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Additive Conjoint Isotonic Probabilistic Models (ADISOP)

Published online by Cambridge University Press:  01 January 2025

Hartman Scheiblechner
Hartman Scheiblechner*
Affiliation:
Philipps Universität
*
Requests for reprints should be sent to Hartmann Scheiblechner, FB 04 Universität Marburg, Gutenbergstraße 18, D-35032 Marburg GERMANY.
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Abstract

The ISOP-model or model of twodimensional or bi-isotonicity (Scheiblechner, 1995) postulates that the probabilities of ordered response categories increase isotonically in the order of subject “ability” and item ”easiness”. Adding a conventional cancellation axiom for the factors of subjects and items gives the ADISOP model where the c.d.f.s of response categories are functions of an additive item and subject parameter and an ordinal category parameter. Extending cancellation to the interactions of subjects and categories as well as of items and categories (independence axiom of the category factor from the subject and item factor) gives the CADISOP model (completely additive model) in which the parallel c.d.f.s are functions of the sum of subject, item and category parameters. The CADISOP model is very close to the unidimensional version of the polytomous Rasch model with the logistic item/category characteristic(s) replaced by nonparametric axioms and statistics. The axioms, representation theorems and algorithms for model fitting of the additive models are presented.

Keywords

ordered item response categoriesgraded response modelspolytomous modelsisotonicityisotonic regressioncancellationindependence of conjoint measurement factorsrating scale modelsnonparametric IRT modelsminimum ascending average algorithm MAAmatrix partial ordermultidimensional coordinatewise partial order
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 3 , September 1999 , pp. 295 - 316
Copyright
Copyright © 1999 The Psychometric Society

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