Converging mixed models with large number of random coefficients

 I realize that one approach to this problem would be to reduce the number
of random coefficients that account for individual tree variation (Li et
al., 2012). But since individual tree heights and diameters are only
obtainable from each individual tree, I guess that all coefficients (which
are associated to these variables) should be random (Gelman, 2007). I
wonder if there is any problem with my interpretation of the mixed models
theory?

Perhaps I have misunderstood your mail (I am not familiar with nlme),
but from your description above I think you have misunderstood what
random effects do.

That the tree is random is not an argument for making a variable like
diameter random with the argument that it is a property of the tree.

If you want a general effect (a single estime) of how diameter affects
the outcome, you should have diameter as a fixed effect in your model.

If you want an estimate - per tree - of how diameter affects the
outcome for that particular tree you will need variation of diameter
within that particular tree.

I think you want the former - after all, science tends to be about the
universal stuff, not the particulars - and in that case you should
make diameter a fixed effect, and only keep the tree-id variable as
random.

Diameter was only one example, the same goes for the other variables
as well.



kind regards,

Hans Ekbrand