Ridge regularization for spatial auto-regressive models with multicollinearity issues
Résumé
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 dataset and
evaluate the impact of some socio-economic variables on the COVID-19 intensity
in France.
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