Articlegreen1997

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

Bas T. Hemker · Klaas Sijtsma · Ivo W. Molenaar · Brian W. Junker

156 citations0/0 files storedPsychometrika

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Statistical Methods and Bayesian Inference

Abstract

In a restricted class of item response theory (IRT) models for polytomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait ϑ. MLR implies two stochastic ordering (SO) properties, denoted SOM and SOL, which are both weaker than MLR, but very useful for measurement with IRT models. Therefore, these SO properties are investigated for a broader class of IRT models for which the MLR property does not hold. In this study, first a taxonomy is given for nonparametric and parametric models for polytomous items based on the hierarchical relationship between the models. Next, it is investigated which models have the MLR property and which have the SO properties. It is shown that all models in the taxonomy possess the SOM property. However, counterexamples illustrate that many models do not, in general, possess the even more useful SOL property.

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References

2012Applications of Item Response Theory To Practical Testing Problems 1982A Rasch Model for Partial Credit Scoring 1978A Rating Formulation for Ordered Response Categories 1968ESTIMATION OF LATENT ABILITY USING A RESPONSE PATTERN OF GRADED SCORES1 1969Estimation of Latent Ability Using a Response Pattern of Graded Scores 1992A Generalized Partial Credit Model: Application of an EM Algorithm 1972Estimating Item Parameters and Latent Ability when Responses are Scored in Two or More Nominal Categories 1971A Theory and Procedure of Scale Analysis

Cited by

2000Latent and Manifest Monotonicity in Item Response Models 2016PerFit : An R Package for Person-Fit Analysis in IRT 2008Nonparametric IRT analysis of Quality-of-Life Scales and its application to the World Health Organization Quality-of-Life Scale (WHOQOL-Bref)2001The Use of Restricted Latent Class Models for Defining and Testing Nonparametric and Parametric Item Response Theory Models 2008Nonparametric Person-Fit Analysis of Polytomous Item Scores 1998

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