Spatial cluster detection with threshold quantile regression
Spatial cluster detection with threshold quantile regression
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DOI：
10.1002/env.2696
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发表时间：
2021-07
期刊：
影响因子：
1.7
通讯作者：
Junho Lee;Ying Sun;Huixia Judy Wang
中科院分区：
文献类型：
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作者：
Junho Lee;Ying Sun;Huixia Judy Wang
空间聚类检测，即识别与背景变化相关的不同数据模式相关的空间相邻单元，对于识别回归系数的空间异质性非常有用。一些基于回归模型的空气质量数据的实际研究表明，空气污染及其预测因子之间不仅存在空间异质性，而且存在异方差。由于低空气质量是一个众所周知的死亡率、各种心肺疾病和早产的危险因素，因此尾部的分析将比空气污染分布的中心更有意义。在本文中，我们开发了一种使用阈值分位数回归模型来捕捉空间异质性和异方差的空间聚类检测方法。我们在分位数回归模型中引入两个阈值变量来定义空间聚类。所提出的用于识别空间聚类的检验统计量是Wald过程在阈值参数空间上的最大值。在给定的分位数水平上，在整个空间域上分位数回归系数相同的零假设下，我们建立了检验统计量的极限分布。通过仿真研究对所提方法的性能进行了评价。该方法还应用于分析美国东北部颗粒物（PM 2.5）浓度和气溶胶光学深度（AOD）数据，以研究不同分位数水平上AOD与PM 2.5相关性的地理异质性。
Spatial cluster detection, which is the identification of spatial units adjacent in space associated with distinctive patterns of data of interest relative to background variation, is useful for discerning spatial heterogeneity in regression coefficients. Some real studies with regression‐based models on air quality data show that there exists not only spatial heterogeneity but also heteroscedasticity between air pollution and its predictors. Since the low air quality is a well‐known risk factor for mortality, various cardiopulmonary diseases, and preterm birth, the analysis at the tail would be of more interest than the center of air pollution distribution. In this article, we develop a spatial cluster detection approach using a threshold quantile regression model to capture the spatial heterogeneity and heteroscedasticity. We introduce two threshold variables in the quantile regression model to define a spatial cluster. The proposed test statistic for identifying the spatial cluster is the supremum of the Wald process over the space of threshold parameters. We establish the limiting distribution of the test statistic under the null hypothesis that the quantile regression coefficient is the same over the entire spatial domain at the given quantile level. The performance of our proposed method is assessed by simulation studies. The proposed method is also applied to analyze the particulate matter (PM 2.5 ) concentration and aerosol optical depth (AOD) data in the Northeastern United States in order to study geographical heterogeneity in the association between AOD and PM 2.5 at different quantile levels.