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

With 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 S_ν the sum of item responses of individual ν and Θ_ν its latent parameter; we show i) S_ν is a sufficient statistic for θ_ν and ii) a property of “stochastic ordering” of the conditional distributions G_θ/S. The second property, less known, is, to our knowledge, nowhere satisfactorily demonstrated.