@article{oai:nagoya.repo.nii.ac.jp:00002430,
author = {村上, 隆 and MURAKAMI, Takashi},
journal = {名古屋大學教育學部紀要. 教育心理学科},
month = {Dec},
note = {Consider a data matrix Z, which is of the form : variables×subjects, and it can be partitioned into m sets of rows and g groups of columns. Z can be seen as an m×g super matrix, the elements of which are p_k×N_s matrices Z_'s (k=1,…, m; s=1,…, g). Assume that rows of Z_ have zero mean for each group, and have unit variance across all the groups. Let us call the data which can be arranged as Z multiset-multigroup one. This paper proposed a method for component analysis of multiset-multigroup data. The basic model is written as Z_=A_kC_G_s+E_, k=1,…, m, (1) s=1,…, g; where A_k is the p_k×q_k first order loading matrix for variables of k-th sets, C_ is the q_k×r_s second order loading matrix of s-th group on k-th first order components which are defined as F_≡C_G_s, (2) and G_s is the r_s×N_s second order component score matrix for s-th group; E_ denotes the p_k×N_s residual matrix. The basic model is a natural extension of Kroonenberg & de Leeuw (1977)'s TUCKER 2 model for three-mode data which can be written as Z_k=AC_kG+E_k, k=1,…, m, The criterion to be minimized is [numerical formula] under the constraints [numerical formula] and, G_s_s/N_s=I, s=1,…, g, (5) An alternating least squares algorithm, which is also a slight modification of TUCKALS 2 solving TUCKER 2 problem, is derived and it is adapted to handle the data with large N_s's. One of the most distinct feature of the output of this method is that the first ordr loading matrices can be interpreted as correlation matrices between variables and first order components such as [numerical formula] This hierarchical component model is not only able to explain the data more parsimoniously than individual analysis of each element matrix but also more sensitive to the group differences of loadings than analysis of all groups as a whole. An application for the data with two sets-Peer and Self ratings, and two groups-males and females was demonstrated as an illustrative example., 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。},
pages = {155--166},
title = {<原著>多集合-多群データの階層的主成分分析},
volume = {38},
year = {1991}
}