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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.

Analysis of University Enrollment Flow among Japanese Prefectures by Using External Analysis of Asymmetric Multidimensional Scaling