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*To*: hmontald@metz.une.edu.au*Subject*: Re: df with random effects*From*: Arthur Gilmour <gilmoua@ornsun.agric.nsw.gov.au>*Date*: Tue, 2 Jun 1998 13:09:56 +1000 (EST)*Cc*: asreml@chiswick.anprod.CSIRO.AU*Reply-To*: Arthur Gilmour <gilmoua@ornsun.agric.nsw.gov.au>*Sender*: owner-asreml

> Hello: > > In the example Ex11a, we have 3 lines and 9 sires,(actually the sires are nested > in the lines). There is 65 observations and 74 animals in total. The addition of > an animal effect or a sire effects does not change the degrees of freedom of the > error (62), which are 65-2-1. The test for lines will be with 2, 62 df with any > 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 freedom. 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 'residual' variance. 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 53: 983-997]. 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 test 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 > > Hugo > <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> 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 ASREML is currently free by anonymous ftp from pub/aar on ftp.res.bbsrc.ac.uk Point your web browser at ftp://ftp.res.bbsrc.ac.uk/pub/aar/ in the IACR-Rothamsted information system http://www.res.bbsrc.ac.uk/ To join the asreml discussion list, send the message subscribe to asreml-request@chiswick.anprod.CSIRO.au The address for messages to the list is asreml@chiswick.anprod.CSIRO.au <> <> <> <> <> <> <> "Seek first the kingdom of God and His righteousness" Jesus; Matthew 6: 33 <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

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