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式处理当地进程统计分析中的几个基本问题。这种研究很重要，因为在生物物理和社会环境中收集的所有数据都是各种过程的结果，许多过程的一个基本特征是它们发生的地理规模。该项目将侧重于评估捕捉空间过程规模的方法。它将为分析复杂现象(如天气、经济市场和人口动态)提供新的统计上合理的方法，这些现象是从全球(宏观)到局部(微观)范围内发生的多个相互作用过程的结果。该项目将提供有关统计方法的新视角，以分析空间过程在空间上表现出异质性的方式。它将有助于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。该项目将有助于转变空间统计建模，使其不再侧重于产生可能极具误导性的平均结果，而是产生局部结果，从而更有力地洞察整个世界的空间运作过程。研究人员将开发一套全面的开源软件，为研究人员和从业人员提供多尺度的局部统计分析。尽管调查模型参数可能的空间变化的技术已经有很长的历史，但这种模型的开发和应用在过去20年里变得越来越普遍。该项目将专注于统计模型，这些模型直接从数据中估计过程异质性，而不是预先指定的组，通常提供对样本中每个位置的过程的估计。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、地理加权回归和某些类型的贝叶斯空间变化系数模型。已提议对这些方法进行多比例尺扩展，以便为模型内的每一种单独关系得出一个单独的比例尺指标。然而，这种模型仍处于初级阶段，在充分发挥其潜力之前，需要解决几个问题，如稳健推理、实质性解释、敏感性和有效计算。研究人员将为三个不同的本地建模框架开发多尺度扩展。将对这些框架的推理和预测能力进行比较，以评估每个框架的相对优势和劣势。调查人员将通过评估来自当地模型的规模指标的含义来得出规模的标准定义，他们将从可概括性、可解释性和健壮性方面分析这些指标。这一裁决反映了NSF的法定使命，并通过使用基金会的智力优势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.