Any thoughts on this post by @f2harrell on the value of building up marginal effect estimates from reasonably adjusted conditional ones?
I’m somewhat surprised this issue hasn’t been approached from an information theoretic or Bayesian decision theoretic experimental design perspective.
Awhile back, I posted a number of links that describe Bayesian experimental design. In that framework, maximizing expected utility is equivalent to maximizing the information from the experiment.
It seems clear to me that the methods described in BBR and RMS entail maximizing information from the entire design, collection, and analysis.
It also seems clear that observational research generally has more noise in the channel, and must take more effort at increasing the information rate.
I don’t see why it isn’t possible to borrow the framework of information theory to evaluate the channel capacity of the various proposals, and then rank them in terms of information rate and ease of implementation.