I have been wrestling with some model problems for a few weeks now and would like some help.
I am trying to determine whether fish catch rates have changed following an event using GAMM. Because catch rates are highly seasonal, Day of year (DOY) is used as a smoother. Fixed effects include season, pre/post event, and their interaction; Fishing zone is included as a random effect to account for repeated visits. I have added a variance structure (VarIdent) to allow variation based on month. Here is the full model:
gamm1.1<-gamm(CPUE~s(DOY, fx=FALSE, k=-1, bs="cr") + ts3$Prepost*ts3$Season, data=ts3, random=c(list(Year=~ 1),(list(FZ=~1))), control=lmeControl(niterEM=1000, msMaxIter=500), weights.lme=varIdent(form=~1 |fMonth), method="ML")
I am interested in including an offset for soak time, since it varies seasonally- in cold months we do not catch much, and as a result soak time is longer. Here is the offset added:
gamm1.2<-gamm(CPUE~s(DOY, fx=FALSE, k=-1, bs="cr") + ts3$Prepost*ts3$Season + offset(ts3$soak.hr), data=ts3, random=c(list(Year=~ 1),(list(FZ=~1))), control=lmeControl(niterEM=1000, msMaxIter=500), weights.lme=varIdent(form=~1 |fMonth), method="ML")
However, adding an offset does 2 things:
1) Greatly increases the AIC value. I assume this is because soak time is a continuous variable and it is adding a lot of model complexity. 2) Creates an extreme pattern in the residuals.
Here is the gam check and some other diagnostics on the model without the offset (first 8 plots)
And look at what happens to the residuals vs. fitted when the offset is included:
My questions are:
1) Why does adding an offset do this? It is correlated with season, but I don't understand why the pattern is so strong.
2) Are these two models comparable with AIC? The AIC of the offset model is triple that of the other model.
3) Finally, is there a way to account for this new residual pattern while keeping the offset, or is using an offset in this situation not advisable?
Thanks in advance.