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[R-meta] extract pval from robust function

Hi Roger,

Have you tried using str() to figure out the structure and going from there?

Whether ICs are useful when one is using cluster-robust inference methods is an interesting question. I don't see why not. Cluster-robust inference methods are for making inferences about the model coefficients, while ICs are for figuring out what model may be the best (or least bad) approximation to the underlying true data generating mechanism (DGM).

We typically use cluster-robust inference methods when we are worried about the model being misspecified (e.g., not capturing all dependencies). In the present context, this often results from using an overly simplistic V matrix (assuming independent sampling errors or using a roughly approximated V matrix) but could also result from an underspecified random effects structure. In any case, we then suspect that the model is a less than ideal approximation to the DGM, but by comparing several different such misspecified models, we can still see which one(s) are better approximations. In essence, all models are misspecified, so that is an inherent reality we have to accept when using ICs for model selection.

Best,
Wolfgang