This paper investigates the adequacy of the matrix exponential spatial specifications (MESS) as an alternative to the widely used spatial autoregressive models (SAR). To provide as complete a picture as possible, we extend the analysis to all the main spatial models governed by matrix exponentials comparing them with their spatial autoregressive counterparts.

We propose a new implementation of Bayesian parameter estimation for the MESS model with vague prior distributions, which is shown to be precise and computationally efficient. Our implementations also account for spatially lagged regressors. We further allow for location-specific heterogeneity, which we model by including spatial splines. We conclude by comparing the performances of the different model specifications in applications to a real data set and by running simulations. Both the applications and the simulations suggest that the spatial splines are a flexible and efficient way to account for spatial heterogeneities governed by unknown mechanisms.

本文研究了矩阵指数空间规范 (MESS) 作为广泛使用的空间自回归模型 (SAR) 的替代方案的充分性。为了提供尽可能完整的图片，我们将分析扩展到由矩阵指数控制的所有主要空间模型，并将它们与其空间自回归对应物进行比较。

我们为具有模糊先验分布的 MESS 模型提出了贝叶斯参数估计的新实现，该模型被证明是精确且计算高效的。我们的实现还考虑了空间滞后的回归器。我们进一步允许特定位置的异质性，我们通过包括空间样条来建模。我们通过将应用程序中不同模型规范的性能与真实数据集和运行模拟进行比较来得出结论。应用和模拟都表明，空间样条曲线是一种灵活有效的方法来解释由未知机制控制的空间异质性。