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 beli ef states that can be represented by a distributive lattice. By incorporati ng misclassification errors under local independence assumptions, the latti ce structure is transformed into a latent class model for observed response stares. We apply this model to survey responses dealing with government we lfare programs and suggest that our approach can retrieve information where unidimensional and multidimensional models do not fit. The concluding sect ion discusses directions future work.