1999/09/01 by Hartman Scheiblechner · 5 citations
Decision Sciences · Computer Science · Mathematics · #Multi-Criteria Decision Making #Bayesian Modeling and Causal Inference #Psychometric Methodologies and Testing #Mathematics #Polytomous Rasch model #Axiom #Rasch model #Item response theory #Nonparametric statistics #Additive model #Local independence #Probabilistic logic #Independence (probability theory) #Representation (politics) #Statistics #Psychometrics
paper · doi:10.1007/bf02294297
openalex publication_date 1999/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23
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.