From: Spencer Graves <spencer.graves_at_pdf.com>

Date: Tue 03 Oct 2006 - 22:54:28 GMT

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Wed Oct 04 08:58:44 2006

Date: Tue 03 Oct 2006 - 22:54:28 GMT

I actually see two violations of the "compound symmetry" assumptions in the Oats example numbers you provide below. You mentioned the fact that the 3 different numbers in cor(random.effects(f4OatsB)) are all different, when compound symmetry would require them to all be the same. In addition, note that in VarCorr(fm4OatsB), Corr does not equal sigma1^2/(sigma1^2+sigma.e^2), as suggested by the theory.

One might naively expect that the algorithm might constrain the parameter estimates to meet this compound symmetry assumption. I don't know why the algorithm does not produce that, but it doesn't bother me much that it doesn't, because the numbers are close, especially since this data set includes only 3 varieties and 6 blocks, producing 6 estimated random effects for each variety.

Someone more knowledgeable may provide more detailed comments.

Hope this helps. Spencer Graves

Mi, Deming wrote:

> Dear R users,

*> I have a question about the patterned variance-covariance structure for the random effects in linear mixed effect model.
**> I am reading section 4.2.2 of "Mixed-Effects Models in S and S-Plus" by Jose Pinheiro and Douglas Bates.
**> There is an example of defining a compound symmetry variance-covariance structure for the random effects in a
**> split-plot experiment on varieties of oats. I ran the codes from the book and extracted the variance and correlation
**> components:
**>
**>> library(nlme)
**>> data(Oats)
**>> fm4OatsB <- lme(yield~nitro, data=Oats, random=list(Block=pdCompSymm(~Variety-1)))
**>> VarCorr(fm4OatsB)
**>>
**> Block = pdCompSymm(Variety - 1)
**> Variance StdDev Corr
**> VarietyGolden Rain 331.5271 18.20788
**> VarietyMarvellous 331.5271 18.20788 0.635
**> VarietyVictory 331.5271 18.20788 0.635 0.635
**> Residual 165.5585 12.86695
**>
**> This is a compound symmetry variance-covariance structure. I then tried to find out the standard deviation and
**> correlation matrix of the BLUPs predictors of the random effects and wish all three standard deviations would be close
**> to 18.20788 and the correlation structure would be consistent with a compound symmetry structure.
**>
**>
**>
**>> sd(random.effects(fm4OatsB))
**>>
**> VarietyGolden Rain VarietyMarvellous VarietyVictory
**> 16.01352 15.17026 19.83877
**>
**>> cor(random.effects(fm4OatsB))
**>>
**> VarietyGolden Rain VarietyMarvellous VarietyVictory
**> VarietyGolden Rain 1.0000000 0.6489084 0.8848020
**> VarietyMarvellous 0.6489084 1.0000000 0.6343395
**> VarietyVictory 0.8848020 0.6343395 1.0000000
**>
**> The correlation structure is far from a compound symmetry structure, and the standard deviation of three random effects are
**> all different from 18.20788. On the contrary, the result is more like the one from a general positive-definite
**> variance-covariance structure.
**> Can anyone tell me why I did not see a compound symmetry structure from the BLUPs predictors of the random effects or if
**> I am doing something wrong?
**> Thank you!
**> Deming Mi
**> deming.mi@vanderbilt.edu
**>
**>
**> [[alternative HTML version deleted]]
**>
**> ______________________________________________
**> R-help@stat.math.ethz.ch mailing list
**> https://stat.ethz.ch/mailman/listinfo/r-help
**> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
**> and provide commented, minimal, self-contained, reproducible code.
**>
*

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Wed Oct 04 08:58:44 2006

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.1.8, at Wed 04 Oct 2006 - 00:30:07 GMT.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help.
Please read the posting
guide before posting to the list.
*