Reasons to prefer low bias with higher variance over the alternative (and vice versa) I am trying to understand the bias-variance tradeoff in practice. I have read several related questions and answers, but still have a few questions:

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*Assume we are estimating a structural equation model (SEM) and we are able to choose between two estimators: one with high bias but low variability, and one with low bias but high variability. In what settings would a researcher prefer the first vs. the latter?


*Related to the first question: with lowest MSE values representing the optimal tradeoff between variance and bias, would it ever make sense to choose an estimator with higher MSE values over one with lower MSE values? If so, when?


*If we'd pick the less biased version, would meta-analyses be useful to attenuate the high variance issue?
 A: a) Neither bias nor imprecision are desirable, and I don't recall anyone arguing that one is (in principle) worse than the other.  The issue is that they are both reasons why your sample statistic differs from the population parameter it estimates.  Bias and imprecision could be relatively worse in a particular condition or using a particular estimator, which is what the trade-off is all about (see next point).
b) No, you would never prefer an estimator with higher (R)MSE. (Root-)mean-squared error sums the (squared) bias and sampling variance, so it is a composite summary of "how incorrect you can expect your estimate to be, on average," taking both bias and imprecision into account.  Thus, (R)MSE provides a reasonable way to compare one estimator that is biased but precise vs. another that is imprecise but unbiased.
c) Yes, if the meta-analysis aggregates a sufficient amount of data, then it could overcome the lack of precision of unbiased estimation. But finding unbiased results is a huge practical problem for meta-analysis (e.g., publication bias).
