Below... > > 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? > > For some aspects, yes. Given that R provides you with the > means to fit > robust linear models, why not use them and find out if they make a > difference to the aspects you are interested in? > > -- > Brian D. Ripley, [EMAIL PROTECTED] > Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ > University of Oxford, Tel: +44 1865 272861 (self) > 1 South Parks Road, +44 1865 272866 (PA) > Oxford OX1 3TG, UK Fax: +44 1865 272595 >
Or do your inferences in a way that does not depend on normality, perhaps via (careful to honor the multilevel sampling assumptions) bootstrapping? Cautions apply. First, linear mixed models is actually a nonlinear modeling technique, as is robust linear fitting. So the process may be sensitive to initial values I believe this was pointed out to me by Professior Ripley, though in a different context. I would appreciate any more informed comments and qualifications about this. Second, both the normal theory inference and bootstrapping are asymptotic and therefore approximate. I believe this was the point Prof. Ripley was making when he said "For **some** aspects..." Comparing results under various assumptions is always a good idea to check sensitivity to those sets of assumptions, though it may emphasize the fact that choice of the "right" analysis may be a complex and application and data specific issue. Cheers, -- Bert Gunter Genentech Non-Clinical Statistics South San Francisco, CA ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
