Weighted estimators in difference_in_means

[lukesonnet]

None of our weighted DIM estimators have the same standard errors as lm_robust(), except for the clustered and block-clustered cases which match because they farm all the work out to lm_robust (there may still be degrees of freedom discrepancies anyways).

Currently, I am able to replicate weights::wtd.t.test() and fits with the estimates I've been able to find online, but this doesn't match lm_robust(..., se_type = "HC2")

devtools::install_github("DeclareDesign/estimatr", ref = "weightdim")
n <- 8
dat <- data.frame(y = rnorm(n), z = c(0, 1), w = runif(8))
lm_robust(y ~ z, data = dat, weights = w)
difference_in_means(y ~ z, data = dat, weights = w)

with(dat, weights::wtd.t.test(y[z==1], y[z==0], w[z==1], w[z==0])

What underlies weights::wtd.t.test() are the same weighted variance and means we get from SDMtools that @acoppock linked in Slack.

We can:

a) figure this out b) farm all weighted estimation to lm_robust, erroring if there are matched pairs and weights as lm_robust can't accomadate this case (Imai et al talk about weights, but for specific estimands) c) basically error whenever someone tries to do weighted d-i-m for now and (i) do nothing or (ii) transparently tell them they should use lm_robust

[acoppock]

I think we've settled on (b) pending figuring it out, i.e. (a) is the goal for a future version

[lukesonnet]

(b) is implemented in 8886b94, leaving this issue open and tagging as future to figure this out.