Analytical power calculations for structural equation modeling: A tutorial and Shiny app

Conducting a power analysis can be challenging for researchers who plan to analyze their data using structural equation models (SEMs), particularly when Monte Carlo methods are used to obtain power. In this tutorial, we explain how power calculations without Monte Carlo methods for the χ² test and the RMSEA tests of (not-)close fit can be conducted using the Shiny app "power4SEM". power4SEM facilitates power calculations for SEM using two methods that are not computationally intensive and that focus on model fit instead of the statistical significance of (functions of) parameters. These are the method proposed by Satorra and Saris (Psychometrika 50(1), 83-90, 1985) for power calculations of the likelihood ratio test, and that described by MacCallum, Browne, and Sugawara (Psychol Methods 1(2) 130-149, 1996) for RMSEA-based power calculations. We illustrate the use of power4SEM with examples of power analyses for path models, factor models, and a latent growth model.