Note that mash uses two distinct strategies to improve accuracy of effect estimates: (i) it shrinks estimates towards zero, which improves average accuracy because most effects are null; (ii) in the presence of “structured effects”, it shares information across conditions to improve accuracy. For example, if a unit has effects that are similar across a subset of conditions, averaging the effect estimates in those conditions will improve accuracy. Both these strategies contribute to the strong performance of mash in the “shared, structured” scenario.
