New Methods and Software for Spatial-Regression Analysis

描述（由申请人提供）：健康、社会科学和许多其他领域的研究人员正面临着越来越多、越来越大的空间数据集，这些数据集允许探索空间（横截面）依赖关系和相互作用。该项目的目标是创建新的统计方法和软件，以扩大空间回归方法和可分析数据集的范围。新的方法和软件将为研究界提供重要的工具，以更好地了解人类行为的空间方面及其对健康的影响。该项目将推导和统计分析广义矩法（GMM）和工具变量（IV）估计方法，用于重要类别的横截面和面板数据空间回归模型，其中最大似然（ML）估计器无法公式化，或者其统计性质尚未正式建立。该项目还将在广泛使用的统计软件程序Stata中实施这些方法，特别注意用户友好性、数值效率和处理大型数据集的能力。横截面单元通常是异质的。项目的第一阶段考虑了一个重要的横截面空间模型，允许在创新中未知形式的异方差。第一阶段项目为该模型导出了一种新的GMM/IV估计方法的统计特性。分析和仿真结果表明，GMM/IV估计方法可以成功地应用于这种情况，而标准ML方法则不能。结果还表明，GMM/IV估计器的计算时间比可比的ML估计器要短得多。第一阶段项目所考虑的模型属于通常被称为Cliff-Ord模型的一类空间模型。以往的Cliff-Ord模型估计方法主要集中在横截面数据的模型上。Cliff-Ord模型对面板数据的扩展是稀疏的。此外，这些扩展只考虑随机效应规范，不考虑内生变量的溢出效应，也不考虑时间动态，因此这些模型可能不适用于许多应用。第二期工程有两个总体目标。首先，它将开发新的GMM/IV估计器，完成渐近分布理论，用于允许固定效应的更一般的面板数据空间回归模型；内生变量、外生变量和扰动的溢出效应；时间动态;和系统公式。新的GMM/IV估计器将处理ML估计器不能正确表述或ML估计器的估计理论目前已知的情况。其次，它将在Stata中实现估算方法，使其易于为研究界所用，并开发工具，减少估算的计算成本，以适应大型数据集。该项目将产生重大的广泛影响，促进对卫生和其他领域主题的可靠实证分析，在Stata制定和实施纳入空间（横断面）依赖关系和相互作用的估算方法。这些工具将帮助我们更好地了解人类行为的空间方面及其对健康的影响，包括疾病的传播，这将通过更好的公共卫生政策和规划造福社会。

DESCRIPTION (provided by applicant): Researchers in health, social sciences, and many other fields are confronting an increasing number of ever-larger spatial datasets that permit the exploration of spatial (cross-sectional) dependencies and interactions. The objective of this project is to create new statistical methods and software that expand the scope of spatial-regression methods and analyzable datasets. The new methods and software will provide the research community with important tools to better understand spatial aspects of human behavior and their effect on health. The project will derive and statistically analyze generalized method of moments (GMM) and instrumental variable (IV) estimation methods for important classes of cross-sectional and panel-data spatial- regression models for which maximum likelihood (ML) estimators cannot be formulated, or where their statistical properties have not yet been formally established. The project will also implement those methods in the widely used statistical software program Stata, paying particular attention to user friendliness, numerical efficiency, and the ability to handle large datasets. Cross-sectional units are often heterogeneous. Phase I of the project considered an important cross- sectional spatial model allowing for heteroskedasticity of unknown form in the innovations. The Phase I project derived the statistical properties of a new GMM/IV estimation method for this model. Analytic and simulation results showed that the GMM/IV estimation method can be successfully applied in this situation, whereas the standard ML methods cannot. The results also demonstrated that the GMM/IV estimators can be computed in signficantly less time than comparable ML estimators. The model considered by the Phase I project belongs to a class of spatial models often referred to as Cliff-Ord models. Previous estimation methods for Cliff-Ord models have focused mostly on models for cross-sectional data. Extensions of Cliff-Ord models to panel-data are sparse. Also, these extensions only consider random-effects specifications, and do not allow for spillovers in the endogenous variables, or for time dynamics, and hence these models may not be appropriate in many applications. The Phase II project has two general aims. First, it will develop new GMM/IV estimators, complete with asymptotic distribution theory, for more general panel-data spatial-regression models which allow for fixed effects; spillovers in the endogenous variables, exogenous variables, and disturbances; time dynamics; and systems formulations. The new GMM/IV estimators will handle cases in which either ML estimators cannot be properly formulated or the estimation theory for ML estimators is currently known. Second, it will implement the estimation methods in Stata to make them readily available to the research community, and develop tools that reduce the computational cost of estimation to accommodate large datasets. This project will have substantial broad impacts by facilitating sound empirical analysis of topics in health and other fields by developing and implementing in Stata estimation methods that incorporate spatial (cross-sectional) dependencies and interactions. The tools will help us better understand the spatial aspects of human behavior and their effects on health, including the spread of disease, which will benefit society through better public health policy and planning.