[R-sig-ME] lme and prediction intervals

[Ben Bolker]

Douglas Bates wrote:
> On Sat, Apr 3, 2010 at 11:12 PM, D Chaws <cat.dev.urandom at gmail.com> wrote:
>> Ok, issue solved for the most straightforward random effects cases.
>> Not sure about nested random effects or more complex cases.
> 
> Assuming that you can make sense of lsmeans in such a case.  You may
> notice that lsmeans are not provided in base and recommended R
> packages.  That isn't an oversight.  Try to explain what lsmeans are
> in terms of the probability model.
> 
> Anyway, if you are happy with it, then go for it.  I'll just give you
> a warning from a professional statistician that they are a nonsensical
> construction.

  lsmeans may not make sense in general (I don't really know, I have a
somewhat weird background that mostly doesn't include SAS), but there's
nothing wrong with wanting predictions and standard errors of
predictions, which be definable (?) if one can specify (a) whether a
given random effect is set to zero or included at its conditional
mean/mode value (or, for a simulation, chosen from a normal distribution
with the appropriate variance-covariance structure (b) whether random
effects not included in the prediction (and the residual error) are
included in the SE or not.  I agree that specifying all this is not as
easy as specifying "level", but can't one in principle do this by
specifying which random effects are in/out of the prediction or the SE?

  My hope is that, after building code for a reasonable number of
examples, the general principles will become sufficiently clear that a
method with an appropriate interface can then be written (note use of
the passive voice).  The hardest part I discovered for doing this with
existing lme and lme4 objects is recalculating the random-effects design
matrix appropriately when a new set of data (with different
random-effects factor structure) is specified ...

  Ben Bolker