[R-sig-ME] multivariate normality (MVN) assumption in MCMCglmm

[John Morrongiello]

Dear list,
I've fit a multivariate mixed model using the MCMCglmm package with six response variables. I have log transformed some of these responses and assume they follow a multivariate normal distribution. Univariate plots of response variables indicate that they look pretty 'normal'. I have two questions:


1)      Is there a more formal way than univariate histograms/qqplots to test that the assumption of multivariate normality is met in a multivariate mixed model?

2)      How robust are multivariate mixed models to the assumption of MVN?

I've previously used tests like Mardia's MVN test, Rayston's MVN test (MVN package) and the Shapiro-Wilk MVN test(mvnnormtest package). However, I get the feeling they are not necessarily doing what I think they are as the response variables are strongly conditional on other fixed effects in the multivariate MCMCglmm, and the data are not independent (i.e. repeated measures of each trait nested within individuals).

Cheers
John

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