, Volume 60, Issue 2, pp 281–304

Isotonic ordinal probabilistic models (ISOP)

  • Hartmann Scheiblechner

DOI: 10.1007/BF02301417

Cite this article as:
Scheiblechner, H. Psychometrika (1995) 60: 281. doi:10.1007/BF02301417


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.

Key words

sample-independenceisotonic regressionprobabilistic pair comparison systemsordinal instrumental independenceraw score systemsscoring functions

Copyright information

© The Psychometric Society 1995

Authors and Affiliations

  • Hartmann Scheiblechner
    • 1
  1. 1.FB 04 Universität MarburgMarburgFRG