| Abstract: |
In this paper, we focus on the modeling of a specific type of three-way three-mode binary data that often occurs in personality psychology, the modes of which consist of (1) persons, (2) situations, and (3) mediating cognitive-affective variables (CAV) as well as behaviors. Underlying such data, personality psychologists typically assume a two-step sequential process situation -> CAV -> behavior, the two steps of which may be characterized in terms of if-then links. It is further hypothesized that these two types of if-then links may differ across persons. An important challenge for personality psychology then consists of retrieving the place and the nature of the key individual differences in the process under study. To meet this challenge, we present a new classification model, called CLASSI, that belongs to the family of hierarchical classes models. The latter is a family of multiway classification models for binary data that constitute the Boolean counterparts of three-mode principal component models for real-valued data. The new CLASSI model includes two core arrays that represent the two types of if-then links, as mentioned above, as well as individual differences therein. A simulated annealing algorithm for fitting the CLASSI model to data is discussed. |
