[R-sig-ME] lmer stand dev of coefficients

Douglas Bates bates at stat.wisc.edu
Sun Dec 21 16:32:22 CET 2008

On Sun, Dec 21, 2008 at 3:55 AM, Iasonas Lamprianou
<lamprianou at yahoo.com> wrote:
> Dear friends
> when I use sd(coef(mymodel)$myvariable) I get 0.21
> However, the summary of the model gives
> Error terms:
>  Groups      Name        Std.Dev.
>  myvariable (Intercept) 0.33
>  Residual               0.76
> Why dont I get the same value (0.21 instead of 0.33)?

Because they are estimates of different quantities:
sd(coef(mymodel)$myvariable) is an estimate (although it is not
entirely clear what the properties of such an estimate would be) of
the conditional standard deviation of the random effects given the
data, whereas 0.33 is the maximum likelihood estimate or REML estimate
of the unconditional standard deviation of the random effects.  We
would expect the conditional standard deviation to be smaller than the
unconditional standard deviation.

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