Estimation and model selection of higher-order spatial autoregressive model: An efficient Bayesian approach

In this paper we consider estimation and model selection of higher-order spatial autoregressive model by an efficient Bayesian approach. Based upon the exchange algorithm, we develop an efficient MCMC sampler, which does not rely on special features of spatial weights matrices and does not require the evaluation of the Jacobian determinant in the likelihood function. We also propose a computationally simple procedure to tackle nested model selection issues of higher-order spatial autoregressive models. We find that the exchange algorithm can be utilized to simplify the computation of Bayes factor through the Savage-Dickey density ratio. We apply the efficient estimation algorithm and the model selection procedure to study the “tournament competition” across Chinese cities and the spatial dependence of county-level voter participation rates in the 1980 U.S. presidential election.