The weighted inner-product model is discussed for a class of techniques of multidimensional scaling incorporating individual differences. Data to be anlyzed are sets of arbitrary ones, from some individuals, expressing similarity between objects. The model discussed is such that an inner product of position vectors, in a space, corresponding to the objects represents given similarity between the objects. A set of parameters called weights is utilized for indicating individual differences. In order to determine the vectors and the parameters, a least-squares criterion to be minimized is defined. For minimization of the criterion, an iterative computation procedure is proposed considering quantitative data. The model and the procedure are further extended to treat ordinal data. Illustrative examples are attatched with using artificial data and real survey data.
In this paper we introduce a method which selects the differential reactions of personality using Sual Rosenzweig P-F Study.1) According to the above means of selection, we present a method to score the differential individuality of personality. Some classifications of personality are demonstrated as the application of the measurement of reactions.
In the method of triadic combinations three entities (stimuli, dissimilarities, etc.) are rank ordered in a specific order. When those entities are stimuli themselves, the subject is typically asked to choose, first, the most dominant stimulus among three stimuli presented at a time according to some prescribed criterion, and then the least dominant one among two remaining stimuli. If, on the other hand, those entities represent dissimilarities defined on a triad of stimuli, the subject is instructed to choose, among the three stimuli, the most similar stimulus pair and then the most dissimilar pair. In either case the procedure establishes an observed rank order among three entities. The rank order data collected by this method were conventionally analyzed by Thurstone's model of comparative judgments by reducing them to pair comparison data. A new approach to the method of triadic combinations is proposed in view of the fact that it is a special case of the directional ranking method (i.e., rank orderings are performed in a specific direction). A maximum likelihood estimation procedure is developed and implemented in the form of a FORTRAN program. An illustrative example is given to demonstrate the feasbility of the procedure.
PARAFAC is a three mode factor analytic method developed by R.A. Harshman and is useful for data analysis. The fundamental idea says xijk ≈ ?? ais bjs cks where xijk is given by measurement for i=1, 2…, I, j=1, 2, …, J, k=1, 2, …, K; ais, bjs, and cks are unknown solutions for the s-th factor, s=1, 2, ..., S. However the computer program of PARAFAC developed by Harshman seems to require great skill to understand how to handle it and select the optimal solution through many steps. Here a new fool-proof algorithm not to require any skill is presented.
Recent development of latent structure analysis due to Goodman (1974a, b) enabled us to build a cognitive model of perceptions of class, status and level of living. We propose a) that individuals covertly evaluate in a cognitive space their relative standing within the stratification systems, b) that two of the basic dimensions of the space pertains to cognition of the position in the labor market and life chances, c) that overt evaluation, i.e., identification, of class and level of living is derived from cognition in the first and second dimensions, respectively, but not jointly, and, d) that status identification is affected by the two types of cognition. To test our model, the SSM survey data collected in 1975 were used. The evidence obtained from the present analysis confirmed our propositions.