[R] Robustness of linear mixed models

[Bruno L. Giordano]

Hello,

with 4 different linear mixed models (continuous dependent) I find that my 
residuals do not follow the normality assumption (significant Shapiro-Wilk 
with values equal/higher than 0.976; sample sizes 750 or 1200). I find, 
instead, that my residuals are really well fitted by a t distribution with 
dofs' ranging, in the different datasets, from 5 to 12.

Should this be considered such a severe violation of the normality 
assumption as to make model-based inferences invalid?

Thanks a lot,
    Bruno