I am trying to model two variables showing a non-linear relationship, as shown in the scatterplot below, with a Generalized Additive Mixed Model in R (package 'gamm4). The data represents roughly 15 years of data about wildlife monitoring, across more than 150 areas.
The response variable does not follow a Gaussian distribution (skewness=4.31, kurtosis=27.15, see histogram below) and I would like to know which distribution may be suitable to model the error term of a GAMM.
Unfortunately, I have seen that most of the 'family' options are available for GAM only, and cannot be used for mixed-effect models. I have noticed that gamm4 allows for a Tweedie distribution of the error, which can be a suitable option for my data. Indeed, an automatic specification of the optimal parameter cannot be achieved for GAMM (e.g like in GAM: family=tw()) and I have do specify the shape parameters by myself.
I guess it will be a matter of trial and error. I would like to ask you two things:
- Do you think that the Tweedie distribution can be a valuable distribution for the error? What about other distributions?
- How can I decide the most suitable values (theta and power) for the Tweedie distribution?
- Is there any approach for unknown shape parameters, based performance iteration, for the package 'gamm4'?
I have mentioned the package 'gamm4', but even older packages (e.g 'gamm') are accepted.