GIS区域数据时空线性建模方法

Space-time linear modeling method for GIS lattice data

GIS区域数据时空分析研究是指在区域对象空间拓扑结构保持不变的情况下,属性数据随时间变化的时空过程和时空格局的探测、建模和预测。其统计模型需要考虑时序相关性和空间关联性两方面因素,时空线性建模通常采取空间回归模型和时序回归模型相结合的方法。在现有区域时空线性模型的基础上,给出了多阶多元时空线性回归模型的一般形式,并针对一阶时空线性回归模型,研究了在回归参数不同限定条件下的模型特定形式及相互关系,分析了模型中权重矩阵的构建方法,提出了一种结合最小二乘和最大似然的模型参数估计双层迭代算法,并对模型的实际应用进行了分析。

Space-time analysis of GIS lattice data includes detecting, modeling and predicting space-time processes or patterns of lattice attributes changed with time, while spatial topological structures are simultaneously kept invariable. Its statistical modeling need consider two aspects of dependent factors in both space and time, and its space-time linear model usually takes the combination of spatial regression model and time-series regression model. Based on existing space-time linear mod- els of lattice data, a general form was provided for multi-order and multivariate space-time linear regression model. Furthermore, the first-order space-time linear model was specially focused, and several specific forms of this model and their interrelationships were analyzed under different restricted conditions of regression parameters, and the building methods of weight matrix in the model were also discussed, and finally a double-layer iterative algorithm combining ordinary least squares （OLS） with maximum likelihood（ML） was proposed to estimate the model parameters. At last, some practical questions of the model were briefly discussed and probed through its illustration.