Distance metric choice can both reduce and induce collinearity in geographically weighted regression
Distance metric choice can both reduce and induce collinearity in geographically weighted regression
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DOI：
10.1177/2399808318784017
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
A. Comber;Khánh Chi;M. Q. Huy;Quan Nguyen;Binbin Lu;H. H. Phe-H.;P. Harris
中科院分区：
文献类型：
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作者：
A. Comber;Khánh Chi;M. Q. Huy;Quan Nguyen;Binbin Lu;H. H. Phe-H.;P. Harris
本文探讨了地理加权回归等局部回归模型中不同距离度量对共线性的影响。以越南hhomeNội的房价数据为例，通过完全改变功率和旋转参数来创建不同的闵可夫斯基距离，分析表明，距离度量选择对局部共线性既有负面影响，也有积极影响。在地理加权回归中，最大共线性的Minkowski距离近似于曼哈顿距离（功率= 0.70），旋转30°，最小共线性的Minkowski距离参数化为功率= 0.05，旋转70°。结果表明，距离度量选择可以为解决空间变系数建模中的局部共线性问题提供有用的额外调整组件，并且理解距离度量和共线性的相互作用可以洞察数据关系的性质和结构。讨论首先考虑探索和选择不同的距离度量来最小化共线性，作为局部脊回归、套索和弹性网方法的替代方法。其次，它讨论了距离度量选择如何通过选择进一步帮助最小化局部共线性的距离度量来扩展额外优化局部模型拟合（套索和弹性网）的方法。第三，它确定需要研究核带宽、距离度量和共线性之间的关系，作为进一步工作的一个领域。
This paper explores the impact of different distance metrics on collinearity in local regression models such as geographically weighted regression. Using a case study of house price data collected in Hà Nội, Vietnam, and by fully varying both power and rotation parameters to create different Minkowski distances, the analysis shows that local collinearity can be both negatively and positively affected by distance metric choice. The Minkowski distance that maximised collinearity in a geographically weighted regression was approximate to a Manhattan distance with (power = 0.70) with a rotation of 30°, and that which minimised collinearity was parameterised with power = 0.05 and a rotation of 70°. The results indicate that distance metric choice can provide a useful extra tuning component to address local collinearity issues in spatially varying coefficient modelling and that understanding the interaction of distance metric and collinearity can provide insight into the nature and structure of the data relationships. The discussion considers first, the exploration and selection of different distance metrics to minimise collinearity as an alternative to localised ridge regression, lasso and elastic net approaches. Second, it discusses the how distance metric choice could extend the methods that additionally optimise local model fit (lasso and elastic net) by selecting a distance metric that further helped minimise local collinearity. Third, it identifies the need to investigate the relationship between kernel bandwidth, distance metrics and collinearity as an area of further work.