Abstract
This simulation study was conducted to compare the performances of Frequentist and Bayesian approaches in the context of power to detect model misspecification in terms of omitted cross-loading in CFA models with respect to the several variables (number of omitted cross-loading, magnitude of main loading, number of factors, number of indicators per factor and sample size) and (to) investigate the efficiency of BSEM approach to detect cross-loadings. BSEM approach allows including and estimating certain number of cross-loadings by specifying informative piror with small-variance for cross-loadings in the model. By this way, BSEM approach enables researchers to come up with models that better represent the substantive theory. At this simulation study, model misspecification was considered as major misspecification (cl=0.3) and minor misspecification (cl=0.1) according to the amount of omitted cross-loading. Results of this study revealed that Frequentist approach was so sensitive to minor model misspecification whereas Bayesian approach with non-informative prior was so sensitive to the major model misspecification. Finally, it was concluded that the power of BSEM approach to detect cross-loading varied according to the both amount and number of cross-loadings and for large amount of cross-loading the performance of this approach was so well.
Highlights
It is assumed that educational and psychological measures reflect underlying and non-observable latent construct(s)
When the relationships between the constructs and their indicators are modelled by considering that each indicator is only related to one factor of the construct but not certainly related to other factors, this leads the researchers to misspecified measurement models
Biased parameter estimations are obtained as the consequence of testing a misspecified measurement model, fit indexes, which will indicate that this model is a “valid” model, can be obtained
Summary
It is assumed that educational and psychological measures reflect underlying and non-observable latent construct(s). The information about these latent constructs can be obtained through their effects on observed variables. Examining the factor structure of measures in terms of exploring and describing the connections between the educational and psychological measures and latent variables underlying these measures is quite important in making accurate and appropriate decisions related to the measured construct. The oldest and most common models known in specifying the relationships between observed variables and underlying latent constructs are factor analytic models [1]. In CFA, unlike EFA, a priori factor structure is specified for the relationships between the latent factors and observed variables/measures, and the level of fit between this factor structure and sample data is examined. The basic equation of a CFA model is as follows: yi =τ +Ληi +εi (1)
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