From: Arthur <asremlforum_at_VSNI.CO.UK>

Date: Thu, 10 Dec 2009 09:44:46 +0000

Date: Thu, 10 Dec 2009 09:44:46 +0000

Dear luan sheng,

There is a difference between equivalent models and various ways of writing the same model. So for a job

Quadratic regression

AnimalID !P

Wt

Age

Age2 !=Age !^2

pedigree.txt

data.csv

An same animal model with quadratic regression can be written as

Wt ~ mu Age Age.Age !r AnimalID

or

Wt ~ mu Age Age2 !r AnimalID

or

Wt ~ mu Age pow(Age,2) !r AnimalID

An equivalent model is

Wt ~ pol(Age,2) !r AnimalID

The first 3 forms will give the same regression coefficviencts.

The fourth will give the same solution for the Animal effects, and the same

residual variance, but different regression coefficients for intercept, linear and quadratic coefficients because they are based on an orthogonalized version of the columns of the design matrix.

The design coefficients used for the pol() form are reported in the

.res file. The first column (intercept is unchanged). The second column

is formed by subtracting the mean Age from Age and scaling so the range is -1 to 1. The third is based on Age^2, adjusted for intercept and Age and rescaled.

The t value for the quadratic coefficient will be the same for all models, even though the actual coefficients will differ.

Say you have 4 Ages 1, 2, 3, 4

The design matrix for the original variables is

1 1 1

1 2 4

1 3 9

1 4 16

Standard orthogonal contrasts design matrix would be

1 -3 1

1 -1 -1

1 1 -1

1 3 1

However ASReml generates slightly different coefficients

after inserting some interpolation points so the quadratic curve could be plotted smoothly.

I trust this helps.

------------------------

Arthur Gilmour

Retired Principal Research Scientist (Biometrics)

-------------------- m2f --------------------

Sent using Mail2Forum (http://www.mail2forum.com).

Read this topic online here:

http://www.vsni.co.uk/forum/viewtopic.php?p=1114#1114

-------------------- m2f --------------------

Received on Fri Dec 10 2009 - 09:44:46 EST

This webpage is part of the ASReml-l discussion list archives 2004-2010. More information on ASReml can be found at the VSN website. This discussion list is now deprecated - please use the VSN forum for discussion on ASReml. (These online archives were generated using the hypermail package.)