Testing assumption multilevel analysis

Please keep the list in CC.

As Ben Bolker mentioned in his reply: for most things, the assumptions
carry over from the non-mixed case and the graphical diagnostics are
done the same way. I would in general avoid explicit statistical tests
of model assumptions (e.g. various tests of normality) because, like all
tests, they have failure modes (especially related to sensitivity and
specificity) and don't actually tell you what any potential violation of
assumptions is doing to your statistical procedure.

For multicollinearity, there is one additional diagnostic that lme4
gives you in its summary output, namely the correlation of fixed
effects. The exact meaning of this is perhaps a little technical
(https://stat.ethz.ch/pipermail/r-sig-mixed-models/2009q1/001941.html),
but in practical terms a high correlation suggests that there may be
multicollinearity. Multicollinearity also tends to show itself in
inflated standard errors (in the fixed effects), much as it does for
standard linear regression.

Regarding independence of errors: I find that to be an assumption that
is often best checked by knowing something about your data generating
process. For example, there may be some autocorrelation in the errors
between observations due to the way data are collected.

Best,
Phillip