Assessing Measurement Equivalence in Ordered-Categorical Data

Abstract

Assessing measurement equivalence in the framework of the common factor linear models (CFL) is known as factorial invariance. This methodology is used to evaluate the equivalence among the parameters of a measurement model among different groups. However, when dichotomous, Likert, or ordered responses are used, one of the assumptions of the CFL is violated: the continuous nature of the observed variables. The common factor analysis of ordered-categorical data (CFO) has been described in several works, but none evaluate its power and Type I error rate in the evaluation of measurement equivalence (ME). In this simulation study, we evaluated ME under four different conditions: size of group (300, 500 and 1000), type of DIF (thresholds, loadings), amount of DIF (0.25, 0.40), and equality/impact of the distributions. The parameters used for the data generation came from one scale with nine items with three ordered categories. The results were evaluated according to three decision rules: a) the significance of the difference in chi-square values obtained in two nested models, b) the significance of the difference in chi-square values between two nested models with Bonferroni corrections, and c) the difference between the values of the Comparative Fix Index (CFI) obtained in two nested models. The results showed good power as well as good control of the false positives for both the chi-square Bonferroni correction and CFI difference index.