generalized-additive-models | A document | Machine Learning library

Note that for this model it might make more sense to use a Tweedie response via family tw with gam() and bam(), which can't be used with gamm(). In fact, Simon Wood and Matteo Fasiolo fit these data with a location scale Tweedie GAM (wherein they model the mean, variance and power parameters of the Tweedie distribution each with a separate linear predictor [model]).

At @BenBolker's suggestion: I wouldn't even bother testing the random effect in this model specifically, and often I don't care if it is significant or not. It depends on the question or hypothesis I am working on. Often I want it in the model due to some clustering in the data that I want included in the model regardless of the significance.

However, I'm not convinced that the theory of the (Generalized) likelihood ratio test (GLRT) doesn't apply to the use of quasi-likelihood in this instance. Simon Wood presents derivations in Appendix A of the 2nd edition of his textbook on GAMS that show that the previously-derived results for maximum likelihood estimation (which include results for the GLRT) hold if we replace the log likelihood with the log quasi likelihood. This, at least Simon seems to be arguing, would suggest that the interpretation of the test I mention below and which is implemented in summary.gam() for random effects, is as reliable as if it were based on a proper likelihood.

Unless I really needed to, I'd fit this model with gam() or bam() and then gamm4() (the latter from the gamm4 package), before gamm(), especially for non-Gaussian models, as the gamm() function has to fit this model as a mixed effects model using penalised quasi likelihood, which is not necessarily the best way of estimating these models.