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, one 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.
