Power Analysis for Mixed-Models: A Model-Implied Simulation-Based Power Estimation Approach

Asymptotic properties such as consistency and convergence of parameters in generalized linear mixed models (GLMMs) remain largely underexplored, despite their high practical relevance. This is primarily due to the mathematical complexity of GLMMs, especially in designs with crossed random effects. For experimental practice, where GLMMs are frequently used to account for random effects for subjects and items, this has important consequences for performing power analysis to determine sufficient sample sizes. In particular, it leads to power analysis being used far less frequently than in traditional fixed-effects models. Simulation-based approaches offer a flexible alternative, but they remain constrained by high computational costs, long runtimes, and inaccuracies introduced through interpolation. This project aims to investigate the asymptotic properties of GLMM parameters and leverage them to develop model-implied, simulation-based power analyses. Overall, this study provides a foundation for future implementations of power analysis tools grounded in asymptotic theory.