Estimating power in (generalized) linear mixed models: an open introduction and tutorial in R.

Linear mixed-effect models are a powerful tool for modelling fixed and random effects simultaneously, but do not offer a feasible analytic solution for estimating the probability that a test correctly rejects the null hypothesis. Being able to estimate this probability, however, is critical for sample size planning, as power is closely linked to the reliability and replicability of empirical findings. Although various tools for conducting a simulation-based power analysis for mixed-effect models are available, there is a lack of guidance on how to appropriately use them in different scenarios. In this tutorial paper, we discuss and elaborate how to estimate power for mixed-effects models in different use cases and outline important considerations and pitfalls. We provide code and resources for performing simulation-based power analyses on openly accessible data sets. Our aim is to help researchers build intuitions about simulation-based power analyses and empower them to set up highly powered research designs when sophisticated analysis procedures like mixed-effect models are outlined as inferential procedures.