[R] Negative Binomial GAMM - theta values and convergence

[Raeanne Miller]

Hi there,

My question is about the 'theta' parameter in specification of a NB GAMM.

I have fit a GAM with an optimum structure of:

SB.gam4<-gam(count~offset(vol_offset)+
  s(Depth_m, by=StnF, bs="cs")+StageF*RegionF,
             family=negbin(1, link=log),
             data=Zoop_2011[Zoop_2011$SpeciesF=='SB',])

However, this GAM shows heterogeneity in the residuals, and the model fit is not great. I would like to add a random effect to this GAM, for station (StnF), and a spatial correlation structure, for Depth_m. When trying to fit an equivalent GAMM to start with, I used the formula:

 SB.gamm1<-gamm(count~offset(vol_offset)+
        s(Depth_m,by=StnF,bs="cs")+StageF*RegionF,
               family=negative.binomial(theta=1.41), niterPQL=50,
               data=Zoop_2011[Zoop_2011$SpeciesF=='SB',])

The theta=1.41 came from SB.gam4, using the theta.ml() command. However, this model does not converge, even with 5000 iterations. When I increase theta to 6, the model converges, but I'm not sure why. I have also tried theta=c(1,10), which converges, but gives me lots of warnings:

Warning messages:
1: In y + .Theta :
  longer object length is not a multiple of shorter object length

 Can anyone tell me why this might be?

The model also does not ever converge if I replace family=negative.binomial()  with family=negbin(). I've looked at the help files for GAM and GAMM, and I'm not sure what the difference between these is?

I have attached code to create my dataset, for those interested.

With many thanks,

Raeanne
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