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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