[R-sig-ME] design matrices in MCMCglmm

Jarrod Hadfield j.hadfield at ed.ac.uk
Sat Mar 28 09:01:33 CET 2015

Hi Alexandre,

The design matrices should be identical for both effects (z_{ij}=1 if  
the jth individual is the mother of individual i). The difference is  
in the correlation structure of the random effects. For environmental  
maternal effects they are assumed iid (i.e. an identity matrix) but  
for the maternal genetic effects they are assumed to be proportional  
to the A matrix. inverseA will return the inverse of A if you pass it  
the pedigree. It is this inverse that is required for forming the MME.



Quoting Alexandre Martin <alexandre.m.martin at gmail.com> on Fri, 27 Mar  
2015 16:39:40 -0400:

> Dear all,
> I am working on estimating maternal effects (genetic and environmental)
> with MCMCglmm that is new for me.
> I am trying to apply to MCMCglmm what is shown in online Muir's course
> notes made for SAS. Leanning on Henderson’s Mixed Model Equation, these
> notes explain how to solve MME to predict random effects “by hand”.
> Here is my concern:
> I do not know how to extract the design matrices for a MCMCglmm model,
> e.g. the relatedness matrix or the one for maternal genetic effects. I
> want that to understand how the design matrices are constructed by
> comparing them to what they are supposed to look like.  For instance,
> the design matrix for maternal genetic effects should relate offspring
> to all the individuals that are in the pedigree, whereas the design
> matrix for maternal environmental effects should just relate offspring
> to their mothers. Does such a difference exist when MCMCglmm constructs
> its design matrices? If not, how to include such different matrices in
> models?
> Any help will be greatly appreciated. Thank you!
> Alexandre
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