The Circles of Our Minds: A Nonparametric IRT Model for the Circumplex

A nonparametric item response theory (IRT) model for the circumplex is introduced, based on (1971) nonparametric IRT model for cumulative scaling, and (1984) nonparametric IRT model for unfolding. Some examples of circumplex representations in the social sciences are given. Model fit is based first on an extension of Loevinger’s coefficient of homogeneity using quadruples as elementary units of analysis. Diagnostics for the probabilistic circumplex are suggested. Assignment of (ordinal) scale values is based on the notion of item steps, as developed by (1983). The model presented here is based on dichotomous pick any/k data. Suggestions for extension to rank m/k data and to polytomous data are discussed.