[R-sig-ME] Looking for an effect of relatedness in non-normal data (MCMCglmm)

[Jarrod Hadfield]

Hi Megan,

Its hard to say how much of a problem it is without seeing the  
distribution of the *residuals* and the phylogenetic effects.  
Certainly, the normal likelihood is not robust to outliers because of  
its thin tails, and this will be a problem for MCMCglmm (and linear  
mixed models fitted in other packages). You can run MCMCglmm on  
permuted data, but I always find it hard to permute the data under the  
correct null hypothesis. For example, if you just naively permute the  
data then a phylogenetic heritability of zero is part of the null  
hypothesis, even though this may not be the null hypothesis you would  
like to reject. This may be a problem if the statistic you are using  
depends on the phylogenetic heritability. As an alternative have you  
tried a cube-root transformation?  This is the Wilson-Hilferty normal  
approximation for the Gamma.

Cheers,

Jarrod








Quoting Megan Bartlett <mkbartl at ucla.edu> on Sun, 27 Jul 2014 22:34:32 -0700:

> Hi everyone,
>
> I'd like to use MCMCglmm to look at the importance of phylogenetic
> relatedness to variation in a plant drought tolerance trait, while also
> accounting for a random effect of study site and a fixed effect of climate.
> The difficulty is that my drought tolerance trait data is significantly not
> normally distributed (according to the *shapiro.test* function), even when
> log or square-root transformed (all p < 0.001). This comes from the fact
> that some arid species are very drought tolerant, producing a right-skewed
> trait distribution. My data is best-fit by a gamma distribution, according
> to the* fitdistrplus* package, but my data is better fit by a normal
> distribution than any other family that MCMCglmm can model.
>
> I know there are ways to fit mixed-effects models that allow for
> permutation tests, to avoid assuming normal distributions, but these
> packages (coin, lme4), don't allow for specifying a phylogenetic
> relatedness matrix. This leads me to the problem that it seems incorrect to
> use MCMCglmm to estimate a signal of relatedness for this non-normal data,
> but it also seems incorrect to use packages that allow for permutation
> tests without accounting for relatedness.
>
> So, to try to figure out a way around this, my questions are:
>
> 1) How non-normal is "too" non-normal for MCMCglmm, if no other
> distribution family is a better option? Is it ever acceptable to fit
> non-normal data this way?
>
> 2) There seem to be permutation tests (like in the *coin* package) that can
> handle significance testing for mixed-effects models, but not for models
> with the phylogenetic relatedness matrix specified. Does something like
> this exist that I'm not aware of?
>
> 3) Or, is there a way to apply a permutation test to the MCMCglmm output?
>
> Thanks very much for your help!
>
> Best,
>
> Megan
>
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>
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