Trey Causey writes:

Do you have suggestions as to model selection strategies akin to Bayesian model averaging for multilevel models when level-2 inputs are of substantive interest? I [Causey] have seen plenty of R packages and procedures for non-multilevel models, and tried the glmulti package but found that it did not perform well with more than a few level-2 variables.

My quick answer is: with a name like that, you should really be fitting three-level models!

My longer answer is: regular readers will be unsurprised to hear that I’m no fan of Bayesian model averaging. Instead I’d prefer to bite the bullet and assign an informative prior distribution on these coefficients. I don’t have a great example of such an analysis but I’m more and more thinking that this is the way to go. I don’t see the point in aiming for the intermediate goal of pruning the predictors; I’d rather have a procedure that includes prior information on the predictors and their interactions.

An a non-statistician could I request a post or two on examples of good and bad priors? There’s some resources and articles but too often they use “toy” examples which is annoying. Can you some up some real-world examples of “good” and “bad” priors.

Rahul:

See my 2006 paper in Bayesian Analysis.

It is possible to estimate models with MCMC in MLwiN. It’s something worth looking into.