Re: [R] variance-covariance structure of random effects in lme

From: Spencer Graves <>
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
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> mailing list PLEASE do read the posting guide and provide commented, minimal, self-contained, reproducible code. Received on Wed Oct 04 08:58:44 2006

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