Basically I’m modelling tree fruiting patterns using mgcv bams and auto regressive (1) models have much better outcomes using itsadug::compareML(). (bam AR(1) was chosen due to limitations associated with binomial data) Further, this AR is backed up by biological theory. However, the best models when I use AR techniques often don’t include terms that are included in the non-AR models. I understand this to be a common occurrence, the AR term explains much of the variance, leaving smaller predictions for the remaining terms.

I’ve seen discussions on here warning that AR GAMs should be interpreted with care, and Gavin Simposon’s AR GAM post (part 1), ends with hinting that there are some serious diagnostic criteria that should be considered, but part 2 never came out, and I’m struggling to find resources on interpretation. Much more common are simple introductory articles.

I guess the fundamental question is thus: the two different types of model will make different statements about the effects of a given predictor, which should be believed?

If the non-AR model finds that month is a useful predictor, but the AR model finds it ultimately superfluous, does month have an effect? Is month relevant due to effects like light patterns, or just because of correlational structure? I guess this is a classic ‘no models are true, some are useful’ situation.

This problem persists even inside of a predictor. My temperature:vpds tensor product spline will cite a particular region as increasing the probability in non-AR models, but will suggest another region does so in AR models (in addition to the first).

I’m presently leaning towards including both sets of models in my paper, and noting that the AR models provide better predictions, but the non-AR models can provide insight into the effect of variables. Even then I wonder what’s more useful? The model that best fits the data without any AR? Or the non-AR version of the AR model (i.e, set the autocorrelation parameter to 0 keeping the same predictors). I’m leaning towards the former, because I feel strange about the models that have almost no predictors.