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A New Strategy for Testing Structural Equation Models

One of the most important issues in structural equation modeling concerns testing model fit. We propose to retain the likelihood ratio test in combination with decision criteria that increase with sample size. Specifically, rooted in Neyman–Pearson hypothesis testing, we advocate balancing α- and β-error risks. This strategy has a number of desirable consequences and addresses several objections that have been raised against the likelihood ratio test in model evaluation. First, balancing error risks avoids logical problems with Fisher-type hypotheses tests when predicting the null hypothesis (i.e., model fit). Second, both types of statistical decision errors are controlled. Third, larger samples are encouraged (rather than penalized) because both error risks diminish as the sample size increases. Finally, the strategy addresses the concern that structural equation models cannot necessarily be expected to provide an exact description of real-world phenomena.