Measuring Bandwidth Uncertainty in Multiscale Geographically Weighted Regression Using Akaike Weights
Measuring Bandwidth Uncertainty in Multiscale Geographically Weighted Regression Using Akaike Weights
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DOI：
10.1080/24694452.2019.1704680
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发表时间：
2020-02-11
影响因子：
3.9
通讯作者：
Wolf, Levi John
中科院分区：
文献类型：
--
作者：
Li, Ziqi;Fotheringham, A. Stewart;Wolf, Levi John
带宽是地理加权回归模型中的一个关键参数，与正在检查的潜在空间异质过程发生的空间尺度密切相关。通常，基于某些准则（例如赤池信息准则（AIC））选择单个最佳带宽（地理加权回归）或一组特定于协变量的最佳带宽（多尺度地理加权回归），然后以该带宽的选择为条件进行参数估计和推理。在本文中，我们发现带宽选择在单尺度和多尺度地理加权回归模型中都受到不确定性的影响，并证明这种不确定性是可以测量和解释的。基于模拟研究和凤凰城肥胖率的实证例子，我们表明可以通过 Akaike 权重来定量测量带宽不确定性，并可以获得带宽的置信区间。了解带宽不确定性可以提供有关不同进程运行规模的重要见解，特别是在比较特定协变量的带宽时。此外，可以基于考虑带宽选择不确定性的 Akaike 权重来计算无条件参数估计。
Bandwidth, a key parameter in geographically weighted regression models, is closely related to the spatial scale at which the underlying spatially heterogeneous processes being examined take place. Generally, a single optimal bandwidth (geographically weighted regression) or a set of covariate-specific optimal bandwidths (multiscale geographically weighted regression) is chosen based on some criterion, such as the Akaike information criterion (AIC), and then parameter estimation and inference are conditional on the choice of this bandwidth. In this article, we find that bandwidth selection is subject to uncertainty in both single-scale and multiscale geographically weighted regression models and demonstrate that this uncertainty can be measured and accounted for. Based on simulation studies and an empirical example of obesity rates in Phoenix, we show that bandwidth uncertainties can be quantitatively measured by Akaike weights and confidence intervals for bandwidths can be obtained. Understanding bandwidth uncertainty offers important insights about the scales over which different processes operate, especially when comparing covariate-specific bandwidths. Additionally, unconditional parameter estimates can be computed based on Akaike weights accounts for bandwidth selection uncertainty.