Ridge regularization for spatial autoregressive models with multicollinearity issues

This work proposes a new method for building an explanatory spatial autoregressivemodel in a multicollinearity context. We use Ridge regularization to bypassthe collinearity issue. We present new estimation algorithms that allow for theestimation of the regression coefcients as well as the spatial d...

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Bibliographic Details
Published inAdvances in statistical analysis : AStA : a journal of the German Statistical Society
Main Authors Chavez-Chong, Cristina O., Hardouin, Cécile, Fermin, Ana-Karina
Format Journal Article
LanguageEnglish
Published Springer Verlag 01.04.2024
Subjects
Statistics
Spatial cross-validation
Permutation tests
Ridge regularization
Variable importance
Spatial autoregressive models
Multicollinearity
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Summary:This work proposes a new method for building an explanatory spatial autoregressivemodel in a multicollinearity context. We use Ridge regularization to bypassthe collinearity issue. We present new estimation algorithms that allow for theestimation of the regression coefcients as well as the spatial dependence parameter.A spatial cross-validation procedure is used to tune the regularization parameter. Infact, ordinary cross-validation techniques are not applicable to spatially dependentobservations. Variable importance is assessed by permutation tests since classicaltests are not valid after Ridge regularization. We assess the performance of ourmethodology through numerical experiments conducted on simulated synthetic data.Finally, we apply our method to a real data set and evaluate the impact of somesocioeconomic variables on the COVID-19 intensity in France.
ISSN:1863-8171
1863-818X
DOI:10.1007/s10182-024-00496-0