Detecting Differential Item Functioning with Confirmatory Factor Analysis and Item Response Theory: Toward a Unified Strategy

Document Type


Publication Date



item response theory, differential item functioning, mean and covariance structures, measurement equivalence, confirmatory factor analysis, thresholds, sample size, IRT, DIF, CFA, MACS

Digital Object Identifier (DOI)



In this article, the authors developed a common strategy for identifying differential item functioning (DIF) items that can be implemented in both the mean and covariance structures method (MACS) and item response theory (IRT). They proposed examining the loadings (discrimination) and the intercept (location) parameters simultaneously using the likelihood ratio test with a free-baseline model and Bonferroni corrected critical p values. They compared the relative efficacy of this approach with alternative implementations for various types and amounts of DIF, sample sizes, numbers of response categories, and amounts of impact (latent mean differences). Results indicated that the proposed strategy was considerably more effective than an alternative approach involving a constrained-baseline model. Both MACS and IRT performed similarly well in the majority of experimental conditions. As expected, MACS performed slightly worse in dichotomous conditions but better than IRT in polytomous cases where sample sizes were small. Also, contrary to popular belief, MACS performed well in conditions where DIF was simulated on item thresholds (item means), and its accuracy was not affected by impact.

Was this content written or created while at USF?


Citation / Publisher Attribution

Journal of Applied Psychology, v. 91, issue 6, p. 1292-1306