Abstract:

Structural equation modeling (SEM) is an important statistical tool in psychology, management, and sociology. However, many studies that use SEM lack analyses and reports of statistical power. Studies with low statistical power may result in a waste of labor and material resources; studies may even be led astray because of failure to test real effects, thereby making incorrect conclusions. In addition, low statistical power may cause researchers to mistake poorly fitted models for well-fitted models. Consequently, researchers may draw incorrect conclusions. At present, the Satorra-Saris, MacCallum, and Monte Carlo methods are the three main types of statistical power analysis methods for SEM. The Satorra-Saris and MacCallum methods are based on various important conclusions on the χ² distribution given by the earlier works of Satorra and Saris. These methods are applicable for analyzing the statistical power of χ²-based tests in SEM. The Monte Carlo method is based on the work of Muthén and Muthén, and it uses simulations to analyze the statistical power, which can be applied to a wide range of test situations in SEM. Among the three types of analytical methods, the MacCallum method is the simplest and least computationally intensive; however, it has the narrowest scope of application. The Monte Carlo method is the most complex and computationally intensive, and it has the widest scope of application. The Satorra-Saris method has moderate complexity, computation intensity, and scope of application. In practice, researchers can choose the appropriate analysis method according to the purpose of the test, test method, availability of alternative models, ease of use of the method, and computational power. The Satorra-Saris method is recommended when the test is based on the χ² distribution (e.g., the χ² test, likelihood ratio test, Wald test, and test of model fit index), the alternative model is clear, and the test object is simple; the MacCallum method is recommended if the alternative model is unknown. The Monte Carlo method is recommended when simulation or resampling methods are used, or when the target of the test is complex. In addition, when researchers try to evaluate the model fit for SEM, there is a conjugate relationship between the statistical power analysis and the equivalence test. Therefore, researchers have proposed a new method in recent years to evaluate the model fit of SEM, which can be conditionally interchanged to some extent.

Key words: structural equation model, statistical power, fitting test, test of model parameters