The Modifiable Areal Unit Problem,in a Regression Model Whose Independent Variable Is a Distance from a Predetermined Point

This paper deals with the modifiable areal unit problem in the context of a regression model where a dependent variable is an attribute value (say, income) of an atomic data unit (say, a household) and an independent variable is a distance from a predetermined point (say, a central business district) to the atomic data unit (a disaggregated model). We apply this disaggregated model to spatially aggregated data in which the dependent variable is the average income over a spatial unit and the independent variable is the average distance from each household in a spatial unit to the predetermined point (an aggregated model). First, estimating the slope coefficient by the least squares method, we prove that the variance of the estimator for the slope coefficient in the aggregated model is larger than that in the disaggregated model. Second, focusing on variations in the variance of the estimator for the slope coefficient in the aggregated model with respect to the number of zones, we obtain the number of zones in which the variance is close to that in the disaggregated model. Third, we obtain the zoning system that has the minimum variance for a fixed number of zones. We also calculate the maximum variance in order to examine the range of the variance.     

中日全面战争后的在日华侨、印侨网络

以近代日本在成为亚洲主权国家过程中经济方面的经历为线索,将居住在神户的华侨和印侨作为研究对象,探讨了华侨通商网络在20世纪30年代得以扩展、1940年后衰退的原因;简述了30年代起印侨通商网络的显著发展;揭示了欧洲近代帝国主义的本质与亚洲华侨、印侨通商网络的形成与扩展间的密切关系。