Analyzing Observed Composite Differences Across Groups

Methodology ◽  
2013 ◽  
Vol 9 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Holger Steinmetz
Keyword(s):  
Monte Carlo ◽  
Structural Equation Modeling ◽  
Measurement Invariance ◽  
Structural Equation ◽  
Monte Carlo Study ◽  
Equation Modeling ◽  
Factor Loadings ◽  
Latent Mean Differences ◽  
Partial Invariance ◽  
Mean Differences

Although the use of structural equation modeling has increased during the last decades, the typical procedure to investigate mean differences across groups is still to create an observed composite score from several indicators and to compare the composite’s mean across the groups. Whereas the structural equation modeling literature has emphasized that a comparison of latent means presupposes equal factor loadings and indicator intercepts for most of the indicators (i.e., partial invariance), it is still unknown if partial invariance is sufficient when relying on observed composites. This Monte-Carlo study investigated whether one or two unequal factor loadings and indicator intercepts in a composite can lead to wrong conclusions regarding latent mean differences. Results show that unequal indicator intercepts substantially affect the composite mean difference and the probability of a significant composite difference. In contrast, unequal factor loadings demonstrate only small effects. It is concluded that analyses of composite differences are only warranted in conditions of full measurement invariance, and the author recommends the analyses of latent mean differences with structural equation modeling instead.

scholarly journals Bootstrapping technique in structural equation modeling: a Monte Carlo study

2018 ◽  
Vol 1132 ◽  
pp. 012072
Author(s):  
Nor Iza Anuar Razak ◽  
Zamira Hasanah Zamzuri ◽  
Nur Riza Mohd Suradi
Keyword(s):  
Monte Carlo ◽  
Structural Equation Modeling ◽  
Structural Equation ◽  
Monte Carlo Study ◽  
Equation Modeling

Is Self-Compassion Universal? Support for the Measurement Invariance of the Self-Compassion Scale Across Populations

Assessment ◽  
2020 ◽  
Vol 28 (1) ◽  
pp. 169-185 ◽  
Author(s):  
István Tóth-Király ◽  
Kristin D. Neff
Keyword(s):  
Structural Equation Modeling ◽  
Measurement Invariance ◽  
Structural Equation ◽  
Secondary Data ◽  
The Self ◽  
Equation Modeling ◽  
Exploratory Structural Equation Modeling ◽  
Self Compassion ◽  
Wide Range ◽  
Compassion Scale

The Self-Compassion Scale (SCS) is a widely used measure to assess the trait of self-compassion, and, so far, it has been implicitly assumed that it functions the same way across different groups. This assumption needs to be explicitly tested to ascertain that no measurement biases exist. To address this issue, the present study sought to systematically examine the generalizability of the bifactor exploratory structural equation modeling operationalization of the SCS via tests of measurement invariance across a wide range of populations, varying according to features such as student or community status, gender, age, and language. Secondary data were used for this purpose and included a total of 18 samples and 12 different languages ( N = 10,997). Multigroup analyses revealed evidence for the configural, weak, strong, strict, and latent variance–covariance of the bifactor exploratory structural equation modeling operationalization of the SCS across different groups. These findings suggest that the SCS provides an assessment of self-compassion that is psychometrically equivalent across groups. However, findings comparing latent mean invariance found that levels of self-compassion differed across groups.

scholarly journals Testing measurement invariance and latent mean differences across gender groups in college students’ Internet-specific epistemic beliefs

2015 ◽  
Vol 31 (4) ◽  
Author(s):  
Yen-Lin Chiu ◽  
Chin-Chung Tsai ◽  
Jyh-Chong Liang
Keyword(s):  
Measurement Invariance ◽  
Gender Gap ◽  
Structural Equation ◽  
Epistemic Beliefs ◽  
Equation Modeling ◽  
The Internet ◽  
And Gender ◽  
Mean Differences ◽  
Gender Groups ◽  
Latent Mean Analysis

<p>The purposes of this study were to investigate the measurement invariance and gender differences in the Internet-specific epistemic beliefs between male and female undergraduates. A total of 735 university students in Taiwan were surveyed using the Internet-specific epistemic beliefs questionnaire (ISEQ). By conducting structural equation modeling (SEM), the measurement invariance and latent mean comparisons across gendered groups were tested. After the invariance tests were all satisfied, the latent mean analysis approach was conducted. The results of the latent mean comparisons revealed that a gender gap occurred in the uncertainty, complexity and source of Internet-specific epistemic beliefs; however no gender difference was found in the justification dimension. In general, the study findings suggest that differences in beliefs regarding Internet-based knowledge exist between undergraduate males and females. The gendered issue of Internet-based learning and epistemic beliefs cannot be ignored. Finally, some suggestions for developing Internet-related curricula and instruction were also proposed.</p>

scholarly journals Accounting for Differential Item Functioning Using Bayesian Approximate Measurement Invariance

2019 ◽  
Vol 80 (4) ◽  
pp. 638-664 ◽  
Author(s):  
Georgios D. Sideridis ◽  
Ioannis Tsaousis ◽  
Abeer A. Alamri
Keyword(s):  
Measurement Invariance ◽  
Structural Equation ◽  
Equation Modeling ◽  
P Value ◽  
National Examination ◽  
Item Functioning ◽  
Using Data ◽  
Mean Differences ◽  
Bayesian Structural Equation Modeling ◽  
Approximate Measurement

The main thesis of the present study is to use the Bayesian structural equation modeling (BSEM) methodology of establishing approximate measurement invariance (A-MI) using data from a national examination in Saudi Arabia as an alternative to not meeting strong invariance criteria. Instead, we illustrate how to account for the absence of measurement invariance using relative compared to exact criteria. A secondary goal was to compare latent means across groups using invariant parameters only and through utilizing exact and relative evaluative-MI protocol suggested equivalence of the thresholds using prior variances equal to 0.10. Subsequent differences between groups were evaluated using effect size criteria and the prior-posterior predictive p-value (PPPP), which proved to be invaluable in attesting for differences that are beyond zero, some meaningless nonzero estimate, and the three commonly used indices of effect sizes described by Cohen in 1988 (i.e., .20, .50, and .80). Results substantiated the use of the PPPP for evaluating mean differences across groups when utilizing nonexact evaluative criteria.

A note on the cutoff values of alternative fit indices to evaluate measurement invariance for ESEM models

2019 ◽  
Vol 44 (2) ◽  
pp. 166-174
Author(s):  
Ying Jin
Keyword(s):  
Measurement Invariance ◽  
Structural Equation ◽  
Mean Squared Error ◽  
Simulated Data ◽  
Index Formula ◽  
Equation Modeling ◽  
Approximation Formula ◽  
Fit Indices ◽  
Cutoff Values ◽  
Partial Invariance

This research examines the performance of the previously proposed cutoff values of alternative fit indices (i.e., change in comparative fit index [[Formula: see text]], change in Tucker–Lewis index [[Formula: see text]], and change in root mean squared error of approximation [[Formula: see text]]) to evaluate measurement invariance for exploratory structural equation modeling (ESEM) models with simulated data. It is important to revisit these cutoff values because they were used widely in validity studies utilizing ESEM models to evaluate measurement invariance for ordinal indicators, but in fact, these cutoff values were developed under confirmatory factor analysis models with continuous indicators. Results of this study show that different cutoff values of [Formula: see text], [Formula: see text], and [Formula: see text] should be used for ESEM models with ordinal indicators. Evaluation of partial invariance for ESEM models is also discussed.

Testing Measurement Invariance Across Spanish and English Versions of the Physical Self-Description Questionnaire: An Application of Exploratory Structural Equation Modeling

2014 ◽  
Vol 36 (2) ◽  
pp. 179-188 ◽  
Author(s):  
Inés Tomás ◽  
Herbert W. Marsh ◽  
Vicente González-Romá ◽  
Víctor Valls ◽  
Benjamin Nagengast
Keyword(s):  
Structural Equation Modeling ◽  
Measurement Invariance ◽  
Structural Equation ◽  
Cross Cultural ◽  
Spanish Version ◽  
Equation Modeling ◽  
Exploratory Structural Equation Modeling ◽  
Alternative Approach ◽  
Cultural Comparisons ◽  
Sport And Exercise

Test of measurement invariance across translated versions of questionnaires is a critical prerequisite to comparing scores on the different versions. In this study, we used exploratory structural equation modeling (ESEM) as an alternative approach to evaluate the measurement invariance of the Spanish version of the Physical Self-Description Questionnaire (PSDQ). The two versions were administered to large samples of Australian and Spanish adolescents. First, we compared the CFA and ESEM approaches and showed that ESEM fitted the data much better and resulted in substantially more differentiated factors. We then tested measurement invariance with a 13-model ESEM taxonomy. Results justified using the Spanish version of the PSDQ to carry out cross-cultural comparisons in sport and exercise psychology research. Overall, the study can stimulate research on physical self-concept across countries and foster better cross-cultural comparisons.

scholarly journals We need to change how we compute RMSEA for nested model comparisons in structural equation modeling

2021 ◽  
Author(s):  
Victoria Savalei ◽  
Jordan Brace ◽  
Rachel T. Fouladi
Keyword(s):  
Structural Equation Modeling ◽  
Measurement Invariance ◽  
Structural Equation ◽  
Model Comparison ◽  
Equation Modeling ◽  
Future Research ◽  
Chi Square ◽  
Nested Model ◽  
Nested Models ◽  
Difference Test

Comparison of nested models is common in applications of structural equation modeling (SEM). When two models are nested, model comparison can be done via a chi-square difference test or by comparing indices of approximate fit. The advantage of fit indices is that they permit some amount of misspecification in the additional constraints imposed on the model, which is a more realistic scenario. The most popular index of approximate fit is the root mean square error of approximation (RMSEA). In this article, we argue that the dominant way of comparing RMSEA values for two nested models, which is simply taking their difference, is problematic and will often mask misfit. We instead advocate computing the RMSEA associated with the chi-square difference test. We are not the first to propose this idea, and we review numerous methodological articles that have suggested it. Nonetheless, these articles appear to have had little impact on actual practice. The modification of current practice that we call for may be particularly needed in the context of measurement invariance assessment. We illustrate the difference between the current approach and our advocated approach on three examples, where two involve multiple-group and longitudinal measurement invariance assessment and the third involves comparisons of models with different numbers of factors. We conclude with a discussion of limitations and future research directions.

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