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Isotonic Ordinal Probabilistic Models (ISOP)

Published online by Cambridge University Press:  01 January 2025

Hartmann Scheiblechner
Hartmann Scheiblechner*
Affiliation:
Philipps Universität Marburg
*
Requests for reprints should be sent to Hartmann Scheiblechner, FB 04 Universität Marburg, Gutenbergstrage 18, D-35032 Marburg, FRG.
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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.

Keywords

sample-independenceisotonic regressionprobabilistic pair comparison systemsordinal instrumental independenceraw score systemsscoring functions
Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 2 , June 1995 , pp. 281 - 304
Copyright
Copyright © 1995 The Psychometric Society

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Footnotes

I wish to thank 3 reviewers and 2 editors who contributed a lot to the readability and precision of the article.

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