[ADMB Users] Poisson GLM with a linear link function

[Mark Payne]

Dear ADMBers,

I have a problem that is essentially a poisson GLM with a linear link function i.e.

y | lambda ~ Pois(lambda)

lamba = a*x1 + b*x2 + c*x3.....

where  y are my observations, lambda is the expected value, x are the explanatory variables, and a-c are the coefficients that I want to estimate. Now, a linear link function is relatively unusual in this context, but it arises from the process that I am modelling and therefore is a fixed part of the model - essentially the underlying process giving rise to the observations is a linear sum by nature, and I am then observing the results via a counting process.

Unfortunately, the problem is that the mean value in the poisson likelihood, lambda, needs to be kept strictly positive, otherwise the likelihood is undefined. The question is, how can I best do this in ADMB *and* maintain the linear structure of my model? Are there any tricks in ADMB or transforms that could be used to make this problem more stable?

Best wishes,

Mark