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
[EMAIL PROTECTED]
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