A Bayesian MIMIC Model for Testing Non-uniform DIF in Two and Three Groups

Multiple-indicator multiple cause (MIMIC) models have become a popular latent variable method to detect di erential item functioning (DIF) by practitioners. The ease of including groups for DIF testing and the implementation of MIMIC models in structural equation modeling software have helped drive the use of MIMIC models by applied researchers. However, there are several shortcomings within the methodological literature that are important questions yet to be addressed. First, only the case of two groups have been studied in simulations studies, yet practitioners are increasingly utilizing MIMIC models on more than two groups (e.g. Fleishman, Spector, & Altman, 2002; Sacco, Casado, & Unick, 2011; Sacco, Torres, Cunningham-Williams, Woods, & Unick, 2011; Woods, Oltmanns, & Turkheimer, 2009; Yang, Tommet, & Jones, 2009). Second, MIMIC models can be parameterized to test for non-uniform DIF (e.g. Woods & Grimm, 2011), but in current implementations Type I error rates were too high possibly due to assumption violations in the estimation of the latent interaction. Third, almost all previous simulations for MIMIC models have not considered the MIMIC model’s robustness to violations of the homogeneity of variance assumption (see Carroll, 2014 for an exception). A Monte Carlo simulation study was conducted to address these three shortcomings utilizing a 2 (number of groups) x 3 (latent variance di erences) x 3 (sample size imbalance) factorial design and comparing the proposed Bayesian MIMIC model with an improved version of Lord’s (1980) χ 2. Results of the simulation study indicated that when the assumption of homogeneity of latent variances held the Bayesian MIMIC model was a competitive method for assessing DIF. However, when the assumption was not met the Bayesian MIMIC