多边形统计数据空间分析的不确定性研究——以北京市海淀区人口普查数据为例

普查数据是地理学空间分析的重要数据源。由于受到数据与计算机处理能力的限制,以往的研究对普查数据空间分析的不确定性未给予足够重视,也未形成成熟的研究方法。在建筑物单元的人口普查数据支持下,本文基于多边形统计数据的可塑面积单元问题(Modifiable areal unit problem,MAUP)特征,设计了一种该类数据空间分析不确定性的研究方法,采用不同的尺度(Scale)及分区(Zoning)系统对多边形的统计数据空间分析的准确性进行了分析。实验引入尺度与形态指数,利用可视化分析和数据拟合的研究方法,对尺度及分区对空间分析结果的影响模式进行了模拟。研究结果表明:(1)以统计小区的空间分析,其结果受统计小区空间形态的影响较大,不确定性强,不能充分反映统计数据本身的空间特征;(2)规则格网能较好地保持原始统计数据的空间分布特征,但仍然受尺度及分区影响;(3)规则格网的空间分析结果及其准确性与尺度有较好的拟合关系,不同尺度下的分析结果不确定性是原始数据不同尺度特征的体现;(4)分区效应受空间分析方法的计算尺度影响,两者共同对空间分析结果产生影响。对于固定尺度的规则格网,其邻接多边形数目是分析结果不确定的主要原因。本文研究结果表明,在多边形统计数据空间分析时,应该对其使用规则格网重新聚合,并根据实际应用的需求选择多尺度分析方法,以达到实际应用目的。

The Uncertainty of Polygon-based Statistical Data Spatial Analysis: Case of Census Data of Haidian District, Beijing

In statistic geographic information system, census data, stored as polygon attribute, is a kind of polygon- based statistical data. Moreover, in the studies of geography and social science, polygon-based statistical data is a main data source for uncovering spatial patterns of social phenomena by spatial analysis. However, due to the limitation of data and restriction of computer processing power, uncertainty of polygon-based statistical data spatial analysis is always ignored, and there is no well methodology for analyzing such uncertainty. To address this question, we developed a method concerning modifiable areal unit problem (MAUP) to evaluate uncertainty of polygon-based statistical data spatial analysis. The population data collected from each buiding in Beijing makes the mehtod applicable. For MAUP, we considered it as scale and aggregation separately. For polygon- based statistical data, we applied census data of Haidian District (Beijing) with polygons of buildings as its georeference. With this method, we introduced scale and shape indices and applied visual analysis and data fitting to detect the uncertainty of five analysis methods: Sum, Mean, Standard deviation, Global Moran's I and Anselin Local Moran's I (LISA). In addition, the relationships between scale, shape indices and the five analysis methods are also revealed in order to demonstrate the way that MAUP affects polygon-based statistical data spatial analysis. The result of the research shows as follows: (1) the results derived from census data spatial analysis with normal census tracts as zone system are arbitrary and have great uncertainty. (2) The results derived from census data spatial analysis with regular nets as zone system well describe the spatial patterns of original data, but still depend on the scale and zoning of the net system. (3) The results derived from census data spatial analysis with regular grid as zone system, are functionally related to the scale of the grid system, and the uncertainty of the results represents multi-scale spatial patterns of original data. And (4) aggregation together with scale affects census data spatial analysis. With regard to regular net system with fixed scale, the number of the neighbors of each polygon affects the results of the analysis. According to the above, it is better to re-aggregate the census data by regular grid system with proper scale and apply multi-scale methods in polygon-based statistical data analysis.