I am using a GAMM to model my data (this is as far as I know the only way I

can use the negative binomial distribution AND a correlation structure

within the model).

I measured animal detections (including zero detections) per hour at 3

different locations in an area. location is a factor in my model and the

other possible explanatory variables are environmental variables and level

of disturbance.

I'm expecting the response to be different at the 3 different locations for

each variable so have been modelling the terms as interactions with each of

the 3 factor levels of location using the 'by' argument in the 'ti'

smoothing term, as well as 'location' as a variable by itself. Does it make

sense to include the main effect as well as the interaction term? for

example for including the variable 'windspeed': if including the term

ti(windspeed, by=location), is it necessary to also include s(windspeed)?

or would it only make sense to inlcude them in separate models only and

compare the models?

As far as I understand the 'by' argument calculates a separate smooth for

each of the factor levels, so if the effect was the same at each location

it wouldn't hurt to use the 'ti' smooth with the 'by' argument if the

effect of the variable was the same at each location.

The issue I'm having is that by including both terms and then doing model

selection gives me many very similar models within a deltaAIC of 6 of the

best model, where the differences lie in the inclusion of main effects when

the 'interaction' is also there. The inclusion of the interaction term

gives bigger changes in AIC compared to the inclusion of the main effect.

This brings me to my other question. Is it possible to compare GAMMs with a

negative binomial family using AIC? e.g. using AIC(mod$lme). If not, what

is the best way to compare them?

Thank you very much for your time

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