I would say that if what you need to do to answer your question properly is
treat a factor as random, because you need to generalize outside your
sample, and you only have 3 levels, then you don't have the data to answer
your question - you need to be less ambitious. However, the common way
around this is to be careful how you write your inference in the discussion.
"We found a strong association between X and Y which we expect to be a
general phenomenon, however so far this has only been tested at 3 sites and
further work is required to confirm ... "

I would also say that it's entirely unrealistic to suggest approach 3 to
everyone who has this sort of problem - it's just too much to expect for
most researchers to use these techniques most of the time. You have to ask
whether a simpler technique is good enough for the circumstances, for the
question being asked.



andydolman@gmail.com

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