Stochastic ordering using the latent trait and the sum score in polytomous IRT models

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 traitϑ. 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.