Development of the method of multivariate spatial analysis and its application in spatial information science

当我们分析一个地区的多组空间数据时，我们使用包括统计方法在内的多变量分析方法。在这种情况下，空间维度与其他属性维度同等对待，这在分析中造成了概念和技术问题。例如，在回归分析中，社区的属性通常作为独立变量包含。这使得误差项的概率分布非常复杂，以至于不可能通过分析获得最大似然。跨空间单元的空间聚集导致了可修改面单元问题，即分析结果依赖于用于聚集的空间单元的定义。为了解决这些问题，有必要在分析变量之间的关系时明确引入空间的概念——以空间分析的视角进行多变量分析。将空间属性定义为一组位置函数，采用空间多元分析方法对其进行分析。为此，我们提出了一种新的多元空间分析方法。该方法应1)明确纳入空间概念，2)适用于探索性空间分析，3)在GIS中具有广泛的应用。第一个需求是解决前面提到的问题。第二个需求是为了应对随着海量空间数据的传播而迅速兴起的探索性空间数据分析需求。第三个要求确保我们不仅可以将该方法应用于空间分析，还可以应用于更一般的多元分析，其中包含空间维度作为定义变量的空间的一部分。在空间上分布的时间序列变量和在空间上测量的误差分布也是位置的函数。它们可以用与本研究中讨论的属性变量相同的方式处理。

When we analyze mare than one set of spatial data in a region, we use multivariate analytical methods including statistical methods. In this case, spatial dimension is treated equivalently as other attribute dimensions, which causes both conceptual and technical problems in analysis. In regression analysis, for instance, attributes of neighborhoods are often included as independent variables. This makes the probability distribution of error terms quite complicated so that it is impossible to obtain the maximum likelihood analytically. Spatial aggregation across spatial units causes the Modifiable Areal Unit Problem, which refers to the dependency of the results of analysis on the definition of spatial units used for aggregation.To resolve the problems, it is necessary to introduce the concept of space explicitly in analysis of the relationship among variables-multivariate analysis with a view of spatial analysis. Regarding the attributes defined over a space as a set of functions of location, we analyze them by a spatial multivariate analysis method.To this end, we develop a new method of multivariate spatial analysis. The method should 1)explicitly incorporate the concept of space, 2)be applicable to exploratory spatial analysis, and 3)have wide applications in GIS. The first requirement is recognized to resolve the problems mentioned earlier. The second requirement is put to answer the demand for exploratory spatial data analysis that has emerged rapidly with the spread of massive spatial data. The third reqirement assures us to apply the method not only to spatial analysis but also mare general multivariate analysis that contains spatial dimensions as a part of space where variables are defined. Time series variables distributed over a space and error distribution measured over a space are also functions of location. They can be treated in the same way as the attribute variables discussed in this research.