Doubly regularized generalized linear models for spatial observations with high-dimensional covariates
arxiv(2024)
摘要
A discrete spatial lattice can be cast as a network structure over which
spatially-correlated outcomes are observed. A second network structure may also
capture similarities among measured features, when such information is
available. Incorporating the network structures when analyzing such
doubly-structured data can improve predictive power, and lead to better
identification of important features in the data-generating process. Motivated
by applications in spatial disease mapping, we develop a new doubly regularized
regression framework to incorporate these network structures for analyzing
high-dimensional datasets. Our estimators can easily be implemented with
standard convex optimization algorithms. In addition, we describe a procedure
to obtain asymptotically valid confidence intervals and hypothesis tests for
our model parameters. We show empirically that our framework provides improved
predictive accuracy and inferential power compared to existing high-dimensional
spatial methods. These advantages hold given fully accurate network
information, and also with networks which are partially misspecified or
uninformative. The application of the proposed method to modeling COVID-19
mortality data suggests that it can improve prediction of deaths beyond
standard spatial models, and that it selects relevant covariates more often.
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