Testing measurement invariance in a conditional likelihood framework by considering multiple covariates simultaneously.

This article addresses the problem of measurement invariance in psychometrics. In particular, its focus is on the invariance assumption of item parameters in a class of models known as Rasch models. It suggests a mixed-effects or random intercept model for binary data together with a conditional likelihood approach of both estimating and testing the effects of multiple covariates simultaneously. The procedure can also be viewed as a multivariate multiple regression analysis which can be applied in longitudinal designs to investigate effects of covariates over time or different experimental conditions. This work also derives four statistical tests based on asymptotic theory and a parameter-free test suitable in small sample size scenarios. Finally, it outlines generalizations for categorical data in more than two categories. All procedures are illustrated on real-data examples from behavioral research and on a hypothetical data example related to clinical research in a longitudinal design.