New Methods and Software for Spatial-Regression Analysis

该项目的主要目标是创建新的统计方法和软件工具，（i）扩大空间回归方法的范围，（ii）扩大可分析数据集的大小。近年来，越来越多的记录观测位置及其属性的更大、更详细的空间数据集可供健康和社会科学研究人员探索。虽然这种情况为增加我们对健康和社会科学中空间依赖性和相互作用的理解提供了重要的新机会，但它也带来了新的挑战，因为基于这些数据集的适当统计推断需要研究人员在模型制定和统计方法中考虑这种空间依赖性。该项目与国家卫生研究所的使命有关（特别是国家老龄化研究所，国家癌症研究所和国家过敏和传染病研究所），因为它将通过开发新的统计模型和方法来分析空间数据集并以用户友好的方式在Stata中实施这些方法，一个主要的商业统计软件包。在项目成员早期工作的部分基础上，该项目的目的是为横截面和面板数据空间回归模型，包括标准最大似然法无法适应的模型，开发新的广义矩法/工具变量法。该项目将正式推导出所有新估计量的大样本分布，并特别注意它们的数值实现，以便它们即使在非常大的样本中也能很容易地使用。我们将使用蒙特卡罗方法来检查有限样本的大样本分布所提供的近似的质量。第一阶段将展示我们的新的GMM/IV估计的好处和可行性的背景下，一个特定的和重要的空间回归模型的横截面数据，允许未知形式的异方差。第二阶段将把方法扩展到面板数据的空间回归模型，包括允许协变量之间未知相关性和未观察到的个体特异性效应的模型。在上述两种情况下，标准ML估计是不可行的。该项目还将展示GMM/IV方法相对于ML方法的显着计算优势，而不会在可行的情况下挑战其实用性。越来越多的记录观测单位位置及其属性的大型数据集的可用性为公共卫生研究人员提供了新的机遇和挑战。该项目将开发用于分析这些数据集的新的空间回归模型和统计方法，并在商业软件中制作这些方法的用户友好、数字高效的实现。

DESCRIPTION (provided by applicant): The broad objective of the project is to create new statistical methods and software tools that (i) expand the scope of spatial-regression methods and (ii) expand the size of analyzable datasets. In recent years, an increasing number of ever-larger and more-detailed spatial datasets that record the location of an observation and its attributes have become available for exploration by health and social science researchers. While this situation presents significant new opportunities for increasing our understanding of spatial dependencies and interactions in heath and social sciences, it also poses new challenges in that proper statistical inference based on these datasets requires that the researchers account for such spatial dependencies in their model formulation and statistical methods. This project is relevant to the mission of the National Institute of Health (and especially to the National Institute on Aging, the National Cancer Institute, and the National Institute of Allergy and Infectious Diseases) in that it will benefit health and social-science researchers by developing new statistical models and methods for analyzing spatial datasets and implementing those methods in a user-friendly fashion in Stata, 1 of the major commercially available statistical software packages. Building in part on earlier work by the project members, the aim of this project is to develop new generalized method of moments (GMM)/instrumental variables (IV) methods for cross-sectional and panel-data spatial-regression models, including models that the standard maximum likelihood (ML) methods cannot accommodate. The project will formally derive the large-sample distribution of all new estimators and pay particular attention to their numerical implementation such that they can be readily used even for very large samples. We will employ Monte Carlo methods to check on the quality of the approximation provided by the large-sample distribution for finite samples. Phase I will demonstrate the benefits and feasibility of our new GMM/IV estimators within the context of a specific and important spatial-regression model for cross-sectional data, allowing for unknown forms of heteroskedasticity. Phase II will extend the approach to spatial-regression models for panel data, including models that allow for unknown correlation between covariates and the unobserved individual-specific effects. In both of the above highlighted situations, standard ML estimation is infeasible. The project will also demonstrate significant computational advantages of the GMM/IV methods relative to ML methods without challenging their usefulness, where feasible. The availability of an increasing number of ever-larger datasets that record the location of an observational unit and its attributes provides new opportunities and challenges for public-health researchers. This project will develop new spatial-regression models and statistical methods for analyzing these datasets, and produce user-friendly, numerically efficient implementations of these methods in commercially available software.