Many behaviors of interest involve discrete response in a temporal and spatial context. These may be the success of plant species in a series of adjacent fields, land-use designations across 30-meter grid cells, popular election outcomes across counties, and levels of crime across neighborhoods and over time. In the transportation arena, such responses include trade-flow distributions across zones, and vehicle-ownership levels across households. All these behaviors can be measured (and/or coded) as discrete responses, dependent on various influential factors and exhibiting some degree of temporal and spatial dependence or autocorrelation. Significant uncertainty generally lingers in predictive models; unobservable yet influential factors remain. The size of such contributions varies, often in a continuous fashion over space. In contrast to time-series data, the dependencies are two dimensional. This added complexity tends to limit model specifications to the use of weight matrices, smaller data sets, and arbitrary correlation patterns. Methods are needed to capitalize on the emergence of huge and highly detailed digital data sets. This work seeks to address existing gaps by developing new statistical models for discrete response data that incorporate the effects of spatial and temporal autocorrelation. The research will develop, estimate, apply, and compare dynamic ordered and unordered probit models for spatial processes, based on a marriage of satellite imagery and more commonly available data bases for urban systems analysis. The first of these models emphasizes ordered responses (such as differing intensities of land use), while the latter recognizes unordered, categorical data (using a latent-response optimization framework). Both sets of models will apply over time and space, using a combination of LandSat satellite imagery and more readily available data sets over several years. Multiple parameter estimation techniques will be explored, including maximum simulated likelihood estimation (MSLE), Bayesian methods, generalized method of moments (GMM), and non-parametric techniques. Model application will be demonstrated using land-cover/land-use data acquired via LandSat satellite imagery for Austin, Texas, and less urbanized regions of the globe as data sets become available. The Austin imagery will be supplemented by U.S. Census data and land-use and transportation-systems data maintained by the region's planning agency.
Almost all data sets have a spatial dimension to them and the world is poised to benefit from improvements in spatial econometric methods and channels of data acquisition for a tremendous variety of applications. The first of these models will be used to better understand and anticipate changes in the intensity of land development (e.g., undeveloped, lightly developed, and highly developed), while the second will be used to appreciate variations in land use over a categorical (rather than ordered) set of designations (e.g., residential versus commercial versus undeveloped). The focus and most challenging aspects of the work are methodological in nature. Nevertheless, the use of land-use data sets offers a meaningful and highly tangible application that demonstrates the value of new spatial econometric methods and the benefits of satellite imagery in tandem with more traditional data sets. The work's primary contributions are specification and estimation techniques for wholly new statistical methods that recognize temporal and spatial dependencies in discrete multiple-response data, and the demonstration of how satellite images can be used for purposes of metropolitan planning and transportation systems modeling. The model specifications and estimation techniques to be developed will fill a key void in the fields of spatial statistics and spatial econometrics, where models of continuous response data are the norm. The generic nature of the spatial econometric methods to be developed makes them applicable to many social, environmental, and other issues, wherever outcomes are discrete in nature and observed over time and space. Their application to land-cover change will enhance current understanding of regional development and human activity patterns, facilitating public and private policy evaluation.
