Ok with a "small amount" of non-normality?

The question that you ask does not admit of an easy answer!
Hopefully the following will shed light on the general tack to be taken.

One can do simulations and check the effect of one or other level of
skewness (usually skewness to the right) on the parameter estimates.

The residuals (whether level 0 or level 1 in your case) are rarely the
right quantities to check for normality.  The way they are offered as
a source of insight in the Pinheiro and Bates book seems to me 
misleading in this respect.  

Consider a split plot design, with treatments estimated at the level of
plots within blocks, as in the kiwishade dataset in the DAAG package.
What matters for comparing treatments is the (approximate) normality
of what in the Genstat world would be called effects at the plot level.  
There are just 12 of these.  They can for this balanced design be 
obtained by basing the analysis on the plot means; they are the 
residuals from that analysis.

Any skewness at the subplot level gets somewhat averaged out.
(There are 4 subplot values per plot.)    The residuals from the lme
model, whether at the subplot or plot level, will exaggerate any 
skewness that may be due to variation between subplots.  Even in this
simple case, these 'effect' estimates are correlated, which somewhat
complicates the checking for normality. 

Direct checks for the distribution of the relevant quantities get quite messy
for unbalanced designs.  Bootstrap methods, having regard to the 
covariance structure, might be considered.  Or make a stab at the
distributions of the relevant component effects (now as in an lme or lmer
sense), and simulate.

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

Ok with a "small amount" of non-normality?

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