[R-sig-ME] predictions and standard errors on model-averaged mixed effects models

[Samantha Franks]

I'm using the MuMIn package to run model selection and model averaging on a
candidate set of 10 lme models. The structure of my global model is as
follows:

Response ~ lme(x1 + x2*x3, random = ~1|species, dat, method="ML")

After using model.sel() on my candidate set of models, it appears that I
have quite a lot of model uncertainty:

   df    logLik     AICc      delta       weight
10  9 -131.0876 280.5062  0.0000000 3.551586e-01
9   7 -133.3542 280.9136  0.4074347 2.897003e-01
8   8 -132.9586 282.1814  1.6751970 1.536943e-01
7   6 -135.1632 282.4800  1.9738133 1.323775e-01
6   5 -137.2159 284.5413  4.0350878 4.722958e-02
4   4 -139.0313 286.1354  5.6292648 2.128350e-02
2   4 -143.6987 295.4704 14.9641822 1.999822e-04
5   6 -141.7289 295.6114 15.1052171 1.863657e-04
1   3 -145.5371 297.1178 16.6115902 8.775287e-05
3   5 -143.5712 297.2518 16.7456510 8.206357e-05

Hence, I would like to use the full model-averaged model-averaged
coefficients produced by model.avg for predictions and plotting the
population-level response of the main effects. So, taking the
model-averaged object like so:

pred <- MuMIn:::predict.averaging(modavg.out, newdata=newdat, level=0) #
population level response

My question specifically pertains to obtaining standard errors on
predictions from model-averaged mixed effects models. On a single model,
this has been addressed nicely on the GLMM Wiki FAQ:
http://glmm.wikidot.com/faq, where the standard errors are calculated on
the covariance matrix.

Setting se.fit=TRUE in predict.averaging:

pred <- MuMIn:::predict.averaging(modavg.out, newdata=newdat, level=0,
se.fit=TRUE)

gives a list of two component objects, the fits and the SEs.

But I wonder how the SEs in this case are calculated by predict.averaging,
and whether in fact they give a valid estimation for the SEs on
model-averaged predictions from mixed effects models? Is there such a thing
as a model-averaged variance-covariance matrix??

Many thanks for any help.
Sam

-- 
Dr Samantha Franks
Research Ecologist
British Trust for Ornithology
The Nunnery, Thetford
IP24 2PU  01842 750050
samantha.franks at bto.org <sam.franks at bto.org>
Twitter <https://twitter.com/_SamanthaFranks>  ReseachGate
<http://www.researchgate.net/profile/Samantha_Franks>

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