Sample size determination for Bayesian hierarchical models commonly used in psycholinguistics

Although Bayesian data analysis has the great advantage that one need not specify the sample size in advance of running an experiment, there are nevertheless situations where it becomes necessary to have at least an initial ballpark estimate for a target sample size. An example where this becomes necessary is grant applications. In this paper, we adapt a simulation-based method proposed by Wang and Gelfand, 2002 (A simulation-based approach to Bayesian sample size determination for performance under a given model and for separating models. Statistical Science, 193-208) for a Bayes-factor based design analysis. We demonstrate how relatively complex hierarchical models (which are commonly used in psycholinguistics) can be used to determine approximate sample sizes for planning experiments. The code is available for researchers to adapt for their own purposes and applications at https://osf.io/hjgrm/.