Algebraic Representations of Beliefs and Attitudes: Partial Order Models for Item Responses

A partial order of discrete beliefs based on a generalization of item order in Guttman scaling generates a nonunidimensional collection of latent belief states that can be represented by a distributive lattice. By incorporating misclassification errors under local independence assumptions, the lattice structure is transformed into a latent class model for observed response states. We apply this model to survey responses dealing with government welfare programs and suggest that our approach can retrieve information where unidimensional and multidimensional models do not fit. The concluding section discusses directions for future work.