This paper develops a localized approach to elastic net logistic regression, extending previous research describing a localized elastic net as an extension to a localized ridge regression or a localized lasso. All such models have the objective to capture data relationships that vary across space. Geographically weighted elastic net logistic regression is first evaluated through a simulation experiment and shown to provide a robust approach for local model selection and alleviating local collinearity, before application to two case studies: county-level voting patterns in the 2016 USA presidential election, examining the spatial structure of socio-economic factors associated with voting for Trump, and a species presence–absence data set linked to explanatory environmental and climatic factors at gridded locations covering mainland USA. The approach is compared with other logistic regressions. It improves prediction for the election case study only which exhibits much greater spatial heterogeneity in the binary response than the species case study. Model comparisons show that standard geographically weighted logistic regression over-estimated relationship non-stationarity because it fails to adequately deal with collinearity and model selection. Results are discussed in the context of predictor variable collinearity and selection and the heterogeneities that were observed. Ongoing work is investigating locally derived elastic net parameters.

中文翻译：

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地理加权弹性网逻辑回归

本文开发了一种用于弹性网逻辑回归的局部方法，扩展了先前的研究，将局部弹性网描述为对局部脊回归或局部套索的扩展。所有这些模型的目标都是捕获跨空间变化的数据关系。地理加权弹性网逻辑回归首先通过模拟实验进行了评估，并被证明为局部模型选择和缓解局部共线性提供了一种可靠的方法，然后应用于两个案例研究：2016年美国总统大选的县级投票模式，与特朗普投票相关的社会经济因素的空间结构，以及与存在于美国本土的网格化地点的解释性环境和气候因素相关的物种存在与缺失数据集。该方法与其他逻辑回归进行了比较。它仅改善了选举案例研究的预测，而选举案例研究在二元响应中表现出比物种案例研究更大的空间异质性。模型比较表明，标准的地理加权逻辑回归高估了关系的非平稳性，因为它不能充分处理共线性和模型选择。在预测变量共线性和选择以及观察到的异质性的背景下讨论了结果。正在进行的工作是研究局部导出的弹性网参数。模型比较表明，标准的地理加权逻辑回归高估了关系的非平稳性，因为它无法充分处理共线性和模型选择。在预测变量共线性和选择以及观察到的异质性的背景下讨论了结果。正在进行的工作是研究局部导出的弹性网参数。模型比较表明，标准的地理加权逻辑回归高估了关系的非平稳性，因为它无法充分处理共线性和模型选择。在预测变量共线性和选择以及观察到的异质性的背景下讨论了结果。正在进行的工作是研究局部导出的弹性网参数。