Level 1 and Level 2). Results include the parameter estimation accuracy as well as the quality of classification at Level 1.  相似文献   

13.
In many applications of multilevel modeling, group-level (L2) variables for assessing group-level effects are generated by aggregating variables from a lower level (L1). However, the observed group mean might not be a reliable measure of the unobserved true group mean. In this article, we propose a Bayesian approach for estimating a multilevel latent contextual model that corrects for measurement error and sampling error (i.e., sampling only a small number of L1 units from a L2 unit) when estimating group-level effects of aggregated L1 variables. Two simulation studies were conducted to compare the Bayesian approach with the maximum likelihood approach implemented in Mplus. The Bayesian approach showed fewer estimation problems (e.g., inadmissible solutions) and more accurate estimates of the group-level effect than the maximum likelihood approach under problematic conditions (i.e., small number of groups, predictor variable with a small intraclass correlation). An application from educational psychology is used to illustrate the different estimation approaches.  相似文献   

14.
Structural equation modeling provides the framework for investigating experimental effects on the basis of variances and covariances in repeated measurements. A special type of confirmatory factor analysis as part of this framework enables the appropriate representation of the experimental effect and the separation of experimental and nonexperimental parts of variance. The constraint of the matrix of loadings is essential for the representation of the effect. Appropriate constraints of loadings are achievable with the aid of the polynomial function. The representation can even bear on several response modes. The usefulness of this method is demonstrated in data obtained by an experimental task with 3 treatment levels with respect to reaction times and error scores. A model with latent variables representing constancy and increase in reaction times and one latent variable representing increase in error scores serves best in these data. Both reaction times and error scores show experimental effects.  相似文献   

15.
The objective was to offer guidelines for applied researchers on how to weigh the consequences of errors made in evaluating measurement invariance (MI) on the assessment of factor mean differences. We conducted a simulation study to supplement the MI literature by focusing on choosing among analysis models with different number of between-group constraints imposed on loadings and intercepts of indicators. Data were generated with varying proportions, patterns, and magnitudes of differences in loadings and intercepts as well as factor mean differences and sample size. Based on the findings, we concluded that researchers who conduct MI analyses should recognize that relaxing as well as imposing constraints can affect Type I error rate, power, and bias of estimates in factor mean differences. In addition, fit indexes can be misleading in making decisions about constraints of loadings and intercepts. We offer suggestions for making MI decisions under uncertainty when assessing factor mean differences.  相似文献   

16.
Socioeconomic status (SES) is often used as control variable when relations between academic outcomes and students' migrational background are investigated. When measuring SES, indicators used must have the same meaning across groups. This study aims to examine the measurement invariance of SES, using data from TIMSS, 2003. The study shows that a latent SES variable has the same meaning across sub-populations with Swedish and non-Swedish background. However, the assumption of scalar invariance was rejected, which is essential for estimation of differences in latent means between groups. Comparisons between models assuming different degrees of scalar invariance indicated that models allowing partial scalar invariance should not be used when comparing latent variable means across groups of students with different migrational backgrounds.  相似文献   

17.
The recovery of weak factors has been extensively studied in the context of exploratory factor analysis. This article presents the results of a Monte Carlo simulation study of recovery of weak factor loadings in confirmatory factor analysis under conditions of estimation method (maximum likelihood vs. unweighted least squares), sample size, loading size, factor correlation, and model specification (correct vs. incorrect). The effects of these variables on goodness of fit and convergence are also examined. Results show that recovery of weak factor loadings, goodness of fit, and convergence are improved when factors are correlated and models are correctly specified. Additionally, unweighted least squares produces more convergent solutions and successfully recovers the weak factor loadings in some instances where maximum likelihood fails. The implications of these findings are discussed and compared to previous research.  相似文献   

18.
Multigroup confirmatory factor analysis (MCFA) is a popular method for the examination of measurement invariance and specifically, factor invariance. Recent research has begun to focus on using MCFA to detect invariance for test items. MCFA requires certain parameters (e.g., factor loadings) to be constrained for model identification, which are assumed to be invariant across groups, and act as referent variables. When this invariance assumption is violated, location of the parameters that actually differ across groups becomes difficult. The factor ratio test and the stepwise partitioning procedure in combination have been suggested as methods to locate invariant referents, and appear to perform favorably with real data examples. However, the procedures have not been evaluated through simulations where the extent and magnitude of a lack of invariance is known. This simulation study examines these methods in terms of accuracy (i.e., true positive and false positive rates) of identifying invariant referent variables.  相似文献   

19.
A brief 15-item version of the California School Climate Scale (Brief-CSCS) is presented to fill a need for a measure that could be used for periodic monitoring of school personnel's general perception of the climate of their school campus. From a sample of 81,261 California school personnel, random subsamples of 2,400 teachers and 2,400 administrators were used in the analyses. Confirmatory factor analyses supported a model in which general school climate was a second-order latent factor composed of 2 first-order latent traits, organizational supports and relational supports. Measurement invariance of factor loadings for teachers and administrators was found. Additional analyses revealed that administrators held more positive perceptions of school climate than teachers, with this difference increasing from primary through high school. The implications for these findings for educational research and policy reform are outlined.  相似文献   

20.
Multilevel Structural equation models are most often estimated from a frequentist framework via maximum likelihood. However, as shown in this article, frequentist results are not always accurate. Alternatively, one can apply a Bayesian approach using Markov chain Monte Carlo estimation methods. This simulation study compared estimation quality using Bayesian and frequentist approaches in the context of a multilevel latent covariate model. Continuous and dichotomous variables were examined because it is not yet known how different types of outcomes—most notably categorical—affect parameter recovery in this modeling context. Within the Bayesian estimation framework, the impact of diffuse, weakly informative, and informative prior distributions were compared. Findings indicated that Bayesian estimation may be used to overcome convergence problems and improve parameter estimate bias. Results highlight the differences in estimation quality between dichotomous and continuous variable models and the importance of prior distribution choice for cluster-level random effects.  相似文献   

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