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design matrices in MCMCglmm

3 messages · Alexandre Martin, Jarrod Hadfield

Original
Alexandre Martin
# 
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
Jarrod Hadfield
# 
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.

Cheers,

Jarrod






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

  
    

      
      
    

  


  


      

    

    
3 days later

    

      
      

        


  

        

      Alexandre Martin
    

    

      
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Hi Jarrod,

Thank you for your help.
My question is now extended to the subject of associative indirect 
genetic effects.

For example in this data set :
id    cage
a    1
b    2
c    1
d    1
e    2
f    2
g    2

cage is a grouping variable describing the composition of cages. For 
instance, individuals a,c,d live in cage 1.

Design matrix Z_cage typically produced by MCMCglmm should be:
      c1   c2
a    1    0
b    0    1
c    1    0
d    1    0
e    0    1
f    0    1
g    0    1
where phenotype of individuals {a, b, ..., g} are linked to cages 1 and 2.

Design matrix Z_mates, however, linking the phenotype of individual i to 
its cage' mates is:
      a    b    c    d    e    f    g
a    0    0    1    1    0    0    0
b    0    0    0    0    1    1    1
c    1    0    0    1    0    0    0
d    1    0    1    0    0    0    0
e    0    1    0    0    0    1    1
f    0    1    0    0    1    0    1
g    0    1    0    0    1    1    0

It is Z_cage that is given by default, whereas it is matrix Z_mates that 
should be used to predict associative effects.

Is it possible to force MCMCglmm to work with Z_mates instead of Z_cage?

Thanks again!

Alexandre

Le 2015-03-28 04:01, Jarrod Hadfield a ?crit :