Separating models, ideas, and data to avoid a paradox: Rejoinder to Humphry

This article is a rejoinder to Humphry’s (2013) comment on Sijtsma (2012). Sijtsma argued that the Rasch paradox does not exist but Humphry replies that the Rasch paradox can occur provided the measurement procedure is precise enough. The rejoinder argues that the debates about the Rasch paradox mingle properties of formal psychometric models, ideas about what people do when they respond to the items in a test, and the kind of data they produce. The three levels of formal models, ideas about response processes, and real data should be distinguished in order to prevent confusion. Then the conclusion remains that the Rasch paradox does not exist.
Keywords: debate on psychological measurement, Rasch paradox, theory as precursor for measurement