Progress in NIRT analysis of polytomous item scores : Dilemmas and practical solutions

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.

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