Strange logLik's

[snip]

I constructed a linear mixed-effects model:

lme1<-lme(lenght~MG+dry.months+rainfall, random=~1|provenance/tree)

[snip]

3)      The variables 'dry.months' and 'rainfall' are the same within
every provenance. What means this for the model?

Without seeing the coefficient estimates it is impossible to tell, really, 
but I've been thinking about this for another model, so here's what I 
think (and hopefully, if it is really wrong someone will correct me)

forgetting about the random effect for a moment, length~dry.months is an 
estimate of the linear relationship between dry.months and leaf length. 
when you add a random effect of the form ~1|provenance you are allowing 
for there to be a different line for every provenance - parallel lines, 
because only the intercept is different. This model partitions the 
variation among provenances into two parts - one explained by the number 
of dry months, and everything else that differs between provenances. Why 
are these things different? Well, imagine you want to predict the leaf 
length in a new provenance not included in your current dataset. You can 
use the coefficient of dry.months times the number of dry months in the 
new provenance to tell you the average leaf length. The estimated variance 
of the random effect of provenance tells you how much additional variation 
you expect in that *average* leaf length. If you want the variance of the 
distribution of leaf lengths then you'd also need to add in the residual 
variance. And of course in your model you have also estimated the 
variation associated with trees within provenances - essentially you now 
have as many parallel lines as there are trees. 

The part that seems somewhat unnatural to me is that you can get an 
estimate of the effect of something that varies among the groups used in 
the random effect - seems like you are accounting for that variation among 
groups in two ways, which feels illegal somehow. I'm guessing that it 
works better when you have more groups.  In addition, if the fixed effect 
was a factor with as many levels as there are groups I think you run into 
problems as well. And by problems I mean a failure to converge. 

hth,

Drew Tyre

School of Natural Resources
University of Nebraska-Lincoln
416 Hardin Hall, East Campus
3310 Holdrege Street
Lincoln, NE 68583-0974

phone: +1 402 472 4054 
fax: +1 402 472 2946
email: atyre2 at unl.edu
http://snr.unl.edu/tyre