A dual latent class unfolding model for two-way two-mode preference rating data

In unfolding for two-way two-mode preference ratings data, the categorization of the set of individuals while the categories are represented in a low dimensional space may be an advisable procedure to facilitate their understanding. In addition to considering groups of individuals of a similar preference pattern, homogeneous groups of objects are also considered, such that within each group there are clustered objects perceived to have similar attributes. A dual latent class model is proposed for a matrix of preference ratings data, which will partition the individuals and the objects into classes, and simultaneously represent the cluster centers in a low dimensional space, while individuals and objects retain their preference relationship. Both the categories achieved and the unfolding configuration are estimated to be simultaneously optimal, by means of a conditional maximum likelihood estimation procedure, in a simulated annealing framework that enables us to take a statistical decision about the parameters of the model. The adjusted BIC statistic is employed to test the number of mixture components, and the dimensionality of the representation. Real and artificial data sets are analyzed to illustrate the model's performance.