Abstract
The concept of an ordinal instrumental probabilistic comparison is introduced. It relies on an ordinal scale given a priori and on the concept of stochastic dominance. It is used to define a weakly independently ordered system, or isotonic ordinal probabilistic (ISOP) model, which allows the construction of separate “sample-free” ordinal scales on a set of “subjects” and a set of “items”. The ISOP-model is a common nonparametric theoretical structure for unidimensional models for quantitative, ordinal and dichotomous variables.
Fundamental theorems on dichotomous and polytomous weakly independently ordered systems are derived. It is shown that the raw score system has the same formal properties as the latent system, and therefore the latter can be tested at the observed empirical level.
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Scheiblechner, H. Isotonic ordinal probabilistic models (ISOP). Psychometrika 60, 281–304 (1995). https://doi.org/10.1007/BF02301417
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DOI: https://doi.org/10.1007/BF02301417