Stochastic Ordering Using the Latent Trait and the Sum Score in Polytomous IRT Models

Stochastic ordering properties are investigated for a broad class of item response theory (IRT) models for which the monotone likelihood ratio does not hold. A taxonomy is given for nonparametric and parametric models for polytomous models based on the hierarchical relationship between the models. (...

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Bibliographic Details
Published inPsychometrika Vol. 62; no. 3; pp. 331 - 347
Main Authors Hemker, Bas T, Sijtsma, Klaas, Molenaar, Ivo W, Junker, Brian W
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.09.1997
Psychometric Society, etc
Subjects
Biological and medical sciences
Fundamental and applied biological sciences. Psychology
Item Response Theory
Mathematical Models
Nonparametric Statistics
Ordering Operations
Polytomous Items
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Psychometrics. Statistics. Methodology
Statistics. Mathematics
Stochastic Analysis
Parametric method
Stochastic model
Item response theory
Non parametric method
Likelihood ratio
Ordering
Psychometrics
Monotonicity
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Summary:Stochastic ordering properties are investigated for a broad class of item response theory (IRT) models for which the monotone likelihood ratio does not hold. A taxonomy is given for nonparametric and parametric models for polytomous models based on the hierarchical relationship between the models. (SLD)
ISSN:0033-3123
1860-0980
DOI:10.1007/bf02294555