The Measurement of Scale and Process Heterogeneity Through Local Multivariate Models

该项目将通过最近开发的三种类型的多尺度模型来解决局部过程统计分析中的几个基本问题。这种研究是重要的，因为在生物物理和社会环境中收集的所有数据都来自各种过程，而许多过程的一个基本特征是它们发生的地理尺度。该项目将侧重于评估捕捉空间过程尺度的方法。它将为分析复杂现象（如天气、经济市场和人口动态）提供新的统计方法，这些复杂现象是由从全球（宏观）到当地（微观）的多种相互作用过程产生的。该项目将提供关于统计方法的新视角，以分析空间过程在空间上表现出异质性的方式。它将促进更有效地使用允许参数随空间变化的模型，而不是反映“一刀切”心态的更传统的全球模型。该项目将有助于将空间统计建模从侧重于产生可能非常具有误导性的平均结果转变为产生局部结果，从而对世界各地跨空间运行的过程产生更有力的见解。研究人员将开发一个全面的、开源的软件套件，为研究人员和从业人员提供多尺度的本地统计分析。虽然研究模式参数可能的空间变化的技术有着悠久的历史，但在过去的二十年中，这种模式的发展和应用越来越普遍。该项目将侧重于统计模型，该模型直接从数据中估计过程异质性，而无需预先指定组，通常提供样本中每个位置的过程估计。这种局部建模框架的例子包括基于特征向量空间滤波的局部回归、地理加权回归和一些贝叶斯空间变系数模型。对这些方法提出了多尺度扩展，允许为模型内的每个单独关系派生单个尺度指标。然而，这样的模型仍处于起步阶段，需要解决一些问题，如鲁棒推理、实质性解释、敏感性和高效计算，才能充分发挥其潜力。研究人员将为三种不同的局部建模框架开发多尺度扩展。这些框架将根据其推理和预测能力进行比较，以便评估每个框架的相对优点和缺点。研究人员将从本地模型中评估量表指标的含义，得出量表的标准定义，并从其通用性、可解释性和稳健性方面分析指标。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will address several fundamental issues in the statistical analysis of local processes through three types of multi-scale models that recently have been developed. Such research is important because all data collected in both biophysical and social environments results from a variety of processes, and a fundamental characteristic of many processes is the geographic scale at which they occur. This project will focus on evaluating methods that capture the scale of spatial processes. It will provide new insights into statistically sound ways for analyzing complex phenomena like weather, economic markets, and population dynamic that result from multiple interacting processes occurring across a spectrum of scales ranging from global (macro) to local (micro). The project will provide new perspectives regarding statistical approaches to analyze the ways through which spatial processes exhibit heterogeneity over space. It will facilitate more effective use of models that allow parameters to vary over space rather than more traditional global models that reflect a "one size fits all" mentality. The project will help transform spatial statistical modeling from being focused on producing average results which are potentially very misleading to producing local results that will generate much more powerful insights into the processes operating across space throughout the world. The investigators will develop a comprehensive, open-source software suite that will make multi-scale local statistical analysis available to researchers and practitioners.Although techniques for investigating possible spatial variation in model parameters have a long history, the development and application of such models has become increasingly pervasive over the last two decades. This project will focus on statistical models that estimate process heterogeneity directly from the data without pre-specified groups, typically providing estimates of a process at every location in a sample. Examples of such local modeling frameworks include eigenvector spatial filter-based local regression, geographically weighted regression, and some kinds of Bayesian spatially varying coefficient models. Multi-scale extensions to these approaches have been proposed that allow for an individual indicator of scale to be derived for each separate relationship within a model. Such models are still in their infancy, however, and several issues, such as robust inference, substantive interpretation, sensitivity, and efficient computation, need to be addressed before they can reach their full potential. The investigators will develop multi-scale extensions for three distinct local modeling frameworks. These frameworks will be compared in terms of their inferential and predictive capabilities in order to assess the relative advantages and disadvantages of each. The investigators will derive a standard definition of scale by assessing the meaning of indicators of scale from local models, and they will analyze the indicators in terms of their generalizability, interpretability, and robustness.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.