Using the truncated auto-poisson model for spatially correlated counts of vegetation

With vegetation data there are often physical reasons for believing that the response of neighbors has a direct influence on the response at a particular location. In terms of modeling Such scenarios the family of auto-models or Markov random fields is a useful choice. If the observed responses are Counts, the auto-Poisson model call be used. There are different ways to formulate the auto-Poisson model, depending on the biological context. A drawback of this model is that for positive autocorrelation the likelihood of the auto-Poisson model is not available in closed form. We investigate how this restriction can be avoided by right truncating the distribution. We review different parameter estimation techniques which apply to auto-models in general and compare them in a simulation study. Results suggest that the method which is most easily implemented via standard statistics software, maximum pseudo-likelihood, gives unbiased point estimates, but its variance estimates are biased. An alternative method, Monte Carlo maximum likelihood, works well but is computer-intensive and not available in standard software. We illustrate the methodology and techniques for model checking with clover leaf Counts and seed count data from ail agricultural experiment.