ABSTRACT
Because measurements in the Behavioral and Social Sciences are often quite fallible, tests consist of a number of separate items whose responses are combined to obtain a more reliable test score (Cronbach, 1951). This, of course, only makes sense if all items measure the same attribute, which implies that their response probabilities should satisfy certain requirements embodied in a, say, common attribute criterion (CAC). To date, a CAC is formulated as a statistical model that explicitly contains a latent variable (CACL). The latent variable, say θ, represents the degree to which a subject possesses the common attribute. See Hambleton and Van der Linden (1997) for an overview. Because the interpretation of the latent variable is independent of a particular test, they are easily interpreted as the ‘true’ attribute. Consequently they are very attractive from a realist perspective (Borsboom, 2003, p. 49). However some conceptual problems arise.
