2022-01-17T07:50:51Zhttps://nagoya.repo.nii.ac.jp/oaioai:nagoya.repo.nii.ac.jp:000022922021-03-01T21:23:23ZHIERARCHICAL COMPONENT ANALYSIS OF MULTISET DATA多集合データのための階層的主成分分析村上, 隆6151MURAKAMI, Takashi6152Let us consider p sets of variables which correspond to different measurement domains. The data consisting of scores of N individuals on the variables of all the sets are called multiset data. Let us assume that n_k variables of each set are essentially multidimensional and several linearly independent composite scores can be constructed from them. Through the analysis of multiset data, one may wish to find out both composite scores for each set and their relationships across sets. There are two extreme methods for analyzing multiset data. One is the principal component analysis applied to each set separately followed by calculation of correlations between component scores; the other the canonical correlation analysis. The former is concentrated on the internal consistency; the latter on the correlations across sets. The problem which we confront with is almost equivalent to what Cronbach (1970) called the bandwidth-fidelity dilemma. As there is no optimal unique solution for the problem, one must find a compromise between opposite principles. We will propose a method, hierarchical component analysis, by which one can choose a solution which is the most balanced for his objective. The basic model is written as [numerical formula] where Z_k is n_k by N data matrix for set k, A_k is n_k by q_k loading matrix for set K, C_k is q_k by Q higher order loading matrix for set k, F is Q by N component score matrix, and E_k is n_k by N error matrix. Between the number of component of each set q_k and the number of higher order component Q, following restrictions are imposed; [numerical formula] Moreover, the model is subjected to following two constraints; [numerical formula] and [numerical formula] The Model is equivalent to separate component analysis when Q=Σq_k, and to simultaneous component analysis of all the sets when Q=q_1=...=q_p When Q is set to be large, the components for each set become internally consistent. On the other hand, when Q is set to be small, correlations of components between sets tend to be large. Therefore, one can seek the balanced solution by changing the number of higher order components. The alternating least squares algorithm is formulated and tested. And the model is generalized to be applicable to the partially three-mode data, that is, the data obtained on the variable sets some of which include the same variables. Through the generalization, it is shown that the quasi three-mode component analysis (Murakami, 1983) is a special case of the model proposed here.国立情報学研究所で電子化したコンテンツを使用している。departmental bulletin paper名古屋大学教育学部1986application/pdf名古屋大學教育學部紀要. 教育心理学科333548http://hdl.handle.net/2237/371503874796https://nagoya.repo.nii.ac.jp/record/2292/files/KJ00000726093.pdfjpn