Connected Categorical Canonical Covariance Analysis for Three-mode Three-way data Sets Based on Tucker Model

When we work with two three-mode three-way data sets, such as panel data, we often investigate two types of factors: common factors, which represent relationships between the two data sets, and unique factors, which show the uniqueness of each data set relative to the other. We propose a method for investigating common and unique factors simultaneously. Canonical covariance analysis is an existing method that allows the estimation of common and unique factors simultaneously; however, this method was proposed for use with two-mode two-way data, and it is limited to quantitative data. Thus, applying canonical covariance analysis to three-mode three-way data sets or to categorical data sets is not suitable. To overcome this problem, we build on the concept of the Tucker model and the concept of non-metric principal component analysis to develop and propose a method suitable the analysis of categorical three-mode three-way data sets. Moreover, we introduce connector matrices, making it easy to determine which factors are common and allowing the selection of different numbers of dimensions for the factors.