In this study, we suggest using information criteria for nested and non-nested model selection problems for the matrix exponential spatial specifications (MESS) under both homoskedasticity and heteroskedasticity. To this end, we consider the deviance information criterion, the Akaike information criterion and the Bayesian information criterion in a Bayesian setting. In the heteroskedastic case, we assume that the error terms have a scale mixture of normal distributions, where the scale mixture variables are latent variables that lead to different distributions. We demonstrate how the integrated likelihood function can be obtained analytically by integrating out the scale mixture variables from the complete-data likelihood function, and how this integrated likelihood function can be used to formulate the information criteria. We investigate the finite sample performance of these criteria in selecting the true model in a simulation study. The results show that these criteria perform satisfactorily and can be useful for selecting the correct model in specification search exercises. Finally, we apply the proposed information criteria to a spatially augmented growth model and a carbon emission model to show their usefulness for both nested and non-nested model selection problems.

在本研究中，我们建议在同方差和异方差下对矩阵指数空间规范（MESS）的嵌套和非嵌套模型选择问题使用信息标准。为此，我们在贝叶斯设置中考虑偏差信息准则、Akaike 信息准则和贝叶斯信息准则。在异方差情况下，我们假设误差项具有正态分布的尺度混合，其中尺度混合变量是导致不同分布的潜在变量。我们演示了如何通过从完整数据似然函数中积分出尺度混合变量来分析获得积分似然函数，以及如何使用该积分似然函数来制定信息标准。我们在模拟研究中选择真实模型时研究了这些标准的有限样本性能。结果表明，这些标准表现令人满意，可用于在规范搜索练习中选择正确的模型。最后，我们将所提出的信息标准应用于空间增强增长模型和碳排放模型展示了它们对于嵌套和非嵌套模型选择问题的有用性。