[R] variance estimates in lme biased?

[Gary Allison]

Pascal,
If every run of my simulation produced results like you saw, I would not 
be concerned.  But a sizable fraction of my simulation runs produce much 
larger standard deviations in level 1, though level 3's estimates stay 
small.  I've posted the results from 500 runs at:

http://david.science.oregonstate.edu/~allisong/R/nestVar_toR2.csv
http://david.science.oregonstate.edu/~allisong/R/nestVar_toR2.pdf
(and the code that produced it)
http://david.science.oregonstate.edu/~allisong/R/NestedSim_toR2.R

- compare the range of estimated variances for level 1 vs. level 3 
(levels with no simulated variance).  For example, what do you make of 
run 6?

My concern is how I am to interpret some experimental results I have 
where both level 1 and level 2 standard deviations are high. I'm perplexed.

Thanks,
Gary

Pascal A. Niklaus wrote:
> Running lme on your data set results exactly in what you expect - or do 
> you expect something different?
> 
> Pascal
> 
>  > L1<-factor(F1f)
>  > L2<-factor(F2f)
>  > L3<-factor(F3f)
>  > lme(value ~ 1,random = ~ 1 | L1/L2/L3)
> Linear mixed-effects model fit by REML
>  Data: NULL
>  Log-restricted-likelihood: 438.9476
>  Fixed: value ~ 1
> (Intercept)
>  0.2955631
> 
> Random effects:
> Formula: ~1 | L1
>        (Intercept)
> StdDev:  0.02472988              <== level F1 which is 0
> 
> Formula: ~1 | L2 %in% L1
>        (Intercept)
> StdDev:    1.140782                <== level F2 which is 1
> 
> Formula: ~1 | L3 %in% L2 %in% L1
>         (Intercept)  Residual
> StdDev: 0.0005512791 0.1020479   <== F3 which is 0 , and F4 which is 0.1
> 
> Number of Observations: 625
> Number of Groups:
>                L1         L2 %in% L1 L3 %in% L2 %in% L1
>                 5                 25                125
> 
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