The author proposed in 1971 one of the optimal scoring methods for detecting clusters and interrelations from multi-way qualitative data, adopting the maximization of squared multiple correlation coefficient as a criterion for scoring. In the present paper, we make clear the meaning of adopting this criterion from the viewpoint of linear regression analysis. Then the method is formalized into more convenient form for computing program, with some related properties. The method has been successfully applied to several sets of artificial three-way binary data whose structures are known beforehand, as well as actual three-way categorical data of anxiety-ridden neurotic patients.
A new procedure is discussed which represents the asymmetric relationships between N objects. These relationships must be defined at the interval levels of measurement in Steven's terminology. This method not only reveals the clustering of the objects but also enables us to give information about both the magnitude and the orientation of the “skewness” between objects in “a” configuration. The procedure optimizes the fit of the model directly to the data by an alternating least squares procedure. It is found to be robust, as the Hessian Matrix of the loss function is positive definite at least in two dimensional case, except for a special case. The method is illustrated with an artificial data and three empirical data.
We treat in this paper the problems which arise in judging whether to visit a hospital for people in incomplete health. Solving these problems will contribute significantly to the induction of an index indicating the necessity for visiting a hospital. Our method is to examine the relation between hospital visiting behaviour and health status, and the relation between the doctors' judgements and the subscribers', applying multiple discriminant analysis to the data on subjective symptoms, laboratory examination, and hospital visiting behaviour obtained from an AMHTS. The results imply the possibility that we can construct an index based only on subjective symptom data which are easily obtained.
In order to analyze the pattern of the geographical and age distributions of the cancer death, the correlation coefficients between any pairs of cancer mortality rates of each site were calculated, using the data on cancer for 18 sites in males and 19 sites in females over the three periods, i.e., (1) from 1958 to 1962, (2) from 1963 to 1967, and (3) from 1968 to 1971. Then factor analysis by varimax method was performed on 54 × 54 correlation matrix for males and 57 × 57 matrix for females. As a result, five factors are extracted, which are commonly recognized in both males and females. Among the five factors extracted, the first one attracted us most, since the fact that bone, bladder, skin and buccal cancers as well as cancers of genital organs excluding ovary clustered in one group suggests a possible relation of those cancers to high atmospheric temperature.
Dr. Hayashi developed one of methods for multidimensional scaling problem, named MDA. This method is a very useful one, but its computation is very difficult. In the present paper, the author shows a modification of its computation with some numerical examples in one dimensional case.