Restricted factor analysis (RFA) is a powerful method to test for uniform differential item functioning (DIF), but it may require empirically selecting anchor items to prevent inflated Type I error rates. We conducted a simulation study to compare two empirical anchor-selection strategies: a one-step rank-based strategy and an iterative selection procedure. Unlike the iterative procedure, the rank-based strategy had a low risk and degree of contamination within the empirically selected anchor set, even with small samples. To detect nonuniform DIF, RFA requires an interaction effect with the latent factor. The latent moderated structural equations (LMS) method has been applied to RFA and has revealed inflated Type I error rates. We propose using product indicators (PI) as a more widely available alternative to measure the latent interaction. A simulation study, involving several sample-size conditions and magnitudes of uniform and nonuniform DIF, revealed that PI obtained similar power but lower Type I error rates, as compared to LMS.
Keywords: Differential item functioning; Factor analysis; Latent moderated structural equations; Measurement invariance; Product indicators.