[R-sig-ME] comparing treatment with different skewness

Ben Bolker bbolker at gmail.com
Thu Mar 3 17:38:15 CET 2011

On 11-03-03 03:11 AM, Maarten de Groot wrote:
> Dear list,
> I have a problem regarding choosing the distribution family for a mixed
> model. I want to compare my response variable y with treatment A,B,C and
> D. In each of the treatments the distribution of y is differently. Is
> there a way to implement this in a mixed model?

  A little more information would be useful.

  If the distributions of the data grouped by treatment are all normal
and share the same variance but differ in their means, then we get the
standard framework for mixed models.

  If the distributions are all normal but differ in their variance by
treatment, then you can use the weights= statement in lme (see
?varClasses) to model different residual variances by treatment.

  If you can transform the response variable so that one or the other of
the above is approximately true, then you can proceed from there.

  If you need to model (e.g.) skew-normal distributions with different
skew parameters in each treatment group, then you are (as far as I know)
beyond the scope of what standard mixed model packages offer, and you'll
have to go to "build your own" tools such as WinBUGS or AD Model Builder
(both free/open source and with available interfaces).

  Ben Bolker

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