[R-sig-ME] glm module in

[Martyn Plummer]

On Tue, 2011-09-20 at 08:50 -0400, Ben Bolker wrote:
> On 09/20/2011 05:34 AM, Martyn Plummer wrote:
> > Hi Ben,
> > 
> > There are two reasons that your model is not recognized by the the glm
> > module. I'll repeat the essential parts of the model:
> > 
> > SibNeg[i] ~ dpois(mu[i])
> > mu[i] <- lambda[i] * z[i] + 0.00001
> > log(lambda[i]) <- offset[i] + alpha + inprod(X[i,],beta) + a[nest[i]]
> > 
> > Firstly, this is not a log-link GLM due to the perturbation you
> > have added to mu[i].  Secondly, and this is the real problem, even
> > without the perturbation JAGS still would not recognize it. 
> > 
> > Normally you can work around this problem by adding log(z) as an offset,
> > but in your case this will not work since z may be zero.
> > 
> > I am aware of this issue: it is a commonly occurring set-up in
> > epidemiological applications, where lambda would a be in incidence rate
> > and z would be the person-time at risk. I'll put this on the TODO list.
> > 
> > Martyn
> 
>   Thanks, Martyn, for the quick response.  Nice to know I wasn't missing
> something too obvious.  It's not critical for this application (I can
> afford to let the model run for 10 minutes), but I wonder if a
> workaround would be to use something like
> 
>    logzzvals <- c(-10,0)
>    lzcat[i] ~ dbern(prob)
>    log(lambda[i]) <- offset[i] + logzvals[lzcat[i]+1] + ...
> 
> ?

I'm afraid not.   An offset normally works in this situation, but if
z[i] == 0 then SibNeg[i] is completely uninformative about the
parameters alpha, beta, and a.  

Martyn

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