Journal of the Korean Geographical Society (대한지리학회지)

The Korean Geographical Society (대한지리학회)
권호 표지

Effects of the Modifiable Areal Unit Problem (MAUP) on a Spatial Interaction Model

공간 상호작용 모델에 대한 공간단위 수정가능성 문제(MAUP)의 영향

  • Kim, Kam-Young (Department of Geography Education, Kyungpook National University)
  • 김감영 (경북대학교 사범대학 지리교육과)
  • Received : 2011.02.09
  • Accepted : 2011.04.19
  • Published : 2011.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

Due to the complexity of spatial interaction and the necessity of spatial representation and modeling, aggregation of spatial interaction data is indispensible. Given this, the purpose of this paper is to evaluate the effects of modifiable areal unit problem (MAUP) on a spatial interaction model. Four aggregation schemes are utilized at eight different scales: 1) randomly select seeds of district and then allocate basic spatial units to them, 2) minimize the sum of population weighted distance within a district, 3) maximize the proportion of flow within a district, and 4) minimize the proportion of flow within a district. A simple Poisson regression model with origin and destination constraints is utilized. Analysis results demonstrate that spatial characteristics of residuals, parameter values, and goodness-of-fit of the model were influenced by aggregation scale and schemes. Overall, the model responded more sensitively to aggregation scale than aggregation schemes and the scale effect on the model was varied according to aggregation schemes.

공간 상호작용의 복잡성, 공간적 재현과 모델링의 필요성에 의해서 공간 상호작용 데이터의 합역이 불가피하다. 이러한 상황에서 본 연구의 목적은 공간 상호작용 데이터를 스케일을 달리하여 합역하거나 혹은 동일 스케일에서 합역 방식을 달리하여 합역하였을 때, 공간 상호작용 모델의 결과가 어떻게 달라지는지 평가하는 것이다. 공간 상호작용 데이터의 합역은 공간단위 수정가능성의 문제(Modifiable Areal Unit Problem: MAUP)를 야기한다. 공간 상호작용 데이터의 합역을 위하여 무작위로 구역 시드를 선정한 후 인접한 공간단위를 할당하는 방법, 구역 시드와 공간단위 사이의 연구 가중 거리를 최소화하는 방법, 구역 내 상호작용 비율을 최대화하는 방법, 구역 내 상호작용 비율을 최소화하는 방법을 사용하였다. MAUP의 영향을 평가하기 위한 공간 상호작용 모텔로 기원지-목적지 제약 포아송 회귀 모델을 이용하였다. 분석 결과는 모델 잔차의 공간적 특성뿐만 아니라 파라미터 추정값, 적합도 등이 MAUP의 영향을 받는다는 것을 보여주었다. 모델은 합역 방식 보다는 합역 수준에 더 민감하게 반응하였고, 모델에 대한 스케일 효과는 구획 방식에 따라 상이하게 나타났다.

Keywords

Acknowledgement

Supported by : 한국학술진흥재단

References

  1. Alvanides, S., Openshaw, S., and Duke-Williams, O., 2000, Designing zoning systems for flow data, in Atkinson, P. and Martin, D., (eds.), GIS and Geocomputation. Innovation in GIS 7, Taylor and Francis, London, 115-134.
  2. Amrhein C. G. and Flowerdew R., 1992, The effect of data aggregation on a Poisson regression-model of Canadian migration, Environment and Planning A, 24(10), 1381-1391. https://doi.org/10.1068/a241381
  3. Barras, R., Broadbent, T. A., Cordy-Haynes, M., Massey, D. B., Robinson, K., and Willis, J., 1971, An operational urban development model for Cheshire, Environment and Planning A, 3(2),115-234. https://doi.org/10.1068/a030115
  4. Batty M. and Sikdar, P. K., 1982a, Spatial aggregation in gravity models. 1. An information-theoretic framework, Environment and Planning A, 14(3), 377-405. https://doi.org/10.1068/a140377
  5. Batty M. and Sikdar, P. K., 1982b, Spatial aggregation in gravity models: 2. One-dimensional population density models, Environment and Planning A, 14(4), 525-553. https://doi.org/10.1068/a140525
  6. Batty M. and Sikdar, P. K., 1982c, Spatial aggregation in gravity models: 3. Two-dimensional trip distribution and location models, Environment and Planning A, 14(5), 629-658. https://doi.org/10.1068/a140629
  7. Batty M. and Sikdar, P.K., 1982d, Spatial aggregation in gravity models: 4. Generalisations and largescale applications, Environment and Planning A, 14(6), 795-822. https://doi.org/10.1068/a140795
  8. Brown, L. A. and Holmes, J. H., 1971, The delimitation of functional regions, nodal regions and hierarchies by functional distance approaches, Journal of Regional Science, 11(1), 57-72. https://doi.org/10.1111/j.1467-9787.1971.tb00240.x
  9. Chun, Y., 2008, Modeling network autocorrelation within migration flows by eigenvector spatial filtering, Journal of Geographical Systems, 10(4), 317-344. https://doi.org/10.1007/s10109-008-0068-2
  10. Flowerdew, R. and Aitkin, M., 1982, A Method of Fitting the Gravity Model Based on the Poisson Distribution, Journal of Regional Science, 22(2), 191-202. https://doi.org/10.1111/j.1467-9787.1982.tb00744.x
  11. Fotheringham, A. S. and O'Kelly, M. E., 1989, Spatial Interaction Models: Formulations and Applications, Kluwer Academic Publishers, Dordrecht, Netherlands.
  12. Guo, D., 2009, Flow Mapping and Multivariate Visualization of Large Spatial Interaction Data, IEEE Transactions on Visualization and Computer Graphics, 15(6), 1041-1048. https://doi.org/10.1109/TVCG.2009.143
  13. Hirst, M. A., 1977, Hierarchical aggregation procedures for interaction data: a comment, Environment and Planning A, 9(1), 99-103. https://doi.org/10.1068/a090099
  14. Kim, K., 2004, Heuristic approaches for p-median location-allocation problem, Journal of Geography Education, 48, 14-30.
  15. Kim, K., Lee, G., and Shin, J., 2010, A study on reconstructing of local administrative districts using spatial analysis and modeling, Journal of the Korean Association of Regional Geographers, 16(6), 673-688 (in Korean).
  16. Kim, K., Shin, J., Lee, G., and Cho, D., 2009, A location model and algorithm for visiting health-care districting for the rural elderly, Journal of the Korean Geographical Society, 44(4), 813-831 (in Korean).
  17. Lee, S., 1999, The delineation of function regions and modifiable areal unit problem, Journal of Geographical and Environmental Education, 7(2), 757-783 (in Korean).
  18. LeSage, J. P. and Pace, R. K., 2008, Spatial econometric modeling of origin-destination flows, Journal of Regional Science, 48(5), 941-967. https://doi.org/10.1111/j.1467-9787.2008.00573.x
  19. Masser, I. and Brown, P. J. B. (eds.), 1978, Spatial Representation and Spatial Interaction, Martinus Nijhoff Social Sciences Division, Boston.
  20. Masser, I. and Brown, P. J. B., 1975, Hierarchical aggregation procedures for interaction data, Environment and Planning A, 7(5), 509-523. https://doi.org/10.1068/a070509
  21. Masser, I. and Scheurwater, J., 1980, Functional regionalisation of spatial interaction data: an evaluation of some suggested strategies, Environment and Planning A, 12(12), 1357- 1382. https://doi.org/10.1068/a121357
  22. Nelder, J. A. and Wedderburn, R. W. M., 1972, Generalized Linear Models, Journal of the Royal Statistical Society A, 135(3), 370-384. https://doi.org/10.2307/2344614
  23. Openshaw, S. and Taylor, P. J., 1981, The modifiable areal unit problem, in Wrigley, N. and Bennett, R. J., (eds.), Quantitative geography: a British view, Routledge, London, 60-69.
  24. Openshaw, S., 1977a, A geographical solution to scale and aggregation problems in region-building, partitioning, and spatial modelling, Transactions of the Institute of British Geographers, NewSeries2, 459-472. https://doi.org/10.2307/622300
  25. Openshaw, S., 1977b, Optimal zoning systems for spatial interaction models, Environment and Planning A, 9(2), 169-184. https://doi.org/10.1068/a090169
  26. Putman, S. H. and Chung, S-H., 1989, Effects of spatial system design on spatial interaction models. 1: The spatial system definition problem, Environment and Planning A, 21(1), 27-46. https://doi.org/10.1068/a210027
  27. Ravenstein, E. G., 1885, The laws of migration, Journal of the Statistical Society of London, 48(2), 167- 235. https://doi.org/10.2307/2979181
  28. Slater, P. B., 1976, A hierarchical regionalization of Japanese prefectures using 1972 interprefectural migration flows, Regional Studies, 10(1), 123- 132. https://doi.org/10.1080/09595237600185121
  29. Slater, P. B., 1981, Comparisons of aggregation procedures for interaction data: An illustration using a college student international flow table, Socio-Economic Planning Sciences, 15(1), 1-8. https://doi.org/10.1016/0038-0121(81)90012-4
  30. Teitz, M. B. and Bart, P., 1968, Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph, Operations Research, 16(5), 955-961. https://doi.org/10.1287/opre.16.5.955
  31. Tiefelsdorf, M. and Boots, B., 1995, The specification of constrained interaction models using the SPSS loglinear procedure, Geographical Systems, 2, 21-38.
  32. Tiefelsdorf, M., 2003, Misspecifications in interaction model distance decay relations: a spatial structure effect, Journal of Geographical Systems, 5(1), 25-50. https://doi.org/10.1007/s101090300102
  33. Webber, M. J., 1980, A theoretical analysis of aggregation in spatial interaction models, Geographical Analysis, 12(2), 129-141.