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] [[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.