The Orders of Central Functions and the Hierarchical Central Places System

Abstract

Vining argued that a hierarchy of central places did not exist and verified that the class system of central places derived from a previous partitioning of an array which appeared as differentiation along a continuum. However, between 1958 and 1967, a number of important papers were published by Berry, Garrison, Barnumn, and Tennant. These papers dealt with taxonomic methods for the empirical study of the hierarchical class system and the extention of central place theory into a more general theory of tertiary activities, Berry's central place theory.In his Snohomish County study, the hierarchical class system of central places was shown to follow from the class system of central functions on the basis of their ranked threshold populations. Furthermore, in his southwest Iowa study, the orders of entry of central functions into central places were presented, using factor analysis. Berry has introduced the concept of threshold as the basis of grouping of central functions and has attemped to reform Christaller's central place theory without the assumption of uniformity concerning purchasing power which was basic to a hexagonal complementary region. The argument requires the concepts of range and threshold which are related to Christaller's concepts of outer and inner limits of the range of a good respectively. But it appears that Berry's central place theory depends on the incorrect interpretation of Christaller's theory. In Berry's theory, the development of a hierarchy depends on the existence of certain range of a good (the trade area of a marginal hierarchical good), related to the threshold size which is the minimum amounts of purchasing power for the supply of a marginal hierarchical good, similar to the lower limit of the range of a good. On the other hand, in Christaller's theory, it depends on the size of a complementary region related to the outer limit of the range of a marginal hierarchical good, which is based on the concept of a hexagonal complementary region. The hierarchical structure, the relation between the orders of central functions and the levels of central places, does not depend on the concepts of range and threshold, but on the concepts of range and complementary region.In agreement with this interpretation of the hierarchical structure, the aim of this paper is to propose the procedure for grouping of 60 central functions by factor analysis, and to show that the orders of central functions are distinct from the groups of central functions.The methods of analysis and the results are as follows.(1) As the results of applications of factor analysis to three kinds of data matrices consisting of the incidence matrix, the establishment matrix, and the central place matrix, it is only in the factor analysis of the central place matrix that factors reveal clearly a distinctive factor pattern. In the central place matrix, sizes of central places are ranked in the column on the base of numbers of functions performed and 60 central functions are ranked in the rows.(2) The factor analysis of the central place matrix with 60 variables (central functions) yields three factors which indicate the presence of three orders of central functions. i.e. lower-middle-higher central functions. In spite of the extractions of three factors, all central functions can not be grouped in three class systems by factor lordings or correlations of 60 variables with each of three factors, for some central functions are under the influence of two or three factors.(3) Similarly, the factor analysis of the central place matrix with 48 variables (sizes of central places) yields three factors which indicate the presence of three levels of central places, i.e. lower-middle-higher central places, and all central functions can be grouped in eight class systems.