A latent trait system is a set of subjects A, a set of items X, and a response function r, mapping A x X into the real numbers. Numerical representations of such a system map A and X into the reals, such that r is represented by a numerical operation. It is shown for an additive latent trait system that its internal structure may be characterized by its automorphism group and that homogeneity and uniqueness of this group make the system ratio scalable. A non-additive case is also considered. Here the two factors are combined in a non-additive way, but the systems internal structure induces an independent system on one of the two factors which is interval-scalable.
Dieser Eintrag ist Teil der Universitätsbibliographie.
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