Cumulative or adjacent logits: Which choice for an ordinal logistic latent variable model?

ABSTRACTWith ordinal response items, a graded response model (GRM) is of cumulative logits type, while the polytomous Rasch model (PRM) is based on adjacent logits. In this work, we compare the two approaches. We show that the PRM is superior to the GRM, with interesting properties that we prove. Note Sν the sum of item responses of individual ν and Θν its latent parameter; we show i) Sν is a sufficient statistic for θν and ii) a property of “stochastic ordering” of the conditional distributions Gθ/S. The second property, less known, is, to our knowledge, nowhere satisfactorily demonstrated.