[R-sig-ME] Parametric bootstrap for mixed models

[Andrew Robinson]

On Wed, Mar 28, 2007 at 06:37:30PM -0500, Douglas Bates wrote:
> I have been considering how to provide functions for the parametric
> bootstrap applied to mixed models.  That is, take an lmer model,
> simulate new responses for a model with this specification and the
> parameters at the estimated parameter values, then obtain the value of
> some statistic for a model fit to the new data.
> 
> It occurs to me that it would be best to split this operation into two
> stages, one to simulate data from a fitted model and a second which
> takes a fitted model, new data and a function to apply to the updated
> model.  The reason it seems best to split write this as two functions
> or methods is because you may want to simulate from one model (the
> null model) and fit another model (the alternative) to get the value
> of the statistic.
>  
> Does this seem a reasonable approach or am I likely to paint myself
> into a corner doing this?  Is anyone sufficiently familiar with some
> of the packages that do bootstrapping to offer an alternative model?
> 
> If I do things this way, the first function can be a method for the
> simulate generic.  Any suggestions of what to call the second one?

Doug, this would be just great.

If it's not too much work, could you extend the update() function from
nlme?

First, provide a function to simulate from a fitted model.  Second,
provide an update function as you did in nlme, and which is a favorite
of mine.  The update function takes a fitted model, a new argument (eg
new data), and updates the fitted model, and a final argument which is
the the user-supplied function to extract whatever statistics they
want.

Cheers,

Andrew

-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-9763
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
http://www.ms.unimelb.edu.au/~andrewpr
http://blogs.mbs.edu/fishing-in-the-bay/