Von Davier, Holland, and Thayer (2004) laid out a five-step framework of test equating that can be applied to various data collection designs and equating methods. In the continuization step, they presented an adjusted Gaussian kernel method that preserves the first two moments. This article proposes an alternative continuization method that…

Two classes of graded response models, one based on the work of L. L. Thurstone and the other on the work of G. Rasch, are juxtaposed and shown to satisfy important but mutually incompatible criteria and to reflect different response processes. Implications of the choice between these models are discussed. (Author/SLD)

A unidimensional model for responses to statements that have an unfolding structure was constructed from the cumulative Rasch model for ordered response categories. A joint maximum likelihood estimation procedure was investigated. Analyses of data from a small simulation and a real data set show that the model is readily applicable. (SLD)