On regression analysis of spatial proportional data with zero/one values

Proportions including exact zero and/or one values observed at spatial locations in a study area are often encountered in environmental and ecological studies. In this paper, we propose a new spatial beta-Bernoulli mixture model that combines a beta distribution and a Bernoulli distribution. The beta component links the original response on the open unit interval (0,1)(0,1) to covariates via regression and is flexible to capture a variety of shapes of the data distributions. Further, the Bernoulli component models the probability of zero/one values with regression. In addition, we propose a novel spatial generalized Tobit model which extends an existing spatial Tobit model by applying an inverse beta cumulative distribution function transformation. A composite likelihood approach is developed for parameter estimation by maximizing a pairwise likelihood function for each model. The standard errors of the parameter estimates are obtained via the inverse of the Godambe information matrix. A simulation study is conducted to evaluate the performance of the proposed models and methods, followed by an ecological data example. Connections among the spatial beta-Bernoulli mixture model, the spatial generalized Tobit model, and the spatial Tobit model are explored using both simulated and real data.