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


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