Advancing Methods for Spatial Analysis in Local Modeling

该项目开发了空间数据的统计方法。数据显示不同空间环境的差异是很常见的，包括犯罪率、选举中的投票偏好和疾病流行率等结果。传统上，研究人员使用的统计模型隐含地假设产生这些结果的过程在不同地点是一致的。然而，导致这种差异的过程在不同的空间背景下可能会有所不同，需要统计方法来解释这种差异。在这项研究中，研究人员开发了统计方法来解决空间邻近结果之间的相关性。作为对他们开发的方法的补充，研究人员正在开发开放源码软件，以使其他学者可以免费使用这些方法。除了方法上的进步，该奖项还支持两名研究生的参与，他们受益于科学研究方面的培训。该奖项支持一位残疾研究人员，这有助于实现扩大科学参与度的目标。在这项研究中，研究人员检查并开发了多个尺度上的数据统计建模方法。具体地说，研究人员提出了多尺度地理加权回归(MGWR)方法，该方法允许预测变量的影响根据其空间背景而变化。这些方法解决了对统计推断的已知挑战，具体地说，如果回归模型没有充分考虑数据集中的规模和结构，则回归模型可能表明存在偏见和相反的影响。在这个项目中，研究人员检查了使用MGWR方法可以在多大程度上解决这些问题。其他目标包括在审查多个假设时调整推论的新方法，以及实施检查模型假设的稳健性的诊断工具。为了推进这些方法，研究人员将建模方法应用于具有空间结构的经验数据集，例如新冠肺炎大流行期间的死亡率、青少年怀孕率和最近选举中的投票趋势。该奖项反映了美国国家科学基金会的法定使命，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 develops statistical methods for spatial data. It is common for data to exhibit variation across spatial contexts, including outcomes such as crime rates, voting preferences in elections, and disease prevalence. Conventionally, researchers have used statistical models that implicitly assume that the processes generating these outcomes are uniform across locations. Yet, the processes that lead to this variation may vary in different spatial contexts, and statistical approaches are needed that account for this variation. In this study, the researchers develop statistical methods that address correlations between spatially proximate outcomes. As a complement to the methods that they develop, the researchers are developing open source software to make these approaches freely available to other scholars. In addition to the methodological advances, the award supports the involvement of two graduate students, who benefit from the training in scientific research. The award supports a researcher with a disability, which contributes to goals of broadening participation in science.In this study, the researchers examine and develop methods for the statistical modeling of data at multiple scales. Specifically, the researchers advance multiscale geographically weighted regression (MGWR) methods, which allows the effects of predictor variables to vary based on their spatial context. These approaches address known challenges to statistical inferences, specifically that regression models may indicate biased and contrary effects if the models do not adequately account for the scale and structure in the dataset. In this project, the researchers examine the extent to which these problems can be addressed with the use of MGWR methods. Additional aims include new methods for adjusting inferences when multiple hypotheses are examined and the implementation of diagnostic tools for examining the robustness of model assumptions. To advance the methods, the researchers apply the modeling approach to empirical datasets with spatial structure, such as mortality during the COVID-19 pandemic, teen pregnancy rates, and voting trends in recent elections.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.