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多集合データのための階層的主成分分析
https://doi.org/10.18999/bulfep.33.35
7756fbe795cc41d8bf56452c776288b4
名前 / ファイル  ライセンス  アクション  

KJ00000726093.pdf (1.1 MB)


Item type  紀要論文 / Departmental Bulletin Paper(1)  

公開日  20060106  
タイトル  
タイトル  多集合データのための階層的主成分分析  
その他のタイトル  
その他のタイトル  HIERARCHICAL COMPONENT ANALYSIS OF MULTISET DATA  
著者 
村上, 隆
× 村上, 隆× MURAKAMI, Takashi 

抄録  
内容記述  Let 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 bandwidthfidelity 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 threemode 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 threemode component analysis (Murakami, 1983) is a special case of the model proposed here.  
内容記述タイプ  Abstract  
内容記述  
内容記述  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。  
内容記述タイプ  Other  
出版者  
出版者  名古屋大学教育学部  
言語  
言語  jpn  
資源タイプ  
資源  http://purl.org/coar/resource_type/c_6501  
タイプ  departmental bulletin paper  
ID登録  
ID登録  10.18999/bulfep.33.35  
ID登録タイプ  JaLC  
ISSN（print）  
収録物識別子タイプ  ISSN  
収録物識別子  03874796  
書誌情報 
名古屋大學教育學部紀要. 教育心理学科 巻 33, p. 3548, 発行日 1986 

フォーマット  
application/pdf  
著者版フラグ  
値  publisher  
URI  
識別子  http://hdl.handle.net/2237/3715  
識別子タイプ  HDL 