Ridge regularization for spatial autoregressive models with multicollinearity issues

IF 1.4 4区 数学 Q2 STATISTICS & PROBABILITY
Cristina O. Chavez-Chong, Cécile Hardouin, Ana-Karina Fermin
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引用次数: 0

Abstract

This work proposes a new method for building an explanatory spatial autoregressive model in a multicollinearity context. We use Ridge regularization to bypass the collinearity issue. We present new estimation algorithms that allow for the estimation of the regression coefficients as well as the spatial dependence parameter. A spatial cross-validation procedure is used to tune the regularization parameter. In fact, ordinary cross-validation techniques are not applicable to spatially dependent observations. Variable importance is assessed by permutation tests since classical tests are not valid after Ridge regularization. We assess the performance of our methodology through numerical experiments conducted on simulated synthetic data. Finally, we apply our method to a real data set and evaluate the impact of some socioeconomic variables on the COVID-19 intensity in France.

具有多重共线性问题的空间自回归模型的岭正则化
本研究提出了一种在多共线性背景下建立解释性空间自回归模型的新方法。我们使用 Ridge 正则化来绕过共线性问题。我们提出了新的估计算法,可以估计回归系数和空间依赖性参数。空间交叉验证程序用于调整正则化参数。事实上,普通的交叉验证技术并不适用于空间依赖性观测。由于传统测试在里奇正则化后无效,因此我们采用置换测试来评估变量的重要性。我们通过对模拟合成数据进行数值实验来评估我们方法的性能。最后,我们将我们的方法应用于真实数据集,并评估一些社会经济变量对法国 COVID-19 强度的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Asta-Advances in Statistical Analysis
Asta-Advances in Statistical Analysis 数学-统计学与概率论
CiteScore
2.20
自引率
14.30%
发文量
39
审稿时长
>12 weeks
期刊介绍: AStA - Advances in Statistical Analysis, a journal of the German Statistical Society, is published quarterly and presents original contributions on statistical methods and applications and review articles.
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