Bivariate analysis with one trait replicated

From: <arthur.gilmour_at_DPI.NSW.GOV.AU>
Date: Thu, 27 Sep 2007 10:21:18 +1000

Dear Kim,
please pass this on to Suzanne Hermesch as I do not have her email

Dear Suzanne,

Let me clarify the response to your query.

Consider two traits of which the second has multiple recordings.

The basic model for trait 1 is
Y1 ~ mu Sex !r animal

and for trait 2 is

Y2 ~ mu Sex Age !r animal ide(animal)

There are two possible bivariate models depending on whether the error
residual covariance
is assumed to be at the sampling level, the animal level or possible both.

1)
If at the sampling level, Y1 is associated with just one of the Y2
observations.
Then, in a multivariate presentation of data, the Y1 observation will be
on the same record as the
corresponding Y2 measure, and be missing for the other Y2 records.

Y1 Y2 ~ Trait Tr,Sex at(Tr,2).Age !r Tr.animal at(Tr,2).ide(animal)
1 2 1
0
Trait 0 US !GP
3*0

Tr.animal 2
Trait 0 US !GP
3*0
animal 0 AINV

2)
If at the animal level, Y1 is associated with all of the Y2
observations.
Then, in a multivariate presentation of data, the Y1 observation does not
belong with
any particular Y2 observation. So, it may be given on a record by itself,
or with
say the first Y2 observation, for convenience.

Y1 Y2 ~ Trait Tr,Sex at(Tr,2).Age !r Tr.animal at(Tr,2).ide(animal)
ide(animal)
1 2 1
0
Trait 0 US !GPZP
3*0

Tr.animal 2
Trait 0 US !GP
3*0
animal 0 AINV

3)
My first guess is that there will not be enough information to fit the
error correlation
at both levels (by changing Z to P in the preceding model).

4) Warning. The scale of measurement of the traits is critical in model
2.
The data should be scaled so that the variance of Y1 and Y2 are similar
because the error varance for Y1 is paertioned into the 2 terms:
residual and ide(animal)
and residual has to be positive for ASReml to work (i.e. ide(animal) not
too big because of the scale of Y2).

Similarly, the error variance for Y2 is partitioned into
residual + ide(animal) + at(Tr,2).ide.animal
and the first and last terms need to be positive (i.e. ide(animal) not
too big because of the scale of Y1)

May Jesus Christ be gracious to you,

Arthur Gilmour, His servant .

Mixed model regression mapping for QTL detection in experimental crosses.
Computational Statistics and Data Analysis 51:3749-3764 now available at
http://dx.doi.org/10.1016/j.csda.2006.12.031

Personal website: http://www.cargovale.com.au/

mailto:Arthur.Gilmour_at_dpi.nsw.gov.au, arthur_at_cargovale.com.au
Principal Research Scientist (Biometrics)
NSW Department of Primary Industries
Orange Agricultural Institute, Forest Rd, ORANGE, 2800, AUSTRALIA

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Received on Mon Sep 27 2007 - 10:21:18 EST

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