coding R structure in a bivariate model

From: Alastair Wilson <Alastair.Wilson_at_ED.AC.UK>
Date: Thu, 14 Jun 2007 12:33:00 +0100

Hello,

I am trying to fit a bivariate animal model where one trait (BW) has
repeated measures on 408 animals, (with phenotype recorded at 13 ages),
and the other trait (ELF) is measured only once. I've performed a
univariate analysis of BW (part 1 below) using a simple random
regression model (on age) for the additive effect, a pe effect, and a
diagonal error structure that has 13 age-specific residual variances.
The univariate analysis of ELF (part 2 below) is a straightforward
animal model partitioning variance into Va and Vr.

However, I'd like to run a bivariate model (part 3) and I'm having
trouble working out how to code the R structure. What I have below (part
3) works but fits a single Vr across all
age classes for BW. What I'd like to end up with the age specific Vr's
for BW (as in my univariate model), a Vr for ELF, and a COVr between BW
at each age and ELF, i.e. a structure like:

?
0 ?
0 0 ?
0 0 0 ?
0 0 0 0 ?
0 0 0 0 0 ?
0 0 0 0 0 0 ?
0 0 0 0 0 0 0 ?
0 0 0 0 0 0 0 0 ?
0 0 0 0 0 0 0 0 0 ?
0 0 0 0 0 0 0 0 0 0 ?
0 0 0 0 0 0 0 0 0 0 0 ?
0 0 0 0 0 0 0 0 0 0 0 0 ?
? ? ? ? ? ? ? ? ? ? ? ? ? ?

Where "?" is a (co)variance to be estimated
Below is the code I have so far, if anyone can offer any suggestions I'd
be very grateful.

Best,

Alastair

####################################
!part 1 # random regression model for BW

# 12 age-specific records for each of 408 animals
#ageF is age as 13 level factor

BW ~ mu age !r !{animal animal.age !} ide(animal)

1 2 2 !STEP 0.001

408
ageF 0 DIAG !S2==1
1 1 1 1 1 1 1 1 1 1 1 1 1 #13 starting values

animal 2
animal 0 US
1.277
0.1132 0.1287
animal

ide(animal) 1
ide(animal) 0 ID 0.1

###########################

!part 2 #univariate animal model for ELF

ELF ~ mu !r animal

##############################

!part 3 #bivariate model

BW ELF ~ Trait at(Tr,1).age !r !{Trait.animal at(Tr,1).animal.age
!} at(Tr,1).ide(animal)

1 2 2

0
Trait 0 US !S2==1
1
0 1

Trait.animal 2
3 0 US
0.3
0.1 1.2
0.1 0.1 0.13
animal 0 AINV

at(Tr,1).ide(animal) 1
ide(animal) 0 ID 0.1

--
Alastair J Wilson
NERC Research Fellow
Alastair.Wilson_at_ed.ac.uk
http://www.biology.ed.ac.uk/research/groups/awilson/
tel. 0131 6513673
Institute of Evolutionary Biology
School of Biological Sciences
The University of Edinburgh
Ashworth Laboratories
The King's Buildings
West Mains Road
Edinburgh EH9 3JT, UK
Received on Mon Jun 14 2007 - 12:33:00 EST

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