Geographical Review of Japan Vol. 66 (Ser. B), No. 2, 156-172, 1993 Effects of Spatial Interaction on Spatial Structure: A Case of Daycentre Location in Malmo Jun YAMASHITA* Abstract The locational structure effects on spatial interaction in distance-decay models have been discussed since the 1970s. This discussion has led many geographers to obtaine distance-decay parameters affected not by spatial autocorrelation but by friction of distance. As BENNETTet al. (1985) stressed, however, we should recognize that spatial structure and spatial interaction are interdependently related. Thus, the present study explores spatial interaction effects on spatial structure. First, using the SIMODEL developed by Williams and FOTHERINGHAM(1984), a distance-decay parameter was estimated for intra-urban trips travelled by pensioners to daycentres in Malmo, Sweden. In addition, location patterns of those daycentres and spatial autocorrelation between them were identified by the nearest neighbour measure and Moran's coefficient, respectively. Second, through solving a location-spatial interaction model, effects of spatial interaction on spatial structure were examined in three cases of distance-decay para meter. It was proven that the three cases of distance-decay parameter caused different location patterns. Combined with previous studies addressed to the spatial structure effects on spatial interaction, the interdependency between spatial interaction and spatial structure was ex plicated. Key Words: spatial interaction, spatial structure, spatial autocorrelation, location-spatial interac tion model, elderly care facility. ates2. In short, the spatial structure effects or I. INTRODUCTION the map pattern effects are defined as locational structure effects of origins and destinations on Relationship between spatial interaction and parameter estimates. As OKUNO (1981, p. 166) spatial structure has provoked controversy mentioned, these effects result from spatial after the development of gravity-type spatial autocorrelation within the parameter estimates. interaction modelsl. Especially, spatial structure To obtain distance-decay parameters affected effects on the spatial interaction have been the not by the spatial autocorrelation, but solitarily main subject of discussion over the last few by friction of distance, some spatial analysts decades. In the middle of the 1970s, CURRYand have presented several solutions. CLIFF and his colleagues (CURRY, 1972; CURRYet al., 1975; ORD (1981) suggested the spatial differenc SHEPPARDet al., 1976), CLIFF and his associates ing method which can weed straightforwardly (CLIFF et al., 1974, 1975, 1976), and JOHNSTON the spatial structure effects from auto (1975) intensively discussed the spatial struc correlated interactions, and some modified stat ture effects on the distance-decay parameter istics which rectify autoregressive errors. In ad calculated through gravity-type spatial interac dition, FOTHERINGHAM(1983) modified the pro tion models. Thereafter, some researchers, in duction constrained model so as to develop the cluding SHEPPARD(1978, 1979), and GRIFFITH competing destinations model, which might and JONES (1980), continuously mentioned the remove autocorrelation effects through embedd spatial structure effects on parameter estim ing the accessibility term in the production * Graduate student at Department of Social and Economic Grography , University of Lund, Solvegatan 13, S-223 62, Lund, Sweden Effects of Spatial Interaction on Spatial Structure 157 constrained model. within an urban area to avoid sampling error. To the contrary, little attention has been There are three large cities, namely, Stockholm, given to the spatial interaction effects on spa Gothenburg, and Malmo, in Sweden. One of tial structure. As BENNETTet al. (1985) pointed these cities, Malmo, was selected as the study out, the spatial structure not only affects spatial area. Besides, the present study intended to interaction, but also has the reaction from it. In solve location-allocation problem of facilities sum, we should recognize that the spatial inter providing services for users without exclusion action and the spatial structure are inter and rejection. This was the reason why public dependently related. Thus, the present study facilities, namely daycentres, were selected as explores the spatial interaction effects on spa the study objective. As a result, the intraurban tial structure using the location-spatial interac interaction travelled by elderly people to day tion model. centres was applied to the production con strained model. Malmo municipality has pro II. METHODS vided various social services for 340,000 cit izens, of which 48,000 were elderly people and Two steps were taken here as analytical almost all the elderly people were pensioners. A methods. First, using the production constrain variety of services has been provided to those ed model, a distance-decay parameter was cal pensioners at daycentres. For example, break ibrated amongst intra-urban trips to elderly fast, lunch and supper are served at restaurants care facilities. In addition, location pattern of within daycentres. Amusements, such as bil those facilities and the spatial autocorrelation liards, playing cards and chess, are offered amongst them were identified by the nearest there. The pensioners can also participate in neighbour measure (CLARK and EVANS, 1954) study circles, such as foreign language, textiles, and Moran's coefficient (MORAN,1950), respect and painting. As illustrated in Figure 1, Malmo ively. Second, through solving a location comprises 38 regions, in which 14 daycentres spatial interaction model based on the produc principally provide their services for pension tion constrained model, effects of spatial inter ers living within the jurisdictional boundary3. action on spatial structure were examined in In this study area, the central business district different cases of the distance-decay parameter. (CBD) is located around the old town and the 1. The Production constrained model The production constrained model developed by WILSON (1971) is formulated as follows: Tij=AiOiWƒÁjexp(ƒÀdij) (1) Ai=[ƒ°jWƒÁjrexp(ƒÀdij)]-1 (2) Oi=ƒ°jTij(3) where Tij: the interaction between regions i and j, Ai: the balancing factor, Oi: the total outflows at region i, Figure 1. Study area in Malmo. Wj: the attraction term, Note. 1. Fridhem 2. Ribersborg 3. Dammfri 4. Kronprinsen 5. Kronborg 6. Gamla Staden 7. dij: the distance between regions i and j, Davidshall 8. Radmansvangen 9. Mollevangen 10. ƒÀ: the distance-decay parameter, Sodervarn 11. Heleneholm 12. Sofielund 13. Augustenborg 14. Rorsjostaden 15. Varnhem 16. ƒÁ: the mass parameter. Vastra Sorgenfri 17. Ostra Sorgenfri 18. Rulltofta 19. Kirseberg 20. Segevang 21. Mellanheden 22. Limhamn Calibration of the distance-decay parameter 23. Djupadal 24. Sibbarp 25. Solbacken 26. Kroksback 27. Sodertorp 28. Kulladal 29. Lindeborg 30. Eriksfalt in this production constrained model requires a 31. Nydala 32. Gulivik 33. Hidby 34. Lundangen 35. large amount of aggregated interaction data Rosengarden 36. Hoja 37. Almgarden 38. Skravlinge. 158 J. YAMASHITA city faces the North Sea on its northern bound were provided through interviews with dir ary so that the built-up area has been expand ectors at each daycentre. Since public transporta ing southward since the Second World War. In tion dominates daily activities of pensioners accordance with the extension of the city, popu (see also, HERBERT and PEACE, 1980; SMITH, lation has been growing on the urban fringe, 1984), the separation term (dij) was determined and in turn the potential value of the elderly by time distance between centroids at each population gently declines from region No. 2 region derived from a bus time table in Malmo4. towards the urban fringe (see Figure 2). In this Here, distance within the same region was meas figure, we find four regions with high elderly ured by one-half time distance from a centroid population, namely regions No. 2, 13, 15 and 24. to the nearest one5. With the help of Multi In the production constrained model, the in dimensional scaling (MDS) method, initial lat teraction term (Tij) was measured by the tices were reassembled to an appropriate inter number of elderly visitors from their residential action space with less stress (GATRELL,1979)6. sites to the daycentres. Out of the 14 day Fortunately, a powerful and reliable calibration centres, 12 were in operation and the other two program for the various spatial interaction were under renovation in February, 1992 (see models, SIMODEL, was developed by WILLIAMS Figure 3). Thereby, the number of trips (Tij) was and FOTHERINGHAM(1984). This program en counted at the 12 daycentres through a ques abled us to offer proper parameter estimates for tionnaire survey. In geographical studies on both distance-decay and mass parameters. Fi shopping behaviour, the attraction term (Wj) nally, some measures of the goodness-of-fit was often represented by total floor area at each tested the performance of the SIMODEL. retail store. From analogy of those studies, the BAXTER(1983) argued, however, that there is no total floor area at each daycentre was used as single acceptable measure of goodness-of-fit on the index of the attraction term. The floor data the spatial interaction models and recom mended the use of several different measures for examining performance by different spatial interaction models. KNUDSENand FOTHERINGHAM (1986) supported this argument and stress ed that the coefficient