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

[Freedom Gumedze]

Douglas and Thierry,
 
Many thanks Douglas for the advice. I will look at the suggestion by
Douglas when the URL is visible.
The omission of the option for the standard errors of the estimated
variances (or std deviations) is understandable to avoid their 'abuse
e.g. in significance testing'. However, they should be available (if
needed) as they can be obtained from the inverse of information matrix
for the var. components.
 
Freedom  

>>> Douglas Bates <bates at stat.wisc.edu> 2012/05/03 04:01 PM >>>
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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