Abstract
Longitudinal studies are the gold standard for research on time‐dependent phenomena in the social sciences. However, they often entail high costs due to multiple measurement occasions and a long overall study duration. It is therefore useful to optimize these design factors while maintaining a high informativeness of the design. Von Oertzen and Brandmaier (2013,Psychology and Aging, 28, 414) applied power equivalence to show that Latent Growth Curve Models (LGCMs) with different design factors can have the same power for likelihood‐ratio tests on the latent structure. In this paper, we show that the notion of power equivalence can be extended to Bayesian hypothesis tests of the latent structure constants. Specifically, we show that the results of a Bayes factor design analysis (BFDA; Schönbrodt & Wagenmakers (2018,Psychonomic Bulletin and Review, 25, 128) of two power equivalent LGCMs are equivalent. This will be useful for researchers who aim to plan for compelling evidence instead of frequentist power and provides a contribution towards more efficient procedures for BFDA.
Highlights
Researchers design experiments to gain knowledge of the world
Longitudinal studies entail especially high costs. These accrue either due to a long overall study duration, for example when a treatment has to be administered over a long period of time, or due to a large number of measurement occasions, for example when non-reusable testing material is spent at each testing event
Formal proof of Bayes Factor Design Analysis’ (BFDA) equivalence for power equivalent models we show formally that two power equivalent models with the same parameter set h will produce the same distribution of the Bayes Factor when comparing two hypotheses about h under data generated by a population model
Summary
Researchers design experiments to gain knowledge of the world. In a world of limited resources, it is ethical to conduct these experiments efficiently (Halpern et al, 2002). Hunter and Hoff (1967) define research efficiency as ‘the amount of useful information obtained per unit cost’. By comparing multiple power-equivalent longitudinal designs based on data and cost estimates from the Berlin Aging Study (BASE; Ghisletta, et al, 2006), von Oertzen and Brandmaier (2013) showed that the overall study costs could be reduced by 16% compared to the original design while keeping the statistical power with respect to the variance of slopes constant. How large the Bayes factors get that an experiment yields, depends on the tested models (described by likelihoods and prior distributions), on the population effect size, on the amount of collected data, that is, the number of observations in the sample, and on the measurement design (Stefan, et al, 2019). 1⁄4 BFB12 ðSÃ; mÃÞ: Since the Bayes factor is identical for both models for any specific outcome of the data, its distribution under any random distribution of (S,m) is identical for both power equivalent models
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: British Journal of Mathematical and Statistical Psychology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
