{"title":"Bayesian power equivalence in latent growth curve models","authors":"A. Stefan, Timo von Oertzen","doi":"10.1111/bmsp.12193","DOIUrl":null,"url":null,"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.","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The British journal of mathematical and statistical psychology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1111/bmsp.12193","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.