[R] random effects with lme() -- comparison with lm()

[Jerome Asselin]

Hi all,

In the (very simple) example below, I have defined a random effect for
the residuals in lme(). So the model is equivalent to a FIXED effect
model. Could someone explain to me why lme() still gives two standard
deviation estimates? I would expect lme() to return either:
a) an error or a warning for having an unidentifiable model;
b) only one standard deviation estimate.

Thank you for your time.
Jerome Asselin

> library(nlme)
> simdat <- data.frame(A=1:4,Y=c(23,43,11,34))
> simdat
  A  Y
1 1 23
2 2 43
3 3 11
4 4 34
> lme(Y~1,data=simdat,random=~1|A)
<...snip...>
Random effects:
 Formula: ~1 | A
        (Intercept) Residual
StdDev:    12.96007 4.860027
<...snip...>
> summary(lm(Y~1,data=simdat))$sigma
[1] 13.84136
> sqrt(12.96007^2+4.860027^2)
[1] 13.84136