Simulation-based sample size planning for Rasch family models

This study investigates simulation-based sample size planning for extended Rasch models, treating them as Generalized Linear Mixed Models (GLMMs). We conducted power analyses to examine the impact of model type (Rasch Model, Linear Logistic Test Model, Rating Scale Model, Linear Rating Scale Model), sample size, item parameters (slope and intercept), and item-design matrices on statistical power. Our findings indicate that while larger sample sizes consistently improve power, polytomous models and those incorporating complex item-design matrices can also yield high power, potentially due to lower asymptotic variances and better fit to simulated data. We demonstrate a practical approach for conducting power analyses for these models using readily available R packages like lme4 and mixedpower, showing equivalent estimates to eRm. We discuss computational costs, data dependency, and the current limitations regarding the application of Partial Credit Models (PCMs). This research provides insights for researchers in experimental psychology and related fields, aiding in the design of robust studies and efficient sample size determination for complex psychometric models.