TRIPAT: a model for analyzing three-mode binary data

A discrete, categorical model is presented for three-mode (conditions by objects by attributes) data arrays with binary entries xijk 2 f0; 1g. Basically, the model attempts a simultaneous classification of the entities or elements of the three modes in a number of common clusters. Clusters are denied by three-mode submatrices of maximum size with entries xijk = 1. In performing a discrete representation of the data structure, the model may be classified as a non-hierarchical clustering procedure. It involves a reorganization of the data array such that the clustering solution is interpreted directly on the data, and it allows for overlapping as well as nonoverlapping clusters. The method is similar to three-mode component models such as CANDECOMP and SUMMAX in the model function to predict the data. An application concerning recall data in a study of social perception is provided.