This paper presents the generalized spatial autoregression (GSAR) model, a significant advance in spatial econometrics for non-normal response variables belonging to the exponential family. The GSAR model extends the logistic SAR, probit SAR, and Poisson SAR approaches by offering greater flexibility in modeling spatial dependencies while ensuring computational feasibility. Fundamentally, theoretical results are established on the convergence, efficiency, and consistency of the estimates obtained by the model. In addition, it improves the statistical properties of existing methods and extends them to new distributions. Simulation samples show the theoretical results and allow a visual comparison with existing methods. An empirical application is made to Republican voting patterns in the United States. The GSAR model outperforms standard spatial models by capturing nuanced spatial autocorrelation and accommodating regional heterogeneity, leading to more robust inferences. These findings underline the potential of the GSAR model as an analytical tool for researchers working with categorical or count data or skewed distributions with spatial dependence in diverse domains, such as political science, epidemiology, and market research. In addition, the R codes for estimating the model are provided, which allows its adaptability in these scenarios.

翻译：本文提出了广义空间自回归（GSAR）模型，这是针对属于指数族的非正态响应变量的空间计量经济学领域的一项重要进展。GSAR模型通过提供更大的灵活性来建模空间依赖性，同时确保计算可行性，从而扩展了逻辑SAR、概率单位SAR和泊松SAR方法。从根本上说，本文建立了关于该模型所获估计量的收敛性、效率与一致性的理论结果。此外，它改进了现有方法的统计特性，并将其扩展到新的分布。模拟样本展示了理论结果，并允许与现有方法进行可视化比较。本文以美国共和党投票模式为例进行了实证应用。GSAR模型通过捕捉细微的空间自相关并适应区域异质性，优于标准空间模型，从而得出更稳健的推断。这些发现凸显了GSAR模型作为一种分析工具的潜力，适用于在政治学、流行病学和市场研究等多个领域处理具有空间依赖性的分类数据、计数数据或偏态分布的研究人员。此外，本文提供了用于估计该模型的R代码，这增强了其在上述场景中的适用性。