Generalized spatial matrix specifications

In this article, we propose a model that generalizes some of the most popular choices in spatial linear modeling, such as the SAR and MESS models. Our idea builds on their representation as link functions applied to a spatial weight <i>W</i>, corresponding to the uniform and exponential distributions, respectively. By allowing for more general families of distribution functions, one can encompass both models and capture different spatial patterns. We provide some insights into the difference between specifications, with emphasis on advantages and shortcomings as well as on interpretation of the parameters and correspondences between models. By exploiting the possibility to obtain a formal power series representation of the link family, we define the quasi maximum likelihood estimator and study its asymptotic properties under Gaussian and non Gaussian errors. By applying our approach to data on 2000 US election participation, as in LeSage and Pace (2007), we show that this model is able to capture a finite order neighboring spillover structure, as opposed to the infinite order implied by both the SAR and MESS models.本文提出了一种可推广空间线性建模领域多款主流模型的框架，其中包括空间自回归模型（Spatial Autoregressive, SAR）与MESS模型。该模型的构建基于将二者表示为施加于空间权重W的连接函数，二者分别对应均匀分布与指数分布。通过引入更具普适性的分布函数族，可同时涵盖这两类模型，并捕捉更为多样的空间格局。本文还对不同模型设定间的差异展开了分析，重点探讨了各类设定的优劣特性、参数解读方式以及模型间的对应关系。通过推导连接函数族的正规幂级数表示形式，本文定义了准极大似然估计量，并分析了其在高斯误差与非高斯误差设定下的渐近性质。参考LeSage与Pace（2007）的研究，本文将所提方法应用于2000年美国大选参选率数据，结果表明，相较于SAR与MESS模型所隐含的无限阶空间溢出效应，本文提出的模型可有效捕捉有限阶邻域溢出结构。