THE INFLUENCE OF MAP PATTERN EFFECT IN SPATIAL INTERACTION MODELS

Abstract

The purpose of this paper is to clarify in detail the influence of map pattern effect on distance parameters in spatial interaction models. This issue has previously been stated by Curry (1972). This paper is based on a study of migration in 1978, and journey-to-work in 1975, which crosses shi (city), machi (town) and mura (village) boundaries in Shiga Prefecture. Figure 1 shows the distribution of these municipal units and their boundaries in Shiga Prefecture. The study uses a doubly-constrained entropy type model, as shown in equation (3). Distance parameter a is calculated using equation (6), which is developed by Kadas and Klafszky (1976). Table 1 shows the results obtained. A map pattern effect consists of the following three elements: (1) inter-point distances (leading element) (2) variation of the value of O or D (supplementary elemants) (3) covariance of values of O and D at the same point Nearest neighbor measure R, spatial autocorrelation statistic (standard deviate of Moran coefficient I) and correlation coefficient r provide a simple technique for measuring (1), (2) and (3) respectively. Matrix of distances (cost of travelling) cij is obtained from both road distance and time from i to j, because it is expected that the physical barrier of Lake Biwa, located in the center of the study area, may distort inter-point distances measured by a straight line. Therefore, element (1) and (2) were investigated using a two dimensional configuration of multi dimensional scaling (Fig. 2). Stress is 6.4% with road distance data, and 9.1% with time distance data. Table 2 shows the map pattern effect in relation to the empirical data. According to this analysis, 50 points show a clustered pattern rather than a purely random pattern (R=1). A simulation model was developed to examine more a comprehensive influence of map pattern effect and to overcome the restraints of intra-urban journey-to-work in previous studies. Three basic patterns were assumed, each pattern including 25 points (Fig. 3). Hypothetical urban area configurations, shown by dotted lines, were obtained from cluster analysis of the locations, which are indicated by X and Y coordinates. Therefore, spatial interaction in a regular pattern can be regarded as only inter-urban, that in a random pattern as both inter-urban and intra-urban, and that in a clustered pattern as only intra-urban. The following assumptions are made: (1) A positive autocorrelation effect operates at an intra-urban level. (2) A positive or negative autocorrelation effect operates at an inter-urban level. (3) For that interaction occurring only at an intra-urban level, sum of O is equal to that of D in an urban area. These assumptions reflect the differences between the two types of interaction. One is a phenomenon occurring only at an intra-urban level, for example, journey-to-work. The other is a phenomenon occurring at both the inter-urban and the intra-urban levels, as represented by migration. In assumption (2), positive autocorrelation is concerned with the latter type of interaction, while negative autocorrelation is concerned with the former. A flow chart of the simulation model is shown in Fig. 4. One hundred distance parameter values per pattern were generated and a total of three hundred values were obtained. An analysis of variance (F=114.95*) to test the significant difference in variation of distance parameters shows the strong influence of the map pattern effect. Absolute values of the distance parameters are lowest in the random pattern and highest in the clustered pattern. That metropolitanization is now under way in Shiga Prefecture means that a nearest neighbor measure approaching a clustered pattern should occur in the future. That value should consequently become larger eventually.