mixed model testing

Whether or not you need a mixed model, e.g. random versus
fixed slopes, depends on how you intend to use results.

Suppose you have lines of depression vs lawn roller weight
calculated for a number of lawns. If the data will always be
used to make predictions for one of those same lawns, a
fixed slopes model is fine.

If you want to use the data to make a prediction for another
lawn from the same "population" (the population from which
this lawn is a random sample, right?), you need to model
the slope as a random effect.

Now for a more subtle point:

In the prediction for another lawn situation, it is possible that
the slope random effect can be zero, and analysts do very
commonly make this sort of assumption, maybe without
realizing that this is what they are doing.  You can test whether
the slope random effect is zero but, especially if you have data
from a few lawns only, failure to reject the null (zero random
effect) is not a secure basis for inferences that assume that
the slope is indeed zero. The "test for zero random effect, then
infer" is open to Box's pithy objection that
"... to make preliminary tests on variances is rather like putting to
sea in a rowing boat to find out whether conditions are sufficiently
calm for an ocean liner to leave port".


John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.

Is there a formal way to prove the need of a mixed model, apart from  
e.g. comparing the intervals estimated by lmList fit?
For example, should I compare (with AIC ML?) a model with seperately  
(unpooled) estimated fixed slopes (i.e.using an index for each  
group) with a model that treats this parameter as a random effect  
(both models treat the remaining parameters as random)?

Thank you!

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