Department of Psychology, Scene Grammar Lab, Goethe University Frankfurt, Frankfurt am Main, Germany.
Oxford Centre for Human Brain Activity, Wellcome Centre for Integrative Neuroimaging, Department of Psychiatry, University of Oxford, Oxford, UK.
Behav Res Methods. 2021 Dec;53(6):2528-2543. doi: 10.3758/s13428-021-01546-0. Epub 2021 May 5.
Mixed-effects models are a powerful tool for modeling 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. A flexible and very intuitive alternative to analytic power solutions are simulation-based power analyses. Although various tools for conducting simulation-based power analyses for mixed-effects models are available, there is lack of guidance on how to appropriately use them. In this tutorial, we discuss how to estimate power for mixed-effects models in different use cases: first, how to use models that were fit on available (e.g. published) data to determine sample size; second, how to determine the number of stimuli required for sufficient power; and finally, how to conduct sample size planning without available data. Our examples cover both linear and generalized linear models and we provide code and resources for performing simulation-based power analyses on openly accessible data sets. The present work therefore helps researchers to navigate sound research design when using mixed-effects models, by summarizing resources, collating available knowledge, providing solutions and tools, and applying them to real-world problems in sample sizing planning when sophisticated analysis procedures like mixed-effects models are outlined as inferential procedures.
混合效应模型是同时对固定效应和随机效应进行建模的有力工具，但对于估计检验正确拒绝零假设的概率，它没有提供可行的解析解决方案。然而，能够估计这个概率对于样本量规划至关重要，因为功效与实证发现的可靠性和可重复性密切相关。一种灵活且非常直观的替代解析功效解决方案是基于模拟的功效分析。尽管有各种用于混合效应模型的基于模拟的功效分析的工具，但缺乏关于如何正确使用它们的指导。在本教程中，我们将讨论如何在不同的用例中估计混合效应模型的功效：首先，如何使用在可用（例如已发表）数据上拟合的模型来确定样本量；其次，如何确定获得足够功效所需的刺激数量；最后，如何在没有可用数据的情况下进行样本量规划。我们的示例涵盖了线性和广义线性模型，并提供了用于对公开可访问数据集执行基于模拟的功效分析的代码和资源。因此，当使用混合效应模型时，本工作通过总结资源、整理现有知识、提供解决方案和工具，并将其应用于样本量规划中的实际问题，帮助研究人员在进行复杂的分析程序（如混合效应模型）作为推断程序时，对合理的研究设计进行导航。
