Bayesian Variable Selection in Spatial Autoregressive Models

Abstract

This paper compares the performance of Bayesian variable selection approaches for spatial autoregressive models. We present two alternative approaches which can be implemented using Gibbs sampling methods in a straightforward way and allow us to deal with the problem of model uncertainty in spatial autoregressive models in a flexible and computationally efficient way. In a simulation study we show that the variable selection approaches tend to outperform existing Bayesian model averaging techniques both in terms of in-sample predictive performance and computational efficiency.

Flexible shrinkage in high-dimensional Bayesian spatial autoregressive models

“…In spatial autoregressive models, the computational burden emanates from the calculation of marginal likelihoods, where no closed form solutions are available. Recent contributions to the literature as a means to alleviating the computational difficulties include a variant of the conventional stochastic search variable selection prior discussed in Piribauer and Crespo Cuaresma (2016). However, shortcomings of this approach include slow mixing and convergence properties in the presence of a large number of available covariates and difficulties in choosing prior hyperparameters.…”

“…Estimates are obtained using the Normal-Gamma (NG) and Dirichlet-Laplace (DL) shrinkage priors sketched above. As a benchmark specification, we compare the results of both setups with a stochastic search variable selection (SSVS) prior put forward by George and McCulloch (1993) and applied to spatial autoregressive models by Piribauer (2016) and Piribauer and Crespo Cuaresma (2016). The SSVS prior as a means to introducing shrinkage on the slope coefficients mimics Bayesian model-averaging frameworks.…”

“…However, such extensions to the spatial autoregressive modeling framework further increase the emanating computational burden of Bayesian model averaging, rendering the approach computationally intractable. For spatial autoregressive model specifications, work by Piribauer (2016) and Piribauer and Crespo Cuaresma (2016), for example, uses Bayesian stochastic search variable selection priors (SSVS, George and McCulloch, 1993) as an alternative to Bayesian model averaging. The comparative flexibility of this approach allows to easily extend and generalize the basic framework to more complex specifications.…”

A Bayesian spatial autoregressive logit model with an empirical application to European regional FDI flows

“…Sampling for the conditional posterior distribution is straightforward by for example employing an additional Metropolis-Hastings step using independent uniform proposals for ξ. Very similar sampling and estimation strategies to account for uncertainty among W have also been employed in Piribauer and Crespo Cuaresma (2016) or LeSage and Pace (2009).…”

“…These virtues of the proposed spatial logit specification appear particularly useful, since recent advances in the spatial econometric literature rely on more flexible model specifications, which can be incorporated in such a modelling framework in a straightforward and computationally efficient way. Examples of such flexible potential extensions include explicitly allowing for non-linearity in the parameters (Cornwall and Parent, 2017;LeSage and Chih, 2018;Koch and Krisztin, 2011;2018;Piribauer, 2016), multivariate spatial econometric frameworks (Crespo Cuaresma et al 2018), shrinkage approaches for big data applications (Pfarrhofer and Piribauer, 2019;Piribauer and Crespo Cuaresma, 2016), uncertainty about the nature of spatial spillovers (Vega and Elhorst, 2013;LeSage and Fischer, 2008), or allowing for continuous spatial effects (Laurini 2017).…”