An adjustment for edge effects using an augmented neighborhood model in the spatial auto-logistic model

Parameter estimation in the spatial auto-regressive models has difficulty due to the edge sites which have unobserved neighborhood sites. Some ad hoc remedies suggested in the literature are the free boundary condition, the toroidal boundary condition or estimation using only internal data sites. However, parameter estimates are often sensitive to assumptions on the unobserved neighborhood sites and all the above assumptions have some apparent shortcomings such as systematic bias or inflated variance. In this paper, we propose a new way to incorporate the edge sites by introducing an augmented random neighborhood, denoted by the augmented neighborhood model, which represents the entire external field. To estimate the model, we derive the EM procedures for the maximum pseudo-likelihood estimator and the maximum likelihood estimator. Several simulation studies show that the random external field provides better performance of the maximum pseudo-likelihood estimator and the maximum likelihood estimator than other assumptions on the edge sites. As an example, we apply the random external field to modeling the distribution of Plantago lanceolata in Kansas.