Collaborative Research: Spatially Additive and Discrete-Choice Spatial Models

Louisiana State University, Baton Rouge LA

Investigators

Abstract

The continued growth in the availability and use of spatial data on a broad range of phenomena have fueled a drive to develop more effective and statistically sound approaches for the analysis of those data. Because spatial data have distinctive characteristics that do not enable the immediate application of many statistical approaches because fundamental assumptions that underlie the use of those approaches, focused inquiries are required into the development of new spatial statistical approaches and careful adaptation in the use of extant statistical methods for spatial analysis. These awards support collaborative research by two spatial econometricians on two different kinds of spatial analytic modeling approaches. The first of these approaches deals with spatially additive models. Traditionally, the two main methods for analyzing spatial data have been (1) to model the conditional mean of the dependent variable and (2) to focus on specification of spatial dependence among observation. The spatially additive model is designed to combine the specification of the conditional mean with the specification of spatial dependence among observations. The proposed development of spatially additive models in this project will be based on recent innovations that allow generalized additive models to be extended to spatial analysis. First, sparse specification of spatial dependence, quadratic log-determinant approximations and bounds, and computational advances have increased both the speed with which spatial estimation can be accomplished and the size of practical problems that can be solved. Second, quadratic bounds and approximations to the log-determinant can lead to a standard sequential quadratic programming solution that permit quick computation and robust optimization. These advances also allow simultaneous parameter estimation and model selection. The second major line of inquiry for this collaborative project consists of the development of multinomial probit estimation methods for regional science modeling problems where the sample data exhibit spatial dependence. Multinomial probit models can be applied to problems where the variable of interest represents a choice between two or more alternatives. Estimation methods and algorithms that are generally applicable are not currently available for the case when the polychotomous dependent variable disturbance process in the relationship exhibits spatial dependence. The methods to be developed through this project will address this issue and have application to location decisions involving spatial data. Theoretical issues relating to use of multinomial probit models and three alternative estimation strategies will be evaluated. The strategies are maximum likelihood estimation, Bayesian estimators based on Markov Chain Monte Carlo (MCMC) estimation, and a hybrid strategy based on MCMC methods and Expectation-Maximization (EM) algorithms. Outcomes from the project are expected to include theoretical development of spatial multinomial probit model specification and estimation as well as algorithms and code that will be of value in the toolkit of methods available to spatial econometricians, regional scientists, and geographers. The new statistical approaches to be developed through this project will complement the approaches developed by these investigators and other leading spatial statisticians, thereby further enhancing the range of tools that researchers can use to effectively analyze a broad range of spatial databases. Because the investigators will make their results available through user-friendly software and documentation, this work should foster continued methodological development as well as enhanced capabilities for geographic and spatial econometric inquiry.