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Bang Quan Zheng; Peter M. Bentler – Structural Equation Modeling: A Multidisciplinary Journal, 2025
This paper aims to advocate for a balanced approach to model fit evaluation in structural equation modeling (SEM). The ongoing debate surrounding chi-square test statistics and fit indices has been characterized by ambiguity and controversy. Despite the acknowledged limitations of relying solely on the chi-square test, its careful application can…
Descriptors: Monte Carlo Methods, Structural Equation Models, Goodness of Fit, Robustness (Statistics)
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Bang Quan Zheng; Peter M. Bentler – Structural Equation Modeling: A Multidisciplinary Journal, 2022
Chi-square tests based on maximum likelihood (ML) estimation of covariance structures often incorrectly over-reject the null hypothesis: [sigma] = [sigma(theta)] when the sample size is small. Reweighted least squares (RLS) avoids this problem. In some models, the vector of parameter must contain means, variances, and covariances, yet whether RLS…
Descriptors: Maximum Likelihood Statistics, Structural Equation Models, Goodness of Fit, Sample Size