“…Several commonly used models and associated test statistics have been developed to detect DIF as a function of membership in observed groups (like gender or ethnicity), including the Mantel-Hansel test (Holland & Thayer, 1988), the standardization method (Dorans & Kulick, 1986), the logistic regression model (for example, Swaminathan & Rogers, 1990), the IRT-based chi-square test (Lord, 1980;Wright & Stone, 1979), the likelihood ratio test (IRT-LRT; Thissen, Steinberg, & Wainer, 1988;Wang & Yeh, 2003), and the multiple indicators multiple causes (MIMIC : Muthén, 1985;1989) model.…”