Marginally Interpretable Spatial Logistic Regression With Bridge Processes

ABSTRACT 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 Gambia.