Model-implied simulation-based power estimation for correctly specified and distributionally misspecified models: Applications to nonlinear and linear structural equation models.

Closed-form (asymptotic) analytical power estimation is only available for limited classes of models, requiring correct model specification for most applications. Simulation-based power estimation can be applied in almost all scenarios where data following the model can be estimated. However, a general framework for calculating the required sample sizes for given power rates is still lacking. We propose a new model-implied simulation-based power estimation (MSPE) method for the z-test that makes use of the asymptotic normality property of estimates of a wide class of estimators, the M-estimators, and give theoretical justification for the approach. M-estimators include maximum-likelihood, least squares estimates and limited information estimators, but also estimators used for misspecified models, hence, the new simulation-based power modeling method is widely applicable. The MSPE employs a parametric model to describe the relationship between power and sample size, which can then be used to determine the required sample size for a specified power rate. We highlight its performance in linear and nonlinear structural equation models (SEM) 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, outperforming alternative approaches, such as the naïve approach of selecting a discrete selection of sample sizes with linear interpolation of power or simple logistic regression approaches. The MSPE appears to be a valuable tool to estimate power for models without an (asymptotic) analytical power estimation.