施設数行列に基づく中心地の階層区分法

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The hierarchical classification of central places, according to the analysis of multivariate data by a quantitative method, is a fundamental and important issue in a study of central place system. Therefore, the methodology based on the analysis of central establishments has been improved until now. Such methods as the location coefficient technique by Davies, factor analysis, principal component analysis, Beavon's method, cluster analysis, have been frequently used. However, each method has advantages and disadvantages so that we must examine its own characteristics. The main aim of this paper is to point out a feature in each method and search a more efficient method to measure the centrality (nodality) of central places. Prior to the concrete examination of methods, we begin to check the following points as the conditions for an efficient method: First, concerning the data, the matrix consisted of the numbers of central establishments is far more reliable than the incidence matrix just indicating the existence of a central function or not. The reason is that the incidence matrix causes not only a loss of the information but also depends on an unadaptable concept of 'threshold population' introduced by Berry and Garrison. Some of geographers indicate that the threshold population is really often neglected for the occurrence of each central function. Second, we decide to adopt the nodality (absolute centrality) rather than the centrality (relative centrality) in Christaller's sense, which is extremely difficult to measure and utilize. Third, it is more convenient to evaluate the nodality by a numerical value, concerning the analysis of recent changes in the nodality of each central place. For this reason, we avoid to adopt Beavon's method and a cluster analysis, which might have any advantage. From these points of view, we analyse the nodality of 87 central places in Okayama prefecture, which have 52 central functions, by using a rank order method and a metric MDS method, plus the methods above mentioned. The result is that we can get the most relevant hierarchical classification of central places, when we employ the coordinates of the first dimension for the metric MDS method and the first principal component scores for the principal component analysis which comes from the variance-covariance matrix and/or cross-product matrix instead of the correlation matrix. On the contrary, both the factor analysis and the principal component analysis in which the correlation matrix is adopted, can not produce a suitable result because the correlation coefficient can not measure the size difference between central places with similar central functions.
地理科学学会の論文

施設数行列に基づく中心地の階層区分法

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