More powerful parameter tests? No, rather biased parameter estimates. Some reflections on path analysis with weighted composites

Abstract

Recently, a study compared the effect size and statistical power of covariance-based structural equation modeling (CB-SEM) and path analysis using various types of composite scores (Deng, L., & Yuan, K.-H., Behavior Research Methods,55, 1460–1479, 2023). This comparison uses nine empirical datasets to estimate eleven models. Based on the meta-comparison, that study concludes that path analysis via weighted composites yields “path coefficients with less relative errors, as reflected by greater effect size and statistical power” (ibidem, p. 1475). In our paper, we object to this central conclusion. We demonstrate that the justification these authors provided for comparing CB-SEM and path analysis via weighted composites is not well grounded. Similarly, we explain that their employed study design, i.e., a meta-comparison, is very limited in its ability to compare the effect size and power delivered across these methods. Finally, we replicated Deng and Yuan’s (ibidem) meta-comparison and show that CB-SEM using the normal-distribution-based maximum likelihood estimator does not necessarily deliver smaller effect sizes than path analysis via composites if a different scaling method is employed for CB-SEM.