Abstract:
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Spatial linear models such as CAR and SAR have been used in several applications to model spatial data collected on a lattice. In most of the existing models spatial dependence is exclusively captured through the covariance structure of the errors.In many spatio-temporal applications a response can depend on a set of predictors, and it is plausible that the relationship of this response to the predictors vary spatially and temporally. An approach relegating the spatio-temporal variation only to the model's error would fail to capture these spatio-temporal changes observed in the relationship of between response and predictors. We propose to explicitly model the spatio-temporal dependence between the response and the predictors in the lattice settings, by assuming that each site on the lattice has its own spatio-temporal relationship. By using fusion penalties between neighboring sites, we jointly estimate the coefficients measuring the impact of explanatory variables on response observed at each site of the lattice. We apply to proposed method to a simulated data sets and to county level spatio temporal data.
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