Estimating power in complex nonlinear structural equation modeling including moderation effects: The powerNLSEM R-package.

The model-implied simulation-based power estimation (MSPE) approach is a new general method for power estimation (Irmer et al., 2024). MSPE was developed especially for power estimation of non-linear structural equation models (SEM), but it also can be applied to linear SEM and manifest models using the R package powerNLSEM. After first providing some information about MSPE and the new adaptive algorithm that automatically selects sample sizes for the best prediction of power using simulation, a tutorial on how to conduct the MSPE for quadratic and interaction SEM (QISEM) using the powerNLSEM package is provided. Power estimation is demonstrated for four methods, latent moderated structural equations (LMS), the unconstrained product indicator (UPI), a simple factor score regression (FSR), and a scale regression (SR) approach to QISEM. In two simulation studies, we highlight the performance of the MSPE for all four methods applied to two QISEM with varying complexity and reliability. Further, we justify the settings of the newly developed adaptive search algorithm via performance evaluations using simulation. Overall, the MSPE using the adaptive approach performs well in terms of bias and Type I error rates.