Modelling sequentially scored item responses

The sequential model can be used to describe the variable resulting from a sequential scoring process. In this paper two more item response models are investigated with respect to their suitability for sequential scoring: the partial credit model and the graded response model. The investigation is carried out by first deriving a property of sequential scoring, which will be called item characteristic curve invariance, and then demonstrating that the partial credit model and the logistic graded response model do not accommodate this property. Therefore, when either of these two models is applied to sequentially scored variables, a specification error is made.