Non normal random effects

Contrary to what is often claimed, it is not the normality of the
random effects themselves that matters, but the normality of 
the sampling distribution of the relevant fixed effect.  In mixed 
models, there is by comparison with iid models the additional 
complication that normality can affect the trade-offs between 
the different components in the fitted model.   Opportunities
for such trade-offs are large if there are several random effects
and there is imbalance or incompleteness (some combinations
of factor levels missing) in the fixed effects structure.  Non-normality
in the random effects can then be both hard to detect and have
implications for inference.

There is an examination of a data set with a relatively complicated 
random effects structure in the overheads at:
http://www.maths.anu.edu.au/%7Ejohnm/r-book/2edn/xtras/mlm-ohp.pdf

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.
http://www.maths.anu.edu.au/~johnm

Non normal random effects

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