The pioneering work of Getis and Ord on local spatial statistics has a counterpart in spatial econometrics in treating spatial heterogeneity. This can be approached from a continuous or a discrete perspective. In a discrete perspective, referred to as spatial regimes, the coefficients vary by discrete subregions of the data. Whereas the estimation of spatial regime regressions is well understood, the delineation of the regimes themselves remains a topic of active interest. Generally speaking, two broad classes of methods can be distinguished, one in which the delineation is carried out separately from the coefficient estimation and one where the two are tightly integrated. Tightly integrated approaches are referred to as endogenous spatial regimes. A number of different methods have been suggested in the literature, including finite mixture models, GWR-based methods, and penalized regression. One drawback of regime delineation is that the results do not necessarily satisfy a spatial contiguity constraint, i.e., observations are grouped despite not being spatially connected. In this paper, we outline a heuristic to determine the spatial regimes endogenously, as an extension of the well-known SKATER algorithm for spatially constrained clustering. This guarantees that the resulting regimes consist of contiguous observations. We outline the method and apply it in the context of the determination of housing submarkets, which is represented by rich literature in applied spatial econometrics. We use a well-known Kaggle data set as the empirical example, which contains observations on house sales in King County, Washington. We compare the estimation of a hedonic house price model using the endogenous spatial regimes approach to a range of more traditional methods, including pooled regression, the use of administrative districts, data-driven regimes based on a-spatial and spatial clustering of explanatory variables, and finite mixture regression. We evaluate the results in terms of fit and assess the trade-offs between the spatial and a-spatial approaches.

Getis 和 Ord 在局部空间统计方面的开创性工作在处理空间异质性方面与空间计量经济学有对应关系。这可以从连续或离散的角度来处理。从离散的角度来看，称为空间制度，系数因数据的离散子区域而异。尽管对空间区域回归的估计已广为人知，但区域本身的描述仍然是人们关注的话题。一般而言，可以区分两大类方法，一类是与系数估计分开进行描绘，另一类是将两者紧密结合。紧密集成的方法被称为内生的空间制度。文献中提出了许多不同的方法，包括有限混合模型、基于 GWR 的方法和惩罚回归。区域划分的一个缺点是结果不一定满足空间连续性约束，即尽管没有空间连接，但观察结果被分组。在本文中，我们概述了一种内生确定空间状态的启发式方法，作为著名的空间约束聚类 SKATER 算法的扩展。这保证了由此产生的制度由连续的观察组成。我们概述了该方法并将其应用于确定住房子市场的背景下，这在应用空间计量经济学的丰富文献中有所体现。我们使用一个著名的Kaggle数据集作为实证例子，其中包含对华盛顿金县房屋销售的观察。我们将使用内生空间机制方法的享乐房价模型估计与一系列更传统的方法进行比较，包括合并回归、行政区的使用、基于解释变量的空间和空间聚类的数据驱动机制，和有限混合回归。我们根据拟合度评估结果，并评估空间和非空间方法之间的权衡。和有限混合回归。我们根据拟合度评估结果，并评估空间和非空间方法之间的权衡。和有限混合回归。我们根据拟合度评估结果，并评估空间和非空间方法之间的权衡。