ISOTONIC ORDINAL PROBABILISTIC MODELS (ISOP)

The concept of an ordinal instrumental probabilistic comparison is int roduced. It relies on an ordinal scale given a priori and on the conce pt of stochastic dominance. It is used to define a weakly independentl y ordered system, or isotonic ordinal probabilistic (ISOP) model, whic h allows the construction of separate ''sample-free'' ordinal scales o n a set of ''subjects'' and a set of ''items''. The ISOP-model is a co mmon nonparametric theoretical structure for unidimensional models for quantitative, ordinal and dichotomous variables. Fundamental theorems on dichotomous and polytomous weakly independently ordered systems ar e derived. It is shown that the raw score system has the same formal p roperties as the latent system, and therefore the latter can be tested at the observed empirical level.