Applicability of the Spatial Aggregation Model for Small Area Interpolation

Recently, spatial data set for fine zone scale becomes more important in urban planning. However, social or economic activity data such as transportation or production output are often difficult to get in the fine zone scale, due to the difficulties in survey. Comparing to these data, demographic data obtained in national census is able to easily get, so then an area interpolation by a regression approach can be applied to estimate the value of objective variable in fine zone. On the other hand, Modifiable Areal Unit Problem (MAUP), often cause a serious problem such as biased estimation of the statistical model parameter due to inadequate treatment for spatial dependencies in the spatial dependency matrix. This study develops a novel spatial econometric model with areal interpolation by using spatial aggregation matrix and spatial decomposition matrix. The proposed model fulfills the pycnophylactic property (i.e. spatial aggregation condition) between fine and source zone. We checked the performance of the proposed model by Monte Carlo simulation (MC) using hypothetical spatial data with the known value of parameters and the controlled error term. Moreover, we empirically examined the applicability of the proposed model for small area interpolation using the dataset in inter-regional passenger traffic. The estimated model proved that the proposed model can perform well for small area interpolation. Keyword: spatial econometric models, spatial aggregation matrix, pycnophylactic property JEL codes: C13(Estimation), C15(Statistical Simulation Methods), C51(Model Construction and Estimation), C52(Model Evaluation, Validation, and Selection) 1 Graduate School of Engineering, Hiroshima University, 4-1, Kagamiyama 1 chome, Higashi-Hiroshima 739-8527, Japan. E-mail: [email protected] 2 Graduate School of Engineering, Hiroshima University, 4-1, Kagamiyama 1 chome, Higashi-Hiroshima 739-8527, Japan. E-mail: [email protected]