[R-sig-ME] Extracting variances of the estimated variance components in lme4

[Douglas Bates]

On Thu, May 3, 2012 at 7:46 AM, Freedom Gumedze
<Freedom.Gumedze at uct.ac.za> wrote:
> Dear all,
>
> How does one extract extracting variances of the variance components in
> lme4?
> vcov(model) only gives the covariance matrix of fixed part of the
> fitted model,
> while VarCorr(model) only gives the estimated variance components
> without their corresponding standard errors.
> Yes the standard errors are asymptotic but how does one extract them
> from the fit?

The omission of standard errors on variance components is intentional.
 The distribution of an estimator of a variance component is highly
skewed and obtaining an estimate of the standard deviation of a skewed
distribution is not very useful.  A much better approach is based on
profiling the objective function.  See
http://lme4.R-forge.R-project.org/slides/2012-03-22-Paris/Profiling.pdf
(that URL may not be visible for an hour or so).


> many thanks,
> Freedom
>>>> Ben Bolker <bbolker at gmail.com> 2012/05/03 02:31 PM >>>
> Angelina Mukherjee <angelina.mukherjee88 at ...> writes:
>
>> I have response measures corresponding to 2 patients. The structure
> is as
>> follows:
>>
>> Patient 1:  Region 1             Region 2              Region 3
>>                S1 S2 S3 S4       S1 S2 S3 S4        S1 S2 S3 S4
>>
>> Patient 2:  Region 1               Region 2            Region 3
>>                 S1 S2 S3 S4       S1 S2 S3 S4        S1 S2 S3 S4
>
>
>  Hmm.  Do you really have only two patients, i.e. a total of
> 24 response values?  I understand that you're trying to do a
> variance decomposition here (no fixed effects, only random
> effects), but your estimates of variance will be extremely
> inaccurate based on only two patients (you might want to consider
> making patient a fixed effect, then you would at least have
> 6 data points (5 df) for the patient:region variance ...
>
>> Each patient has 3 regions and each region has 4 sub-regions.
> (nested
>> design)
>>
>> Fitting   *lme( Response ~ 1, random=~ Patient + Region +Subregion |
>> Patient/Region/Subregion )*
>> allows me to specify covariance structure for the 'sub-region' term.
>>
>> But I'm trying to fit a random effects model of the form as I have
> only 1
>> observation per 'sub-region':
>> *lme( Response ~ 1, random=~ Patient + Region | Patient/Region )*
>>
>> Is there a way I can specify a covariance structure like
>> the auto-regressive (to specify that correlation decreases with
> distance as
>> one moves from Subregion 1 to Subregion 4) for the 'sub-region' term
> only
>> as it is not included in my random effects model but I'd like to
> account
>> for the correlation in it?
>
>   I would think that something like
>
> lme(Response~1, random = ~1|Patient/Region,
>   correlation=corAR1(~Subregion))
>
>  But I also think you're fitting a more complicated model
> than can really be supported by 24 data points ...
>
>  Ben Bolker
>
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