With regards to this question: Is there a rationale why Laplace integration is inappropriate here? It does allow model selection in this fashion, but with your new code Laplace provides F-stats/Pvalues for all terms except those with Time, and the error “Estimated G matrix is not positive definite”
The missing F stats and the Estimated G matrix statements point to an issue that the model is too complex to fit with this amount of data and a single point quadrature. My normal reaction there is to drop back to RSPL methods, and sacrifice IC calculations. One thing you might try is method=quad(fastquad). I am not up to speed on using that option yet, so it didn't occur to me that it might help. When I try, I get an ERROR: Insufficient resources to perform adaptive quadrature with 3 quadrature points. METHOD=LAPLACE, corresponding to a single point, may provide a computationally less intensive possibility
If you have a cloud account, you might be able to increase your MEMSIZE to use this method.
Given that, you could try selecting a covariance structure based on the generalized chi-square/DF ratio. Look for the structure that minimizes the absolute value of ln(generalized chi-squared/DF). That would give the structure that results in the smallest amount of over- or under-dispersion (and no, I don't have a reference for that method, so it is pretty much an ad hoc kind of thing. Any structure selected that way is crucially dependent on the distribution/link used and conditional on the fixed effect solution.
On to the covariate shrub as a mediator that serves as a surrogate for year - here I believe you are correct. I would proceed with caution though, as I doubt the number of shrubs is a complete surrogate for the year effect. Right now I am trying to fit a spline to the variable covar as maybe something better, but it is slow going.
SteveDenham
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