基于指数分布族的广义时空地理加权回归模型研究

地理关系分析是当前地理信息科学的研究热点。发展新的时空非平稳模型，对深入理解自然现象和社会过程具有重要的理论和实践意义。近年来课题组发展了一种具有代表性的时空非平稳模型-时空地理加权回归模型（GTWR）。然而，该模型假设变量服从正态分布以及对时空邻近的各向同性表达，极大限制了它的应用范围和效果。受广义线性模型中指数分布族的启发，本项目拟开展基于指数分布族的广义时空地理加权回归模型研究，试图解决在指数分布族下如何构建地理时空非平稳回归模型的问题。项目将围绕着广义回归模型的构建-模型参数估计的新型算法-权重矩阵的构建-模型的验证与应用为主线进行深入的研究。本项目将在保持GTWR模型良好的可解释性基础上，从深度上和广度上对GTWR模型进行有效扩展，并在广义模型参数估计的两阶段算法以及权重矩阵构建的各向异性邻近性度量方面进行创新研究，研究成果将丰富地理空间建模的理论与算法，意义重大而明显。

Spatiotemporal analysis is one of the frontier problems and hot topics in geoinformatics science. Our research group has recently proposed a temporally and geographically weighted regression (GTWR) model for urban housing prices, and received wide acceptance and applications in the past years, because it is one of the simplest and effective tools having the superior abilities to solve spatiotemporal non-stationary. However, the current GTWR is modeled on the basis of the normal error distribution and the weighing matric is constructed with isotropic spatial relationship, which results in inefficient to capture the spatiotemporal non-stationary in complex settings. Inspired from the exponential family of distributions and the link function in generalized linear model, this proposal advocates to build generalized temporally and geographically weighted regression model by introducing the exponential family of distributions, to broadly and deeply extend the GTWR to be a universal temporally and geographically weighted regression model. We seek contributions on the new developed model to solve the non-stationary modeling for the problem of exponential family, and two stages model parameters estimation method, and the weighting scheme with anisotropic spatial adjacent relationship. In this proposal, we will focus on the following contents: establishing a generalized geographically and temporally weighted regression model, formulating an efficient parameter estimation method with two stages, constructing the weighted matrix by space and time and their fusion, and validating and applying the model to remote sensing drought monitoring. It can be expected that this study will extend the traditional GTWR model and corresponding algorithm theoretically and methodologically and hence improve the model fitted accuracy and reliability of current GTWR model. The contributions are clear and significant.