In this paper, we propose a linked vector multiple correlation analytical graph, where given data are transformed to ranked ones, and propose a new measure which expresses the degree of multiple correlation quantitatively. Weights of contribution of explanatory variables to an objective variable can be determined from this measure. This measure is considered to be reasonable by comparing both with the results of the method by human eyes, and with the one of multiple regression analysis for data which are transformed to ranked data.
A latent factor, which will be called as “prognostic factor”, is extracted from nine explanatory variables observed mainly at the time of surgery from categorical principal component analysis, and it is shown that the factor has the appropriate meaning of prognosis measured on the postsurgical survival periods. Zero value on the prognostic factor is reflected to about five years on the postsurgical survival periods, and it is shown that positive values (or negative values) on the factor mean elongation more than (or shortening less than) about five years on the postsurgical survival periods. Further, this fact is confirmed by categorical canonical discriminant analysis of the same data. The effect of adjuvant chemotherapy is detected in the interaction with the serosal invasion, and elongation of about 34 months on the survival periods is obtained as the significant difference between the treated group with chemotherapy and the control group, at s1 category in serosal invasion.
Some intriguing relationships among four methods of metric and nonmetric multidimensional scaling (MDS) are explicated. It is shown that all four methods of MDS considered here amount to solving, explicitly or implicitly, the stationary point of a matrix which can be generally represented as A'HA, where A is a difference matrix (to be defined), and where H depends on a particular criterion being optimized. H may be a matrix of fixed constants or of functions of unknown parameters (stimulus coordinates) of the representation model. A conceptual distinction is made as to the scale level of measurement in reference to MDS methods and solutions.
Though the study of social indicator is now in the fashion, the social indicator useful both for people and for administrators has neither been modeled nor established probably because of lack of mutual agreements on the methodology. The main purpose of the paper is to analyze objective data and develop a new weighting model for social indicator. We first apply the statistical method (principal component analysis, PCA) to the selection of welfare items. Next, the information thus obtained is utilized to compose the weight for social indicator. Results are compared with weights based on the opinion surveys, and two interpretations given to the similarity of weighting order.