Spatial Autologistic Model with Generalized Dependent Parameter

In the spatial autologistic model, the dependence parameter is often assumed to be a single value. To construct a spatial autologistic model with spatial heterogeneity, we introduce additional covariance in the dependence parameter, and the proposed model is suitable for the data with binary responses where the spatial dependency pattern varies with space. Both the maximum pseudo-likelihood (MPL) method for parameter estimation and the Bayesian information criterion (BIC) for model selection are provided. The exponential consistency between the maximum likelihood estimator and the maximum block independent likelihood estimator (MBILE) is proved for a particular case. Simulation results show that the MPL algorithm achieves satisfactory performance in most cases, and the BIC algorithm is more suitable for model selection. We illustrate the application of our proposed model by fitting the Bur Oak presence data within the driftless area in the midwestern USA.