Polytomous IRT Models and Monotone Likelihood Ratio of the Total Score

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

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

Abstract

In a broad class of item response theory (IRT) models for dichotomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait θ . In this study, it is shown that for polytomous items MLR holds for the partial credit model and a trivial generalization of this model. MLR does not necessarily hold if the slopes of the item step response functions vary over items, item steps, or both. MLR holds neither for Samejima's graded response model, nor for nonparametric versions of these three polytomous models. These results are surprising in the context of Grayson's and Huynh's results on MLR for nonparametric dichotomous IRT models, and suggest that establishing stochastic ordering properties for nonparametric polytomous IRT models will be much harder.

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References

1932A technique for measurement of attitudes 1961Probabilistic Models for Some Intelligence and Attainment Tests 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

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