Examining Simultaneous Power in Structural Equation Modeling

Statistical power is typically thought of univariately. However, the most common statistical models are multivariate, i.e., multiple regression and structural equation modeling. Researchers are likely interested in finding all parameters statistically significant that are non-null in the population. That is, it is desirable to commit no type II errors. The probability of committing no type II errors in an analysis can be termed simultaneous power. What is often ignored is that simultaneous can be substantially lower than the power for a single predictor, or more so if the probability of finding at least one significant result is examined. This expresses the need to explore ways to improve simultaneous power other than increasing sample size. This project examined four ways for simultaneously testing structural coefficients in structural equation modeling in the special case of two exogenous latent variables. Namely, these methods are the delta method, assymptotic confidence intervals based on the distribution of the products, the percentile bootstrap, and the bias-corrected and accelerated bootstrap.