To construct the discriminant function for the diagnosis of CPD, the equality of the two covariance matrices were studied. Two were different significantly, which means the use of linear discriminant function for this case is not reasonable. According to the above conclusion, the quadratic discriminant function with 18 variables were derived and ratios of correct diagnosis were compared. Ratios of correct diagnosis by the former are 84% in the CPD group and 97% in the non-CPD group respectively in comparison with 74% and 82% by the latter. By the random number simulation, the quadratic discriminant function turned out to be unexpectedly stable. Our CPD diagnosis system with the quadratic discriminant function by means of on-line computer is mentioned.
In this paper we have formulated a fuzzy-fuzzy relation which is an extension of the fuzzy one, and have investigated its properties. Using some characteristic property which holds in a family of special fuzzy grades, we have introduced an equivalence relation in an ordinary set. Finally we have demonstrated a classification by the equivalence relation.
For a data matrix composed of subjects by rank orders, a hierarchical clustering method is presented, which partitions subjects into statistically homogeneous clusters on the basis of Kendall's coefficient of concordance W. The algorithm has been found to work successfully. Illustrative examples of the clustering of real data are offered. The method is useful for both preliminary analysis and confirmatory analysis of nonmetric multidimensional scaling of rank order data, especially in large samples. This method is also compared with other hierarchical clustering methods.
By extending the path analytic method, a new algorithm for causal modeling in epidemiological etiologies is developed, which is based mainly on simple correlation coefficients. The utility of the proposed analysis is assessed, relative to cluster analysis, factor analysis, and multiple regression analysis. As the result of this evaluation, it is suggested that multivariate analysis should be used together with causal modeling, since multivariate analysis, especially factor analysis, appears to be a useful tool of confirming the estimated causal model.
In the present paper we present a method of constructing a system dynamics model. When multiple variables are given, we sum them up by principal component analysis. By utilizing the extracted principal components we construct simultaneous differential equations concerning the original variables. Our method has two characteristics. First, usual factor analysis, etc., are restricted to the estimation of the causality between the latent variables and the original variables on their functional relations. Our method can explain dynamic mutual effects among the original variables. Second, contrary to the usual constructions of system dynamics models, our method does not require to give a priori the latent variable (i.e., it is time in usual system dynamics models.) and minimizes subjective judgemrnt in determining the parameters of the model. In the latter half of the paper we give an example of an application of our method to actual data and discuss the implications of the model given by the interpretation of the obtained simultaneous differential equations.
A quantification method was developed for sorting data collected over a sample of subjects. Given multiple sets of sorting data this method finds, in a multidimensional Euclidian space, a configuration of points in such a way that the sum of squared inter-cluster distances averaged over subjects is maximized under suitable normalization conditions. Examples were given to illustrate the use of the method and its relationship to other scaling methods was discussed.