[R-sig-ME] VarCorr vs ranef

[David Afshartous]

For a nice discussion of this topic see p.459 of Gelman & Hill (2007).
(see http://www.stat.columbia.edu/~gelman/)


On 8/31/08 8:52 AM, "D Chaws" <cat.dev.urandom at gmail.com> wrote:

> Thanks so much for the reply.  This still seems very strange.  Even if the
> differences between population and subject effects is the issue, wouldn't
> one expect a bit more similarity between the actual effects for the subjects
> and the population effects inferred from those effects?  Dr. Bates or anyone
> else, can you resolve this mystery?  Alternatively, is there a way to get
> population estimates of the random effects for subjects (contradiction in
> terms?), like fitted.lme with the level = 0 argument?
> 
> All this is in service of an attempt to gain a simple scatterplot between
> two random effects that closely reflect the estimates from VarCorr or
> summary.  I'm sure someone must have a method for this already worked out.
> pairs.lme plots the raw data from ranef, so the discrepancy is still a
> problem there.
> 
> Thanks so much for your help.
> 
> - DC
> 
> On Sun, Aug 31, 2008 at 6:13 AM, Daniel Ezra Johnson <
> danielezrajohnson at gmail.com> wrote:
> 
>> On Sun, Aug 31, 2008 at 6:53 AM, D Chaws <cat.dev.urandom at gmail.com>
>> wrote:
>>> Can someone tell me why correlations between raw random effects are
>>> different from that provided in VarCorr for lme models?
>>> For example:
>>> 
>>> fm1 = lme(distance ~ I(age-8), random = ~ 1 + I(age-8) | Subject, data =
>>> Orthodont)
>>> R# VarCorr(fm1)
>>> Subject = pdLogChol(1 + I(age - 8))
>>>            Variance StdDev Corr
>>> (Intercept) 3.55937  1.8866 (Intr)
>>> I(age - 8)  0.05127  0.2264 0.209
>>> Residual    1.71620  1.3100
>>> 
>>> and
>>> 
>>> R# cor(ranef(fm1))
>>>            (Intercept) I(age - 8)
>>> (Intercept)      1.0000     0.5764
>>> I(age - 8)       0.5764     1.0000
>>> 
>> 
>> This isn't a complete answer, but the figures in VarCorr and the model
>> summary are the population estimates for the random effects (the
>> parameters) while everything derived from ranef() refers to the actual
>> Subjects in the data (the BLUPs).
>> 
>> Look at:
>> 
>>> sd(ranef(fm1))
>> (Intercept)  I(age - 8)
>>  1.7359554   0.1557322
>> 
>> Those figures don't match the VarCorr standard deviations either,
>> especially the second.
>> 
>> I don't know why the BLUPs pattern differently, exactly, but I did
>> look at plot(coefs(fm1)) which suggested Sex should be added as a
>> fixed effect. Once I did that, the correlation between the random
>> effects changed quite a lot (but was still different between VarCorr
>> and ranef; the population correlation was actually negative...)
>> 
>> D
>> 
> 
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> 
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