A model for analyzing spatially correlated binary data clustered in uncorrelated lattices

In recent years, the spatial lattice data has been a motivating issue for researches. Modeling of binary variables observed at locations on a spatial lattice has been sufficiently investigated and the autologistic model is a popular tool for analyzing these data. But, there are many situations where binary responses are clustered in several uncorrelated lattices, and only a few studies were found to investigate the modeling of binary data distributed in such spatial structure. Besides, due to spatial dependency in data exact likelihood analyses is not possible. Bayesian inference, for the autologistic function due to intractability of its normalizing-constant, often has limitations and difficulties. In this study, spatially correlated binary data clustered in uncorrelated lattices are modeled via autologistic regression and IBF (inverse Bayes formulas) sampler with help of introducing latent variables, is extended for posterior analysis and parameter estimation. The proposed methodology is illustrated using simulated and real observations.