Bayesian Power Equivalence in Latent Growth Curve Models

Longitudinal studies are the gold standard for research on time-dependentphenomena in the social sciences. However, they often entail high costs dueto multiple measurement occasions and a long overall study duration. It istherefore useful to optimize these design factors while maintaining a highinformativeness of the design. Von Oertzen and Brandmaier (2013) appliedpower equivalence to show that Latent Growth Curve Models (LGCMs)with different design factors can have the same power for likelihood-ratiotests on the latent structure. In this paper, we show that the notion ofpower equivalence can be extended to Bayesian hypothesis tests of the latentstructure constants. Specifically, we show that the results of a Bayes FactorDesign Analysis (BFDA; Schönbrodt & Wagenmakers, 2018) of two powerequivalent LGCMs are equivalent. This will be useful for researchers whoaim to plan for compelling evidence instead of frequentist power and providesa contribution towards more efficient procedures for BFDA.