Within the statistical literature, a significant gap exists in methods capable of modeling asymmetric multivariate spatial effects that elucidate the relationships underlying complex spatial phenomena. For such a phenomenon, observations at any location are expected to arise from a combination of within- and between- location effects, where the latter exhibit asymmetry. This asymmetry is represented by heterogeneous spatial effects between locations pertaining to different categories, that is, a feature inherent to each location in the data, such that based on the feature label, asymmetric spatial relations are postulated between neighbouring locations with different labels. Our novel approach synergises the principles of multivariate spatial autoregressive models and the Gaussian graphical model. This synergy enables us to effectively address the gap by accommodating asymmetric spatial relations, overcoming the usual constraints in spatial analyses. Using a Bayesian-estimation framework, the model performance is assessed in a simulation study. We apply the model on intercropping data, where spatial effects between different crops are unlikely to be symmetric, in order to illustrate the usage of the proposed methodology. An R package containing the proposed methodology can be found on https://CRAN.R-project.org/package=SAGM.

翻译：在统计文献中，能够建模非对称多元空间效应以阐明复杂空间现象背后关系的显著方法尚存在空白。对于此类现象，任何位置上的观测值都预期由位置内部和位置之间的效应共同产生，其中位置之间的效应呈现非对称性。这种非对称性通过不同类别位置之间的异质性空间效应来体现，即数据中每个位置固有的特征，基于该特征标签，相邻且标签不同的位置之间可假定存在非对称空间关系。我们的新方法综合了多元空间自回归模型与高斯图形模型的原理，通过容纳非对称空间关系，有效填补了这一空白，克服了空间分析中的常见限制。在贝叶斯估计框架下，通过模拟研究评估了模型性能。我们将该模型应用于间作数据（其中不同作物之间的空间效应不太可能对称），以说明所提出方法的应用。包含该方法的R包可在https://CRAN.R-project.org/package=SAGM获取。