Simulation-based sensitivity analysis for sample size planning of Rasch family models

Generalized linear mixed models (GLMMs), including the Rasch item response model (RM) family, are useful statistical models for both experimental and non-experimental studies. Determining an appropriate sample size is crucial for obtaining reliable parameter estimates and ensuring sufficient statistical power in psychometric modeling. Therefore, a sensitivity analysis is essential to evaluate which factors influence power estimates. However, researchers often face challenges in performing power analyses because of its complexity and the lack of accessible software. This study presents a simulation-based sensitivity analysis for sample size planning of extended Rasch models, including the RM, linear logistic test model (LLTM), rating scale model (RSM), and linear rating scale model (LRSM), by treating them as GLMMs. Using the R packages lme4 and mixedpower, we conducted sensitivity analyses to examine how sample size, item difficulty, discrimination, and item-design matrix influence power estimates. Our results indicate that while increasing the sample size naturally enhances power, model complexity and item-design matrices also play an important role. Specifically, LLTM and LRSM, which incorporate item-design matrices, exhibit higher power under complex specifications. Our findings highlight the feasibility of leveraging simulation-based methods for power analysis in extended Rasch models, underscoring challenges related to computational cost and data dependency. To address these limitations, we discuss potential solutions such as surrogate modeling and sequential analyses.