Abstract
Hierarchical classes (HICLAS) models for multi-way multi-mode data constitute a unique family of classification models in that (a) they simultaneously induce a hierarchical classification (of the elements) of each mode and (b) they link the hierarchical classifications together by an association relation that yieldsa predicted (or reconstructed) value for each cell in the data array. For the case of three-way three-mode binary data, the most prominent HICLAS models include INDCLAS and Tucker3-HICLAS. In this paper, we compare the latter two models, introducing the underlying theory of both in substantive terms and showing how a Tucker3-HICLAS analysis may result in a simpler model than that yielded by INDCLAS, although the former is mathematically more complex than the latter (which it includes as a special case). We illustrate by two applications: astudy on anger responses in frustrating situations and a case-study on emotions in interpersonal relations.
Highlights
Since De Boeck and Rosenberg’s (1988) seminal paper on hierarchical classes, the Hierarchical classes (HICLAS) approach has expanded to a distinct family of classification models within the literature
This motivated the development of Tucker3HICLAS, which, like INDCLAS, implies a decomposition of a binary three-way three-mode array X into bundle matrices A, B, and C, but unlike INDCLAS, allows the bundle matrices to differ with respect to the number of columns
We present the results of an INDCLAS and Tucker3-HICLAS analysis of questionnaire data previously reported by Vansteelandt and Van Mechelen (1998)
Summary
Since De Boeck and Rosenberg’s (1988) seminal paper on hierarchical classes, the HICLAS approach has expanded to a distinct family of classification models within the literature. This motivated the development of Tucker3HICLAS, which, like INDCLAS, implies a decomposition of a binary three-way three-mode array X into bundle matrices A, B, and C, but unlike INDCLAS, allows the bundle matrices to differ with respect to the number of columns. On the one hand, the empty judge and symptom classes have disappeared in Tucker3-HICLAS, leaving simpler hierarchical classifications for these modes, while, on the other hand, the associations among the judges, patients, and symptoms (represented by the connections in the center of Figure 5) are slightly more complex than in the INDCLAS graph. Tucker3-HICLAS Model for the Hypothetical Data of Table 1
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