Power analysis for parameter estimation in structural equation modeling: A discussion and tutorial

Abstract

Despite the widespread and rising popularity of structural equation modeling (SEM) in psychology, there is still much confusion surrounding how to choose an appropriate sample size for SEM. Currently available guidance primarily consists of sample size rules of thumb that are not backed up by research, and power analyses for detecting model misfit. Missing from most current practices is power analysis to detect a target effect (e.g., a regression coefficient between latent variables). In this paper we (a) distinguish power to detect model misspecification from power to detect a target effect, (b) report the results of a simulation study on power to detect a target regression coefficient in a 3-predictor latent regression model, and (c) introduce a Shiny app, pwrSEM, for user-friendly power analysis for detecting target effects in structural equation models.

Selection of the Number of Participants in Intensive Longitudinal Studies: A User-friendly Shiny App and Tutorial to Perform Power Analysis in Multilevel Regression Models that Account for Temporal Dependencies

“…Therefore, a more robust power-calculation approach would account for uncertainty regarding the hypothesized model parameters. This can be achieved by performing a sensitivity analysis in which the values of the model parameters are varied to some extent (e.g., Lane & Hennes 2018, Wang & Rhemtulla 2020. This way one can assess whether and to which extent using different possible parameter values influences the obtained power results.…”

Solutions to the problems of incremental validity testing in relationship science

“…Using SEM to conduct incremental validity testing will reduce the (sometimes dramatically high) Type I error rate associated with multiple regression. But this decision may have the cost of increasing the Type II error rate when a true incremental effect is present (Wang & Rhemtulla, 2019;Westfall & Yarkoni, 2016). This observation is somewhat counterintuitive-if SEM "accounts for" measurement error and disattenuates standardized effect sizes at the latent level, shouldn't power increase?…”

“…Power to detect an incremental validity path in SEM varies as a function of model characteristics, including sample size, effect size, factor loadings, and number of indicators per latent variable (Wang & Rhemtulla, 2019; see also Wolf, Harrington, Clark, & Miller, 2013). A desirable level of power (e.g., 80%) might require a much larger sample size-sometimes in the thousands-compared to a comparable multiple regression model (Westfall & Yarkoni, 2016).…”

“…To obtain realistic estimates of target sample size, we recommend that researchers planning to use SEM for incremental validity testing conduct power analysis to detect their target effect of interest (i.e., the incremental effect of the focal predictor on the outcome variable). Such power analysis can be conducted using Monte Carlo simulations (Múthen & Múthen, 2012; for a userfriendly Shiny app for this type of power analysis, see pwrSEM; Wang & Rhemtulla, 2019).…”

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

“…This method provides an empirical estimate of power. For instructions on how to conduct such a study, see the articles by Muthén and Muthén (2002), Schoemann, Boulton, and Short (2017), or Wang and Rhemtulla (2020). In this tutorial we focus on two methods that are not computationally intensive and that focus on model fit instead of the statistical significance of (functions of) parameters: the method introduced by Satorra and Saris (1985) for power calculations of the likelihood ratio test (LRT), and that by MacCallum, Browne, and Sugawara (1996) for the calculation of root mean square error of approximation (RMSEA)-based power.…”