[R-sig-ME] prediction intervals (bands) with lme4

[Emmanuel Curis]

Hello,

On Wed, Aug 14, 2013 at 02:56:44PM +0200, Alexander Bauer wrote:

> For each of these models, i can perform prediction (e.g. with
> fitted()) leading to x predictions. For a large x, the 95% percentile
> confidence interval should be a 95% prediction interval. Did I
> overlook something?

Not sure what a «  95% percentile confidence interval » is.

Assuming your 95 % « percentile confidence interval » means the 95 %
confidence interval of the mean of these predictions, the answer is
« no, it does not give the prediction interval » because it will be as
small as you want, increasing x.

Assuming it means the interval between the 2.5% and 97.5% percentiles
of the x predictions, it is probably correct asymptotically; however,
I would check on two points:

 - how theoretically sounded is the use of bootstrap for this kind of
   problems ;

 - the fact that when doing similar approach for experimental data
   directly, leading to a non-parametric prediction interval, to have
   a 95% interval you should not use these percentiles but instead use
   a correction, see Guttman, « Statistical Tolerance Regions:
   classical and Bayesian », 1970, Numéro 26 de Griffin's statistical
   monographs & courses --- prediction intervals corresponds to the
   b-expectation tolerance intervals in this book.

Sorry not to be more precise, don't have my bibliography available for
the moment...

Please correct if anything above is wrong...

-- 
                                Emmanuel CURIS
                                emmanuel.curis at parisdescartes.fr

Page WWW: http://emmanuel.curis.online.fr/index.html