> In the example Ex11a, we have 3 lines and 9 sires,(actually the sires are
> in the lines). There is 65 observations and 74 animals in total. The addition
> an animal effect or a sire effects does not change the degrees of freedom of
> error (62), which are 65-2-1. The test for lines will be with 2, 62 df with
> number of other random effects?.
> If we use Mixed of SAS with a sire model we got 56 df for the denominator
> for testing
> lines, which comes from deducting 2 df for lines, 9-3 = 6 df for sires/lines
> and 1 df for mu. All other things are identical.
> Could someone explain the difference in df's?.
For testing for line, one can argue for 6, 56, 62 or some intermediate value
as the appropriate error degrees of
The value of 56 is obtained by treating sires as fixed in ASREML.
But if sirtes are then regarded as random, nested within lines, lines
should be tested against the 'sire' variance rather than against the
In general, it is not easy to work out the proper denominator
degrees of freedom for any test of fixed effects in a mixed model.
The EX11A example is sufficient to demonstrate the problem.
If we fit AD ~ mu Line sire we get the analysis of variance
SOurce df MS F
Line 2 2227 16.81 [against Error], 6.8 against Sire
SIre 6 327.2 2.47
Error 56 132.5
If we equate the sire MS to its expection, we get a sire variance component
of about (327.2 - 132.5)/7 = 27.8
From the mixed model fitting AD ~ mu Line !r sire
SOurce df MS F
Line 2 ? 6.43 [ which agrees with the test against Sire above]
Error 62 132.4
The variance component for sires in this model is 27.2; similar to the ANOVA
estimate. It is similar but not exact because the data is not fully
balanced and 7 is only approximately the average progeny per sire [65/9].
This is most obvious in a Split plot analysis where some components
would be tested against an 'Error A' and others against an 'Error B'.
I believe Kenward and ROger (1997) discuss this problem [Biometrics
I thought I had a discussion of this in the manual but apparantly not.
Essentially, only in a few well defined cases can we work out
precisely what the error degrees of freedom should be. However,
we see in the example that ASREML does give the appropriate F statistic
[even if we do not know its proper distribution].
Some programs just quote a Wald statistic distributed as Chi-square but this
assumes the error variance is known [infinite df]. I therefore prefer
the F test where I can usually get some indication [ie use my knowledge
of the structure of the data to quess] of what the error
df should be.
I hope this helps.
> Thank you
Arthur Gilmour PhD email: Arthur.Gilmour@agric.nsw.gov.au
Senior Research Scientist (Biometrics) fax: <61> 2 6391 3899
NSW Agriculture <61> 2 6391 3922
Orange Agricultural Institute telephone work: <61> 2 6391 3815
Forest Rd, ORANGE, 2800, AUSTRALIA home: <61> 2 6362 0046
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