Invariance of Comparisons: Separation of Item and Person Parameters beyond Rasch Models

Abstract: The Rasch model is the most prominent member of the class of latent trait models that are in common use. The main reason is that it can be considered as a measurement model that allows to separate person and item parameters, a feature that is referred to as invariance of comparisons or specific objectivity. It is shown that the property is not an exclusive trait of Rasch type models but is also found in alternative latent trait models. It is distinguished between separability in the theoretical measurement model and empirical separability with empirical separability meaning that parameters can be estimated without reference to the other group of parameters. A new type of pairwise estimator with this property is proposed that can be used also in alternative models. Separability is considered in binary models as well as in polytomous models.