Progress in NIRT Analysis of Polytomous Item Scores: Dilemmas and Practical Solutions

  • Klaas Sijtsma
  • L. van der Andries Ark
Part of the Lecture Notes in Statistics book series (LNS, volume 157)


This chapter discusses several open problems in nonparametric polytomous item response theory: (1) theoretically, the latent trait θ is not stochastically ordered by the observed total score X+; (2) the models do not imply an invariant item ordering; and (3) the regression of an item score on the total score X+ or on the restscore R is not a monotone nondecreasing function and, as a result, it cannot be used for investigating the monotonicity of the item step response function. Tentative solutions for these problems are discussed. The computer program MSP for nonparametric IRT analysis is based on models that neither imply the stochastic ordering property nor an invariant item ordering. Also, MSP uses item restscore regression for investigating item step response functions. It is discussed whether computer programs may be based (temporarily) on models that lack desirable properties and use methods that are not (yet) supported by sound psychometric theory.


Differential Item Functioning Item Response Theory Latent Trait Item Response Theory Model Item Response Model 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Klaas Sijtsma
    • 1
  • L. van der Andries Ark
    • 1
  1. 1.Both authors are at the Department MTOTilburg UniversityTilburgThe Netherlands

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