Bayesian local influence analysis for the spatial autoregressive combined model

This paper develops a Bayesian local influence diagnostic framework for the spatial autoregressive combined (SAC) model, addressing an underexplored area in Bayesian spatial econometrics. While Bayesian influence analysis and MCMC methods are well established, a unified framework for local influence diagnostics in SAC models—capturing both spatial lag and spatial error dependence—has not been previously developed. To the best of our knowledge, this is the first study to construct a coherent Bayesian local influence framework for the SAC model. We propose three perturbation schemes (variance, dependent variable, and explanatory variables) and derive two complementary diagnostic measures based on Kullback–Leibler divergence and Bayes factors. The corresponding influence measures are obtained analytically, and the framework accommodates heteroskedastic errors, enhancing robustness. Computation is implemented via Gibbs sampling and is compatible with software such as Stan and the MATLAB Econometrics Toolbox. The proposed approach is illustrated through simulation studies and two benchmark spatial datasets, demonstrating its effectiveness in detecting influential observations and improving inferential reliability. Overall, the framework provides a novel and unified Bayesian diagnostic tool for SAC models in applied spatial econometrics.