Measurement Invariance with Ordered Categorical Variables

Multi-item ordered categorical scales and structural equation modelling approaches are often used in panel research for the analysis of latent variables over time. The accuracy of such models depends on the assumption of longitudinal measurement invariance (LMI), which states that repeatedly measured latent variables should effectively represent the same construct in the same metric at each time point. Previous research has widely contributed to the LMI literature for continuous variables, but these findings might not be generalized to ordered categorical data. Treating ordered categorical data as continuous contradicts the assumption of multivariate normality and could potentially produce inaccuracies and distortions in both invariance testing results and structural parameter estimates. However, there is still little research that examines and compares criteria for establishing LMI with ordinal categorical data. Drawing on this lack of evidence, the present chapter offers a detailed description of the main procedures used to test for LMI with ordered categorical variables, accompanied by examples of their practical application in a two-wave longitudinal survey administered to 1,912 Italian middle school teachers. The empirical study evaluates whether different testing procedures, when applied to ordered categorical data, lead to similar conclusions about model fit, invariance, and structural parameters over time.