Comparisons of Three Empirical Methods for Partial Factorial Invariance: Forward, Backward, and Factor-Ratio Tests

Abstract

When factorial invariance is violated, a possible first step in locating the source of violation(s) might be to pursue partial factorial invariance (PFI). Two commonly used methods for PFI are sequential use of the modification index (backward MI method) and the factor-ratio test. In this study, we propose a simple forward method using the confidence interval (forward CI method). We compare the performances of the aforementioned 3 methods under various simulated PFI conditions. Results indicate that the forward CI method using 99% CIs has the highest perfect recovery rates and the lowest Type I error rates. A performance that is competitive with this is that produced by the backward method with the more conservative criterion (MI = 6.635). Consistently delivering the poorest performance, regardless of the chosen confidence level, was the factor-ratio test. Also discussed are the work’s contribution, implications, and limitations.

Keywords:

• backward modification index method
• factor-ratio test
• forward confidence interval method
• partial factorial invariance

Notes

¹ COV (ξ, δ) = Covariance between and δ.