Poisson regression with spatially correlated random effects

ADMB Files
Code: spatial.tpl
Data: spatial.dat
Initial values: spatial.pin Expected Results: spatial.par

Model description

Our data yi,j are observed on a regular 10x10 grid of points: {i,j=1,...,10}. It is assumed that yi,j ~ Poisson(li,j), where

log(li,j) = Xi,jb + ei,j.

Here, Xi,jb is a linear predictor and ei,j are Gaussian random variables with covariance
cov(ei1,j1,ei2,j2) = s2 exp(a-1 d),

where d is the Euclidean distance.