A General Model-Implied Simulation-Based Power Estimation Method for Correctly and Misspecfied Models: Applications to Nonlinear and Linear Structural Equation Models

Closed form power estimation is only available for limited classes of models, requiring correct model specification for most applications. Simulation is used in other scenarios, but a general framework in computing required sample sizes for given power rates is still missing. We propose a new model-implied simulation-based power estimation (MSPE) method that makes use of the asymptotic normality property of estimates of a wide class of estimators, the $M$-estimators, and we give theoretical justification for the approach. $M$-estimators include maximum-likelihood estimates and least squares estimates, but also limited information estimators and estimators used for misspecified models, hence, the new power modeling method is widely applicable. We highlight its performance for linear and nonlinear structural equation models (SEM) and a moderated logistic regression model for correctly specified models and models under distributional misspecification. Simulation results suggest that the new power modeling method is unbiased and shows good performance with regard to root mean squared error and Type I error rates for the predicted required sample sizes and predicted power rates. Alternative approaches, such as the na\"ive approach of selecting arbitrary sample sizes with linear interpolation of power or simple logistic regression approaches, showed poor performance. The MSPE appears to be a valuable tool to estimate power for models without (asymptotic) analytical power estimation.