Tucker3 hierarchical classes analysis

This paper presents a new " model for binary three-way three-mode data, called Tucker3 hierarchical classes model (Tucker3-HICLAS). This new ' model generalizes Leenen, Van Mechelen, De Boeck, and Rosenberg's (1999) individual differences hierarchical classes mcxtel (INDCLAS). Like the INDCLAS model, the Tucker3-HICLAS model includes a hierarchical classification of the elements of each mode, and a linking structure among the three hierarchies. Unlike INDCLAS, Tucker3-HICLAS (a) does not restrict the hierarchical classifications of the three modes to have the same rank, and (b) allows for more complex linking structures among the thi'ee hierarchies. An algorithm to fit the Tucker3-HICLAS model is described and evaluated in an extensive simulation study. An application of the model to hostility data is discussed. Key words: three-way three-mode data, binary data, hierarchical lasses, multiway data analysis, cluster-ing