Spatial correlation structure is the most essential tool in a spatial data analysis. However, the difficulty of modelling spatial correlations between two responses collected from two neighbouring locations is a challenge, when it is known that each of the responses may also be influenced by certain visible and/or invisible effects of other neighbouring locations. Further difficulties arise when one deals with spatial binary data as opposed to linear spatial data. In this paper, we resolve this correlation model issue for spatial binary data by using a mixed logits model approach where pair-wise correlations are computed by accommodating both within and between correlations for paired-responses. For inferences, we use the true correlation based generalized quasi-likelihood (GQL) approach. The asymptotic normality of the estimators of the main regression and random effects variance parameters are studied. The model and estimation methodology used are illustrated by a finite sample-based simulation study.

空间相关结构是空间数据分析中最重要的工具。然而，当已知从每个相邻位置收集的两个响应之间的空间相关性时，已知每个响应也可能受到其他相邻位置的某些可见和/或不可见影响的挑战，这是一个挑战。当处理空间二进制数据而不是线性空间数据时，会出现进一步的困难。在本文中，我们通过使用混合对数模型方法解决了空间二进制数据的相关模型问题，在该模型中，通过容纳成对响应的相关内部和之间来计算成对相关。为了进行推断，我们使用了基于真实相关性的广义拟似然（GQL）方法。研究了主要回归估计量和随机效应方差参数的渐近正态性。基于有限样本的仿真研究说明了所使用的模型和估计方法。