Collaborative Research: Models for Dynamic Discrete Response Data with Spatial Autocorrelation: Specification and Estimation

许多令人感兴趣的行为涉及在时间和空间背景下的离散响应。这些可能是一系列相邻领域的植物物种的成功，30米网格单元的土地利用指定，县之间的民意选举结果，以及社区和时间之间的犯罪水平。在交通领域，这些反应包括跨区域的贸易流量分布，以及家庭间的车辆拥有量水平。所有这些行为都可以作为离散响应来测量（和/或编码），依赖于各种影响因素，并表现出一定程度的时空依赖性或自相关性。显著的不确定性通常存在于预测模型中；不可观察但有影响的因素仍然存在。这种贡献的大小随空间的变化而变化，通常是连续的。与时间序列数据相比，依赖关系是二维的。这种增加的复杂性倾向于将模型规范限制为使用权重矩阵、较小的数据集和任意的相关模式。需要有方法来利用庞大和高度详细的数字数据集的出现。这项工作旨在通过开发包含空间和时间自相关影响的离散响应数据的新统计模型来解决现有的差距。该研究将基于卫星图像和更常见的城市系统分析数据库的结合，开发、估计、应用和比较空间过程的动态有序和无序概率模型。第一种模型强调有序响应（如不同的土地利用强度），而后者识别无序的分类数据（使用潜在响应优化框架）。这两套模型都将适用于时间和空间，结合使用陆地卫星图像和更容易获得的数年数据集。将探讨多参数估计技术，包括最大模拟似然估计（MSLE），贝叶斯方法，广义矩量法（GMM）和非参数技术。模型应用将使用通过LandSat卫星图像获得的土地覆盖/土地利用数据进行演示，这些数据来自德克萨斯州奥斯汀和全球城市化程度较低的地区。奥斯汀的图像将由美国人口普查数据以及该地区规划机构维护的土地使用和交通系统数据进行补充。几乎所有的数据集都有一个空间维度，世界正准备从空间计量经济学方法和数据获取渠道的改进中受益，用于各种各样的应用。这些模型中的第一个将用于更好地理解和预测土地开发强度的变化（例如，未开发，轻度开发和高度开发），而第二个将用于通过分类（而不是有序）指定（例如，住宅，商业和未开发）来评估土地使用的变化。这项工作的重点和最具挑战性的方面是方法论的本质。尽管如此，土地利用数据集的使用提供了一种有意义和高度具体的应用，表明了新的空间计量经济学方法的价值以及卫星图像与更传统数据集结合使用的好处。这项工作的主要贡献是全新的统计方法的规范和估计技术，这些方法可以识别离散的多响应数据中的时空依赖性，并演示了如何将卫星图像用于大都市规划和交通系统建模的目的。待开发的模型规范和估计技术将填补空间统计和空间计量经济学领域的一个关键空白，在这些领域，连续响应数据模型是规范。待开发的空间计量经济学方法的通用性使它们适用于许多社会、环境和其他问题，无论结果在本质上是离散的，并随时间和空间而观察。将它们应用于土地覆盖变化将加强目前对区域发展和人类活动模式的了解，促进公共和私人政策评价。

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.