Weighted estimates in model averaging

[DavyJones]

Hello,

I use the following script for model averaging:

proc glmselect data=&infile plots=(EffectSelectPct ParmDistribution);
model depvar=indepvar1 indepvar2 indepvar3
/selection=LASSO(adaptive stop=none choose=SBC) ;
modelAverage nsamples=100tables=(EffectSelectPct(all) ParmEst(all) );
run;

According to the SAS manual (page 4290 of GLMSelect procedure, SAS/STAT 15.1), the parameter estimates and standard deviation printed in the output are simple unweighted (equally weighted) averages. I wonder if there is any way to specify a weight, such as Akaike weight, as suggested by Burnham and Anderson (2002).

[Rick_SAS]

Since no one has commented, I will make a few remarks. 

I do not have a copy of B&A at home, but I believe the Akaike weights were not related to the kind of model averaging that you are doing. As I recall, in B&A, they used the full data set and ran all subsets or regression models. They then assign weights to the various models based on the AIC criterion for each model,

That is different than the MODELAVERAGE statement, which uses bootstrap resamples of the data and then computes an average, which is the bootstrap estimate for the parameter estimates. 

Now, nothing stops you from using a weighted average of the bootstrap estimates, but I don't know whether that makes statistical sense.