Negative weights

[lbittarello]

Is there a reason for which we forbid negative weights (ref)? Some IV weighting schemes use negative weights to isolate compliers.

[lorentzenchr]

I know of 3 reasons:

• Pretty much any statical interpretation of weights requires them to be non-negative, e.g. aggregated observations/frequency weights define a weighted CDF and a CDF must map to [0, 1].
• The optimization problem might become non-convex, even for canonical log-link combinations.
  Note that with only a few negative weights, the opt problem might still be well defined.
• If one uses a true IRLS solver, the LS step takes the square root of the weights.

I also know of one real use case for negative weights:

• In particle physics, one sometimes simulates particles (reactions/interactions) and then assigns negative weights to some simulations (rows) such that the overall probabilities are well calibrated.

I could imagine an option check_for_negative-weights with default True.