Measurement Equivalence of Ordinal Items: A Comparison of Factor Analytic, Item Response Theory, and Latent Class Approaches

Three distinctive methods of assessing measurement equivalence of ordinal items, namely, confirmatory factor analysis, differential item functioning using item response theory, and latent class factor analysis, make different modeling assumptions and adopt different procedures. Simulation data are used to compare the performance of these three approaches in detecting the sources of measurement inequivalence. For this purpose, the authors simulated Likert-type data using two nonlinear models, one with categorical and one with continuous latent variables. Inequivalence was set up in the slope parameters (loadings) as well as in the item intercept parameters in a form resembling agreement and extreme response styles. Results indicate that the item response theory and latent class factor models can relatively accurately detect and locate inequivalence in the intercept and slope parameters both at the scale and the item levels. Confirmatory factor analysis performs well when inequivalence is located in the slope parameters but wrongfully indicates inequivalence in the slope parameters when inequivalence is located in the intercept parameters. Influences of sample size, number of inequivalent items in a scale, and model fit criteria on the performance of the three methods are also analyzed.