This paper starts from the premise that the phenomena we behavioral scientists wish to understand, to explain and to evaluate are historical. It responds to Immanuel Wallerstein's challenge that “using the heavily narrative accounts of most historical research seems not to lend itself... to quantification.... It is a major tragedy of twentieth century social science that so large a proportion of social scientists, facing this dilemma, have thrown in the sponge.” It accepts the thesis of Gallie, Ricoeur and others that “history is a species of the genus story.” Real, deep understanding of such stories and of their component narrative structures requires knowledge of their possible trajectories and outcomes, i.e., the grammar of their plot possibilities. Hence all genuine, realistic explanations of politically interesting historical episodes must be based on prior, quasi-causal understandings of them and their possible alternatives (Wittgenstein: “Essence is expressed by grammar.”)
It is toward the scientific construction of such explanatory, evaluative or emancipatory understandings of world histories, that this paper is directed. Since the scientific literature on story structure may be said to have had its first exemplary discoveries in the analysis of Russian fairy tales (Propp, 1928), we start there and continue through the cognitive science literature on story grammars to Berke's work on the structure of tragedies, and more recent work on philosophical hermeneutics. Given this preliminary, non-exhaustive, but highly suggestive set of qualitative historical narrative/measurement devices, we discuss theorists of world politics in terms of their presupposed, mythic narrative structures: Toynbee, Forrester, Wallerstein and others. To the extent that any one of these illustrations is persuasive, the reader/listener will have accepted the (Wittgensteinian) thesis that the social and behavioral sciences are essentially based on myth.

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This paper proposes a new representation method of multivariate data by face pattern - termed as the face method - considering the human visual characteristics of facial expressions. The visual characteristics of facial expressions illustrated by the face pattern are analyzed by using multidimensional scaling (MDS), and psychometrical distances of facial expressions are then obtained from the configuration formed by MDS. A mathematical formulation of the proposed representation method is derived introducing the obtained psychometrical distances. The verification of the method is performed by some psychometrical experiments, and its efficiency is also tested applying in the classification of multivariate fossil data.

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The traditional factor analytic view of the PARAFAC model and its extension to a four mode situation with the derivation of the maximum likelihood estimation procedure by the generalized EM algorithm was presented. The four mode model was applied to six ASVAB data matrices defined by three specialty (clerical, mechanical, and electrical), times two services, (Air Force and Marine Corps) and successfully recovered the usual four dimensional structure without any rotation. The specialty and service differences was expressed in terms of different weighting of the common factor structure. A model which allows us to compare the factor score means was also investigated.

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This work intends to examine the effectiveness of a new approach, which is more fundamental than foregoing studies, to an analysis of accidents at railroad crossings. As a case study we deal with car accidents which occurred at single-track open crossings of Japanese National Railway. By applying the quantification method Types II and III analyses were made with a main focus on the type of accidents and from viewpoints of various human and physical factors. As a consequence it was apparent that the human factors gave some information, but was not much efficient. With respect to the physical factors, however, several important points for improvement of structure of crossings were suggested for the “front-crossing” accident, the most probable type of accident. Moreover it was suggested that the predictability of occurrence of accident, that is, a discrimination of types of accidents (front-crossing, other types, and no accident) was possible. Neverthless, considering that the number of samples for crossings with no accident were rather few, we must admit that the present model for the discrimination may not be so effective.

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Nonmetric multidimensional scaling which could be applied to a square asymmetric interstimulus proximity matrix is presented. In the model each stimulus is represented as a point and a circle (sphere, hypersphere) whose center is at that point in a multidimensional Euclidean space . The radius of a circle (sphere, hypersphere) tells the skew-symmetry of the corresponding stimulus. In a sense the model is a nonmetric generalization of Weeks and Bentler (1982)' s model. An algorithm to derive the coordinates of points and radii of circles (spheres, hyperspheres) which minimize the discrepancy of the coordinates and radii from the monotone relationship with given interstimulus proximities is described. An application to car switching data among 16 car segments is represented.

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A simple algorithm was developed for estimating optimal linear and quadratic classifiers (OLC & OQC) for non-normal multivariate predictor variables in two-group discriminant analysis. The algorithm is based on the alternating least squares (ALS) principle. The optimal classifiers compared favorably with the linear and quadratic discriminant function (LDF & QDF) methods in true error rate. Possible generalizations of the optimal classifier approach (ridge regression, robust regression based on the weighted least squares, etc.) were discussed.

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