Measurement equivalence: a comparison of methods based on confirmatory factor analysis and item response theory

Current interest in the assessment of measurement equivalence emphasizes 2 major methods of analysis. The authors offer a comparison of a linear method (confirmatory factor analysis) and a nonlinear method (differential item and test functioning using item response theory) with an emphasis on their methodological similarities and differences. The 2 approaches test for the equality of true scores (or expected raw scores) across 2 populations when the latent (or factor) score is held constant. Both approaches can provide information about when measurement nonequivalence exists and the extent to which it is a problem. An empirical example is used to illustrate the 2 approaches.