核因子マトリックスによるTグループの学習動機の変動の解析

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According to Eckart and Young (1936) 's theorem, it is possible to dissolve a given observed data matrix Y intoY=U∧V′ (9)Here U′U=V′V=I and ∧ shows the square roots of the eigenvalues. And further, following Tucker (e. g., 1964), Levin (1965) derivedY=(U∧)∧-1(V∧)′=U∧-1V′=(UT)(P′∧T)-1(VP)′=A G B′ (10)Here, T and P are the orthogonal rotational matrices. By the least square method, it is possible to estimate G in the following manner:G=(A′A)-1A′YB(B′B)-1=A′YB (11)(cf. Tucker, 1966). G was called the core factor matrix. When X is assumed to be a factor score matrix in the conventional sense, the formula (11) may beG≈A′X (15)This shows the principle of the “points of view” procedure in multiple factor analysis (cf. Cliff, 1968).It seems usual to estimate A and B through the simultaneous factorization of YY′ and Y′Y. However, the factorization sometimes fails to assure salient estimated values of weights (or factor loadings) under the assumed number of components (or factors). The present author propose to estimate the weights through simultaneous factorization of correlational matrices based upon YY′ and Y′Y rather than YY′ and Y′Y, and to substitute the obtained weights into A and B. This is our revised “points of view” procedure in factor analysis, and seems to be a very practical one.Bradford (1965) assumed three components concerning motivation for learning in T-group. They consist of individual defensive motivation moving to individual nondefensive feelings (1 st component), group defensive motivation concerned with survival and loyality moving to stages of group maturity in which there is support and acceptance of deviancy (2 nd component), and release of driving forces of trust and desire for individual growth and to help others (3rd component).First of all, using 23 T-group data which are based on 1 item 7 point. questionaire concerning group cohesiveness (cf. The footnote a) of Table 1), we performed the factorization including the orthogonal rotation of session by session correlational matrices, and found that all the assumed components appeared beautifully in the T-group all the members of which succeeded in learning. On the other hand, in the T-group some of members of which failed to learn, the components did not always appear beautifully (cf. Table 1 & Fig. 1). Here we used the principal component analysis and the varimax rotational method. The results suggested to factorize the space of the members of the T-group, too. In other words, they suggested that our “points of view” procedure could be applicable to the analysis of learning process in T-group. We assumed two factors in the members, and rotated the components of learning process under four factors. Here we used the complete centroid factorization and the orthogonal rotational method by the present author (1965).By the core factor matrices (members by components), it will be possible to know that trainers make their judgements for T-group based on the third component of learning. This was followed from the fact that at least an interrelational value (not normalized) between the divided members and their corresponding third components in G was largest (cf. Table 2). And it may be suggested that reproduced data matrix fits
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核因子マトリックスによるTグループの学習動機の変動の解析

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