We will review the application of multidimensional scaling models and methods in the geography from 1960 to 1990 briefly. Multidimensional scaling models and methods have been developed and applied in the many research fields, such as psychology and behavioral sciences. In the geography, multidimensional scaling methods have been used as one of methods of metric analysis and method for analyzing the human behavior. Methods for preference data have been used as method for assessment of land usage. The characteristics in these applications is that the obtained configurations are compared with the actual geographical location of cities and other market areas. We also review the asymmetric multidimensional scaling model, which are based on the modified distance model.
Most studies of time-space convergence in urban systems have used Multi-Dimensional Scaling (MDS). However, two-dimensional configuration in these studies cannot be always regarded as geographic map, particularly for a long-term qualitative change. Q-analysis, a topological language, enables us to understand that change. The objective of this paper is considering methodologies of MDS and Q-analysis in time-space convergence studies. Two studies of time-space convergence in Japan, Murayama's MDS and the author's Q-analysis, are compared from a methodological view. The MDS method reduces multi-dimensional metric space to two-dimensional one, but that tends to break original adjacent relationships. Q-analysis can describe the structure of topological relationships among cities, using the concepts of local dimensionality, nearness, and connectivity. While MDS focuses on the origin and distance, Q-analysis is applicable to a long-term uneven transportation development.
The university enrollment flow among Japanese 47 prefectures for 31 years from 1972 through 2002 was analyzed. University enrollment flow data in the present study consist of 31 tables. Each table is 47×47, the (j, k) element of the i-th table, corresponding to year i, is the number of high school graduates in prefecture j who entered into universities in prefecture k in year i. If we regard the number of high school graduates in prefecture j who entered into universities in prefecture k as the similarity from prefectures j to k, these 31 tables are prefecture×prefecture×year (47×47×31) two-mode three-way similarities. Each table is not necessarily symmetric, because the number of high school graduates in prefecture k who entered into universities in prefecture k is not necessarily equal to those in prefecture j who entered into universities in prefecture j. The two-mode three-way asymmetric similarities were analyzed by the external analysis of two-mode three-way asymmetric multidimensional scaling, where the longitude and the latitude of the capitol of each prefecture were given as the externally given two-dimensional configuration of 47 prefectures. In the external analysis the two-dimensional configuration of 47 prefectures was unaltered. The result of the analysis is compatible with earlier studies obtained by analyzing similar data. The present result showed two large university enrollment regions centered at Tokyo and at Kyoto respectively which also had been suggested by several studies. The present result was compared with the result of the internal analysis of (usual) two-mode three-way asymmetric multidimensional scaling. While the result of the external analysis exaggerated asymmetric relationships among prefectures, two analyses gave results which had similar characteristics in nature.
The aim of this paper is to review the applications of multidimensional scaling (MDS) to the studies of behavioral geography focusing on the spatial analysis of cognitive maps. Although various studies have applied MDS to the spatial cognition or environmental evaluation in other fields, a notable feature of geographic approach lies in the emphasis on careful scrutiny of the spatial patterns and their relationship with geographic environments. Accordingly, methods of spatial analysis for comparing the configurations obtained by MDS with actual maps and aggregating individual data have been developed. This comprises bidimensional regression and standard deviational ellipse. However, several problems remained in the previous studies: methods for analyzing asymmetric nature of cognitive distances, dimensionality of cognitive maps, and hierarchical structure of the spatial knowledge.
Gravity model and it's extended model have been used as models for location analysis in geography. In these models, it was assumed that distance from the origin to the destination was given. However, it is difficult how to measure this distance since the inhabitant of the origin can access to the destination by the several access paths. Multidimensional scaling (MDS) or multidimensional preference model will be applicable in this case for recovering the map in hidden data. Other hand, MDS models try to decompose dissimilarity to distance between 2 points only and are lock of modeling the intensity of the destination or the market. A new model and method will be proposed in this paper, in which the intensity of the destination and distance between the origin and the destination is combined. An application to the real data set will be shown.
In this paper, we restructure the “garbage can model” proposed by Cohen et al. (1972), making its simulation process visible for examination. Previous studies assume that, under “unsegmented structure,” combinations of problems, decision-makers, and solutions are shifted, and decisions are made depending on timing. However, the results of this paper are different. Under “unsegmented structure,” decision-makers (and occasionally problems) move together and their combinations do not change. In addition, it is under “hierarchical structure” that decisions are made depending on timing. Besides, it becomes clear that these results from the simulation actually happen. While demonstrating the simulation process to a manager of a firm, we realized that decision-makers' (and problems') behavior under “unsegmented structure” could be observed in the firm. The review of a case study by March & Romelaer (1976) suggests that decisions depending on timing under “hierarchical structure” can be observed in actual organizations. Through these analyses, two advantages of making the simulation process visible are also clarified. First, it is a convenient tool for confirming the simulation's numerical results and their implications. Second, when we apply the results to an actual organization, it proves to be a strong tool promoting the conversations with managers or staff.
Several researchers have analyzed the brand-switching matrix using multidimensional scaling models. When a brand-switching matrix is analyzed using multidimensional scaling, it is necessary to rescale the matrix because there are differences among the overall sums of the rows and columns that depend on external factors, such as market share. This study introduces a new method that rescales one-mode two-way proximity matrices using entropy which shows the variance of brand-switching. In the present paper, we calculate the entropy of a row and column of a car-switching data, and use the result to reconstruct a new matrix. Then we analyze this matrix using multidimensional scaling. The results suggest that the congurations rescaled using our method can be interpreted as “circumplex”.
The present report analyzes Japanese high school students' fundamental language skills of their mother tongue over the span of a decade. Of special emphasis, are the changes incurred in such trends amongst these students. The Broad-Range Japanese Fundamental Language Skills Test (BRJFLST) was used for the assessment. It consists of a vocabulary comprehension and a Chinese character pronunciation subscale, calibrated with 2PLM based on IRT. Performances of Year 2003 participants were compared with those of 1991-1992 participants. Among the results, a considerable decline was found in the vocabulary level of students in top schools. Accordingly, the necessity for introducing well-organized, long-term investigations based on measurement theories in Japanese school education was discussed.