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This paper studies Bayesian local influence analysis for the spatial autoregressive models with heteroscedasticity (heteroscedastic SAR models). Two local diagnostic procedures using curvature-based and slope-based methods are proposed in the framework of Bayesian perspective. The curvature-based diagnostic are obtained by maximizing the normal curvature of an influence graph based on Kullback-Leibler divergence measure and slope-based diagnostic use the first order derivative of Bayesian factor defined for perturbation. Three perturbation schemes under the heteroscedastic SAR models are suggested and the diagnostic measures are derived respectively. The computations for the proposed diagnostic measures can be easily obtained using Markov Chain Monte Carlo sampler. The proposed methodologies are illustrated using two real examples.

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