In including random effects to account for dependent observations, the odds ratio interpretation of logistic regression coefficients is changed from population-averaged to subject-specific. This is unappealing in many applications, motivating a rich literature on methods that maintain the marginal logistic regression structure without random effects, such as generalized estimating equations. However, for spatial data, random effect approaches are appealing in providing a full probabilistic characterization of the data that can be used for prediction. We propose a new class of spatial logistic regression models that maintain both population-averaged and subject-specific interpretations through a novel class of bridge processes for spatial random effects. These processes are shown to have appealing computational and theoretical properties, including a scale mixture of normal representation. The new methodology is illustrated with simulations and an analysis of childhood malaria prevalence data in the Gambia.

翻译：在引入随机效应以处理观测值间的依赖性时，逻辑回归系数的比值比解释从总体平均型转变为个体特定型。这在许多应用中并不理想，从而推动了大量关于在无随机效应情况下保持边际逻辑回归结构的方法研究，例如广义估计方程。然而，对于空间数据，随机效应方法因其能够提供可用于预测的数据的完整概率表征而具有吸引力。我们提出了一类新的空间逻辑回归模型，通过一类新颖的空间随机效应桥过程，同时保持总体平均和个体特定两种解释。这些过程被证明具有吸引人的计算和理论性质，包括正态表示的尺度混合形式。新方法通过模拟研究以及对冈比亚儿童疟疾患病率数据的分析进行了验证。