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

许多感兴趣的行为涉及在时间和空间背景下的离散反应。这些可能是一系列相邻田地植物物种的成功，30米网格单元的土地用途指定，各县受欢迎的选举结果，以及不同社区和时间的犯罪率。在交通领域，这样的反应包括跨地区的贸易流量分布，以及家庭之间的汽车拥有量水平。所有这些行为都可以被测量(和/或编码)为离散的反应，依赖于各种影响因素，并表现出一定程度的时间和空间相关性或自相关性。预测模型中普遍存在重大不确定性；不可观测但有影响的因素依然存在。这些捐款的大小各不相同，往往是在整个空间以连续的方式进行的。与时间序列数据相比，这种相关性是二维的。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关联模式。需要各种方法来利用巨大而高度详细的数字数据集的出现。这项工作试图通过为离散响应数据开发新的统计模型来解决现有的差距，该模型纳入了空间和时间自相关性的影响。这项研究将基于卫星图像和更常见的城市系统分析数据库，开发、评估、应用和比较空间过程的动态有序和无序概率模型。这些模型中的第一个强调有序的响应(例如不同的土地利用强度)，而后者则识别无序的、分类的数据(使用潜在响应优化框架)。这两套模型将在时间和空间上应用，使用陆地卫星卫星图像和几年内更容易获得的数据集的组合。将探索多参数估计技术，包括最大模拟似然估计(MSLE)、贝叶斯方法、广义矩方法(GMM)和非参数技术。当数据集可用时，将使用通过陆地卫星卫星图像获得的得克萨斯州奥斯汀和全球城市化程度较低地区的土地覆盖/土地利用数据来演示模型应用。奥斯汀的图像将得到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的补充。几乎所有的数据集都有空间维度，世界将从空间计量经济学方法和数据获取渠道的改进中受益，以满足各种应用的需要。第一个模型将被用来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)，而第二个模型将被用于研究按分类(而不是有序)指定的土地使用的变化(例如，住宅与商业与未开发)。这项工作的重点和最具挑战性的方面是方法性的。尽管如此，土地利用数据集的使用提供了一个有意义的、非常具体的应用，它展示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的数据集相结合的好处。这项工作的主要贡献是对识别离散多响应数据中的时间和空间相关性的全新统计方法的规范和估计技术，以及如何将卫星图像用于大都市规划和交通系统建模的演示。即将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，在空间统计和空间计量经济学领域，连续响应数据模型是标准。将要开发的空间计量经济学方法的一般性使它们适用于许多社会、环境和其他问题，无论结果是离散的，还是在时间和空间上观察到的。它们在土地覆盖变化方面的应用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估。

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.