Reliable and More Powerful Methods for Power Analysis in Structural Equation Modeling

Abstract

The normal-distribution-based likelihood ratio statistic is widely used for power analysis in structural Equation modeling (SEM). In such an analysis, power and sample size are computed by assuming that follows a central chi-square distribution under and a noncentral chi-square distribution under . However, with either violation of normality or not a large enough sample size, both empirical and analytical results indicate that the chi-square distribution assumptions are not realistic and consequently methods of power analysis based on such assumptions are not valid. This article describes a Monte Carlo (MC) method for power analysis. A measure of effect size for characterizing the power property of different rescaled statistics is also provided. Robust methods are proposed to increase the power of and other statistics. Simulation results show that the MC method reliably controls Type I errors and robust estimation methods effectively increase the power, and their combination is thus recommended for conducting power analysis in SEM.

Keywords:

• likelihood ratio statistic
• Monte Carlo
• power
• robust estimation
• Type I errors

FUNDING

This research was supported by a grant from the Institute of Education Sciences (R305D140037), and by the National Science Foundation under Grant No. SES-1461355.

Notes

¹ A test statistic is a numerical value aiming to optimally summarize the deviance in the data against the null hypothesis, and the statistic typically depends on the values of parameters computed by a particular estimation method (see, e.g., https://en.wikipedia.org/wiki/Test_statistic).

² As the estimation method varies, the properties of and also vary, and we label the two statistics with additional notation when they are evaluated under robust methods.

³ One could choose a larger number of replications if the range of the involved statistic or its is large.

Additional information

Funding

This research was supported by a grant from the Institute of Education Sciences (R305D140037), and by the National Science Foundation under Grant No. SES-1461355.