:package: :game_die: R/txshift: Efficient Estimation of the Causal Effects of Stochastic Interventions, with Corrections for Outcome-Dependent Sampling
We should have a way of including user-specified estimates for Q, g, and Pi. This should be trivial to implement.
@benkeser concurs
"In general, I think the most important next step is to add the functionality to input our own estimates of Q, g, and Pi. I think we could be seeing excess bias due to the fact that g is not being estimated well (too few or too many bins) AND the regression of the EIF ~ V | Delta = 1 is not being estimated well (surely the main terms GLM is misspecified). Because we have the nice multiple robustness property, we are seeing that the estimates are still consistent...in spite of the fact that we’re doing a shitty job estimating EIF ~ V | Delta = 1 (and g too, since if we fix the number of bins there will be bias asymptotically). However, we’re saved by the fact that we get Q and we get Pi. In fact, we’re truly saved by the fact that we get those guys with a GLM, so that we’re still asymptotically linear. It’s (very) cool that we can already see that this is the case. Nevertheless, the finite-sample coverage is still garbage, so we see that for inference in small samples, we need to be doing a better job getting all the relevant nuisance parameters."
We should have a way of including user-specified estimates for Q, g, and Pi. This should be trivial to implement.
@benkeser concurs "In general, I think the most important next step is to add the functionality to input our own estimates of Q, g, and Pi. I think we could be seeing excess bias due to the fact that g is not being estimated well (too few or too many bins) AND the regression of the EIF ~ V | Delta = 1 is not being estimated well (surely the main terms GLM is misspecified). Because we have the nice multiple robustness property, we are seeing that the estimates are still consistent...in spite of the fact that we’re doing a shitty job estimating EIF ~ V | Delta = 1 (and g too, since if we fix the number of bins there will be bias asymptotically). However, we’re saved by the fact that we get Q and we get Pi. In fact, we’re truly saved by the fact that we get those guys with a GLM, so that we’re still asymptotically linear. It’s (very) cool that we can already see that this is the case. Nevertheless, the finite-sample coverage is still garbage, so we see that for inference in small samples, we need to be doing a better job getting all the relevant nuisance parameters."