Maximum Likelihood for Spatially Dependent Counts
	Lisa Madsen 
	Oregon State University

Abstract: Generalized estimating equations have been successfully used to 
estimate regression parameters from discrete longitudinal data. This 
approach has been adapted for spatially correlated count data with less 
success. It is convenient to model correlated counts as lognormal-Poisson, 
where a latent lognormal random variable carries the correlation. This 
model severely limits the degree of correlation and can lead to serious 
negative bias of standard errors. Other models for correlated discrete 
data may avoid this problem; but using correlation to model dependence 
among discrete random variables is not reasonable, especially for highly 
non-normal distributions with small means. I propose a model which yields 
maximum likelihood estimates of regression parameters when the response 
is discrete and spatially dependent. This model employs a spatial 
Gaussian copula, bringing the discrete distribution into the Gaussian 
geostatistical framework, where correlation completely describes dependence. 
The model yields a log-likelihood for regression parameters that can be 
maximized using established numerical methods. The proposed procedure is 
used to estimate the relationship between Japanese beetle grub counts and 
soil organic matter.