A GENERALIZED DEFINITION OF INTERACTIONS AND SINGULAR VALUE DECOMPOSITION OF MULTIWAY ARRAYS
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概要
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A generalized definition of the sth order interactions is given for multiway arrays, from which the similar properties with ANOVA model are derived. The problem of maximization of the highest order correlation function is solved. Moreover, an expression decomposing multiway arrays is shown as a recurrent algorithm that is an extension of the singular value decomposition of matrices. Applications of the decomposition to multiway contingency tables and to the multiway classified data are outlined. This research develops Iwatsubo(1974)and Yoshizawa(1975), and relates with Bahadur's expression and Lancaster's definition of no interaction for contingency tables. The definition and expression given here are more general and constructive than theirs.
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