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

Daniel Ezra Johnson danielezrajohnson at gmail.com
Sun Dec 21 16:40:22 CET 2008

---------- Forwarded message ----------
From: Daniel Ezra Johnson <danielezrajohnson at gmail.com>
Date: Sun, Dec 21, 2008 at 3:39 PM
Subject: Re: [R-sig-ME] lmer stand dev of coefficients
To: Douglas Bates <bates at stat.wisc.edu>

Can you explain briefly what circumstances would lead these quantities
to be quite different?

Suppose the random effect grouping factor is Subject.

On what basis would the software estimate the unconditional SD of (the
population of) Subjects to be something quite different (and as you
say, usually larger) than that of the particular group of Subjects in
the data?


On Sun, Dec 21, 2008 at 3:32 PM, Douglas Bates <bates at stat.wisc.edu> wrote:
> 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.
> P.S. If you are starting a new topic on the mailing list you don't
> need to quote a previous message to the list and especially not an
> entire digest message.
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