Relating the Ramsay Quotient Model to the Classical D-Scoring Rule

Abstract

In a series of papers, Dimitrov suggested the classical D-scoring rule for scoring items that give difficult items a higher weight while easier items receive a lower weight. The latent D-scoring model has been proposed to serve as a latent mirror of the classical D-scoring model. However, the item weights implied by this latent D-scoring model are typically only weakly related to the weights in the classical D-scoring model. To this end, this article proposes an alternative item response model, the modified Ramsay quotient model, that is better-suited as a latent mirror of the classical D-scoring model. The reasoning is based on analytical arguments and numerical illustrations.