[R] Confidence Intervals for Random Effect BLUP's

[Prof Brian Ripley]

On Fri, 9 Nov 2007, Rick Bilonick wrote:

> On Fri, 2007-11-09 at 10:01 -0800, Bert Gunter wrote:
>> Ummm...
>>
>> Define: "Confidence interval for BLUP" .
>>
>> I know what a confidence interval for a parameter or function of parameters
>> (which is what a predicted value is) is; but a BLUP is neither, so I don't
>> get what a confidence interval for it should mean.
>>
>> Feel free to reply off list, as this is clearly not an R question.
>>
>>
>> Bert Gunter
>> Genentech Nonclinical Statistics
>
> Would you feel better with "prediction interval"? What I'm asking is how
> to access the information from lmer to compute intervals for the BLUPS
> that reflect the uncertainty in these estimates. The code I showed was
> taken from someone who had the same question and the various replies.

I think Bert's point is important: I picked up a student on it in a case 
study presentation on this week because I could think of three 
interpretations, none strictly confidence intervals.  I think 'tolerance 
interval' is fairly standard for prediction of a random quantity: see 
?predict.lm.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595