From: <arthur.gilmour_at_DPI.NSW.GOV.AU>

Date: Mon, 26 Feb 2007 11:38:19 +1100

Date: Mon, 26 Feb 2007 11:38:19 +1100

Dear Matt,

I insert after **AG my comments intop your email.

I wish to run a bivariate animal model and then build this up into a

bivariate random regression and I was hoping for some help.

I want to model how two traits covary firstly phenotypically and then

dividing phenotypic variance into additive and residual components.

So as an example I can run random regressions each trait in this way:

ANIMAL !P # pedigree factor, refers to pedigree file

INC # horn increment growth in sheep

AGE !A # age as a factor in years 1-5

**AG Using !A on AGE and sAge is unsafe as !A causes the data values to

be treated

purely as labels and codes them in the order they appear in the data file.

I gather the years are coded in the data as 1, 2, 3, 4, 5

so AGE *

or AGE !L 1998 1999 2000 2001 2003 #(Assuming 1..5 relates to years

1998..2002)

is safer.

sAGE !A # standardized age (-1 to 1)

**AG sAGE does not actually need to be supplied given ordered levels of

AGE

but as it is, it should be given without any qualifiers, so it is

treated as a

covariate (and in particular, is not recoded )

CYR !A # year of measurement to control for

# environmental effects during the year of growth

WEIGHT # weight of the sheep measured in

Sheep1.ped !ALPHA !MAKE !SKIP 1

incNHMalesrr.asd !SKIP 1 !DOPART 1 !MAXIT 100

!part1

!MVREMOVE

INC ~ mu AGE CYR !f mv

1 2 0 !STEP 0.01

500

AGE 0 US !GP

10*0

!part2

!MVREMOVE

!PVAL sAGE -1 -0.5 0 0.5 1

INC ~ mu AGE CYR !r leg(sAGE,2).ANIMAL !f mv

1 2 1 !STEP 0.01

500

AGE 0 US !GP

10*0

leg(sAGE,2).ANIMAL 2

leg(sAGE,2) 0 US

0.1

0 0.1

0 0 0.1

ANIMAL

The first part gives me phenotypic correlations and covariances for

horn growth and the second part then breaks this down into additive and

residual components using a second order polynomial.

I know the methodology for running a bivariate model:

!part3

INC WEIGHT ~ Trait Trait.AGE !r Trait.ANIMAL

1 2 1

Trait 0 US

3*0

Trait.ANIMAL 2

Trait 0 US

3*0

ANIMAL

However I have no idea how to merge the analysis methods and seperate

both the variances and covariances into the five age groups which I

have. This would be important to me as I want to look at how early

investment in in weight and horn growth affect later trait development

and whether there's any evidence of changing phenotypic, and genetic

correlations with age.

**AG OK,

First, with just 5 ages, it is likely that the quadratic component may not

exist, so the first requirement

is to fit your PART 2 to both traits univariately, to ensure there is

variance present.

Then the extension of part 2 to bivariate (one of several ways of doing

it) is given by

!part4

INC WEIGHT ~ Trait Trait.AGE !r Trait.leg(sAge,2).ANIMAL

1 2 1

Trait 0 US

3*0

Trait.leg(sAge,2).ANIMAL 2

6 0 US !GP # replace zeros with initial values from univariate runs

0 #Trait 1 intercept

0 0 #Trait 1 slope

0 0 0 #Trait 1 quadratic

0 0 0 0 #Trait 2 intercept

0 0 0 0 0 #Trait 2 slope

0 0 0 0 0 0 #Trait 2 quadratic

ANIMAL 0 AINV

You can use the univariate analyses to provide some of these initial

values directly.

Work the otheres out roughly using the error correlation from part 3 to

work out the covariances.

Depending on the amount of data, you will probably find it difficult to

get a positive definite

solution here. I would attempt a linear random regression first.

It may be necessary to change to using an factor analytic formulation

instead of UnStructured, which is also more difficult.

A philosophical issue with this model is that it allows for different

genetic

variances at the different ages but does not allow for different residual

variances.

This is likely to bias the genetic values. So, the model

needs to be extended, maybe by adding

Trait.leg(sAge,2).ide(ANIMAL) or

Trait.AGE.ANIMAL

with appropriate structures.

or splitting the R structure into 5 components (one for each age, assuming

data sorted on AGE)

May you know Jesus Christ and His blessing in 2007,

Arthur Gilmour, His servant .

PS My Mixed Model Regression Mapping paper is now available at

http://dx.doi.org/10.1016/j.csda.2006.12.031

Profile: http://www.dpi.nsw.gov.au/reader/17263

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

fax: 02 6391 3899; 02 6391 3922 Australia +61

telephone work: 02 6391 3815; home: 02 6364 3288; mobile: 0438 251 426

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To join it, mailto:arthur.gilmour_at_dpi.nsw.gov.au

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Received on Fri Feb 26 2007 - 11:38:19 EST

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