[R] nlme and variance-covariance matrices.
Jarrod Hadfield
jarrod.hadfield at imperial.ac.uk
Fri Apr 4 15:19:30 CEST 2003
--
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.
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