This project addresses the modeling of latent variables that are manifested through a mixture of dominance and proximity questions. Dominance (or monotone) items are those for which a stronger agreement or higher score on the item or question is directly related to the respondent having a higher value on the underlying latent trait. Proximity (or unfolding) items are those where the relationship between the strength of the response and the value of the underlying latent trait is non-monotonic, depending instead on the distance between the location of the item and the respondent on the same latent continuum. Initially, an item response theory (IRT) model will be formulated, where the item type is treated as a latent class, and the model is estimated through an expectation-maximization algorithm. The second portion of the project involves the application of the model to three recent, representative studies which utilized only a dominance or monotone model originally, as well as its application to experimental data collected specifically to have both types of items. The final portion of the project involves the dissemination of the research findings, including web-based resources to make the methodology available to practitioners at large.
Historically, no methods have been available for simultaneously modeling dominance and proximity items. This has forced the developers of questionnaires and surveys to construct their instruments out of a single type of item. From the statistical standpoint, the model resulting from this project will serve as a "bridge" between monotone and unfolding models and will further the development of mixture-based approaches to IRT models more generally. From the practitioner's standpoint, the wide availability and easy implementation of models for identifying and analyzing mixtures of dominance and proximity items will provide for the analysis of survey items, roll-call, and other voting data, and a host of other choice-based phenomena. It will allow practitioners to directly test theories concerning the processes generating data across a wide range of fields, reconciling methods that have been at odds for the better part of a century.
