[R] nlme and variance-covariance matrices.

[Jarrod Hadfield]

-- 
Dear R users,

I have data on around 2000 birds from 3 generations for which I know 
an individual's pedigree (i.e. the relationship it shares with other 
individuals e.g brother, uncle, mother) and also a pedigree based on 
foster-families, because half broods were removed from their nest of 
origin and placed in a foster parent's nest.

 From this I want to model two types of random effects.  The first are 
additive genetic effects (Va) and the variance-covariance matrix 
associated with these are nearly always positive-definite and will 
look something like the following:

  1   0   0  0.5   0
  0   1   0  0.5   0
  0   0   1   0    0
0.5 0.5  0   1   0.25
  0   0   0  0.25   1

The elements basically correspond to the proportion of genes shared 
by any two individuals.

The second matrix will model additive maternal effects (Vm) and the 
variance-covariance matrix associated with these effects will usually 
not be positive definite as shown below.

1   1    0    0   0.5
1   1    0    0    0
0   0    1    1    0
0   0    1    1    0
0.5 0    0    0    1

The elements here correspond to the proportion of genes shared by the 
(foster) parents of the two individuals.  In this case 2 individuals 
raised in the same nest that fail to breed in subsequent years will 
have identical variance-covariance elements (row 3&4).

The structure of the random effects for the model will then be:


Va  0
  0  Vm

or possibly,

    Va     Cov(a,m)
Cov(m,a)     Vm


I am quite new to both mixed effect models and R so would like to 
know if it is possible to specify specific variance covariance 
structures and whether non-positive-definite matrices can be used.

Many thanks

Jarrod Hadfield.