Re: Mean of breeding values different from 0 / covariance issue

From: Arthur <asremlforum_at_VSNI.CO.UK>
Date: Tue, 14 Apr 2009 23:34:38 +0100

Dear TOmmy,

"Regarding covariances, i have respectively 10 and 20 levels for year and year of birth. Should I put at least one effect as fixed?" I can't tell you what you should do. Depending on the structure of the data, differences caused be the 'environment' could affect the reported breeding values if say Year effects are fitted as random. Treating Year as fixed ensures there is no 'recovery of "year" information'. It is common for environmental effects to be fitted as fixed, but they are sometimes fitted as random, especially if there are many levels or they are derived on the basis of randomization arguments.

Concerning the correlation structure you mentioned, which could explain a mean of BV different from zero, i'm not sure to understand its origin?

Consider 3 observations: 2 4 6.
Under an independent model, the mean is 4 and the residuals are -2, 0, 2

However, if we add some correlation to the model by saying observations 1 and 2 represent one family, and the 3rd observation represents a second family, we might say that the mean is 4.5, family effects are -1.5 and +1.5 and residuals are -1, +1, 1.5

Now if we make family random, family effects take on values -f, f where f is between 0 (independent model) and 1.5 (fixed model).
For a variance ratio 1.5, mu is 4.333, f is 1.0 so the simple residuals are
-1.333, +.667 +.667

However, if we used a variance structure at the residual level (i.e.
instead of fitting family, we use a correlation matrix to fit the equivalent model),
the residuals would be -2.333, -.333 and 1.667 which do not sum to 0.0

When you use a genetic relationship matrix, you are incorporating the family and individual effects and so the BLUPs do not in general sum to zero.

I trust that helps.

Arthur Gilmour

Retired Principal Research Scientist (Biometrics)

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Received on Wed Apr 14 2009 - 23:34:38 EST

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