There is a long history of spatial regression analysis where it is important to accommodate the spatial correlations among the responses from neighboring locations for any valid inferences. Among numerous modeling approaches, the so-called spatial auto-regression (SAR) model in a linear setup, and the conditional auto-regression (CAR) model in a binary setup, are widely used. For spatial binary analysis, there exists two other competitive approaches, namely the bivariate probit models (BPM) based composite likelihood approach using local lattices; and a ‘Working’ correlations based QL (quasi-likelihood) (WCQL) approach. These correlation models, however, fail to accommodate both within and between correlations among spatial families, where a spatial family is naturally formed within a threshold distance of a selected location, and the member locations between two neighboring families may also be correlated. In this paper, we exploit this latter two-ways, within and between correlations among spatial families and develop a unified correlation model for all exponential family based such as linear, count or binary data. We further exploit the proposed correlation structure based generalized quasi-likelihood (GQL) and method of moments (MM) approaches for model parameters estimation. As far as the estimation properties are concerned, because in practice one encounters a large spatial sample, we make sure that the proposed GQL and MM estimators are consistent.

空间回归分析有很长的历史，其中重要的是要适应来自相邻位置的响应之间的空间相关性，以获得任何有效的推断。在众多建模方法中，线性设置中的所谓空间自回归 (SAR) 模型和二元设置中的条件自回归 (CAR) 模型被广泛使用。对于空间二元分析，还有另外两种竞争方法，即使用局部格的基于双变量概率模型 (BPM) 的复合似然方法；和基于“工作”相关性的 QL（准似然）（WCQL）方法。然而，这些相关模型无法适应空间族之间的相关性内部和之间的相关性，其中空间族是在选定位置的阈值距离内自然形成的，并且两个相邻家族之间的成员位置也可能相关。在本文中，我们利用后两种方式，空间族之间的相关性内部和之间的相关性，并为所有基于指数族（例如线性、计数或二进制数据）开发统一的相关性模型。我们进一步利用所提出的基于相关结构的广义拟似然（GQL）和矩量法（MM）方法进行模型参数估计。就估计属性而言，因为在实践中遇到大空间样本，我们确保建议的 GQL 和 MM 估计量是一致的。空间族之间的相关性内部和之间的相关性，并为所有基于线性、计数或二进制数据的指数族开发统一的相关模型。我们进一步利用所提出的基于相关结构的广义拟似然（GQL）和矩量法（MM）方法进行模型参数估计。就估计属性而言，因为在实践中遇到大空间样本，我们确保建议的 GQL 和 MM 估计量是一致的。空间族之间的相关性内部和之间的相关性，并为所有基于指数族（例如线性、计数或二进制数据）开发统一的相关性模型。我们进一步利用所提出的基于相关结构的广义拟似然（GQL）和矩量法（MM）方法进行模型参数估计。就估计属性而言，因为在实践中遇到大空间样本，我们确保建议的 GQL 和 MM 估计量是一致的。