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Uniqueness of real-valued hierarchical classes models. (English) Zbl 1204.91114

Summary: Two novel uniqueness theorems are derived for the family of hierarchical classes (HICLAS) models, a family of structural decomposition models for \(N\)-way \(N\)-mode data that imply simultaneous hierarchically organized classifications of all modes involved in the data. The theorems generalize earlier results on binary HICLAS models to the integer- and real-valued cases. In addition, they allow for a shorter and insightful proof of a result on Boolean matrix invertibility that goes back to earlier work of R. D. Luce [Proc. Am. Math. Soc. 3, 382–388 (1952; Zbl 0048.02302)] and D. E. Rutherford [Proc. Glasg. Math. Assoc. 6, 49–53 (1963; Zbl 0114.01701)].

MSC:

91C15 One- and multidimensional scaling in the social and behavioral sciences
62J15 Paired and multiple comparisons; multiple testing
15B34 Boolean and Hadamard matrices
62P12 Applications of statistics to environmental and related topics

Software:

Tucker3-HICLAS
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References:

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