We expand logistic regression models to accommodate spatial structure in a functional covariate process, direct spatial structure in responses and a geographically structured random effect. Our proposed model builds upon conditionally specified models, where the joint distribution corresponding to a specified full conditional can be identified up to an unknown constant of proportionality. To tackle the challenges of estimation and inference, we employ two separate double Metropolis–Hastings procedures in the Bayesian framework. Furthermore, we suggest methods for making modelling decisions to distinguish the sources of spatial structure through data-driven diagnostics and model assessments. Finally, we apply the model to a real-world problem involving unemployment rates over time in counties of the Midwestern United States as a functional covariate, poverty rates in those counties at a given time as response variables and state-level random effects.
Kim et al. (Wed,) studied this question.