level two weights for multi-level analysis

mey2016 over 8 years ago

Hi! I am doing an multivariable analysis (in Stata) in which my outcome variable is at the individual level and my predictor variable is at the state level. So, I would like to be able to run a multi-level model. However, the ACS weights are only at the individual level.

Has anyone ever done a multi-level analysis with ACS data (with level two at the state level)? What method have you used to deal with level two weights? E.g. disaggregated the weights for individuals in the states, created a state-level weight, etc.? Any suggestions would be appreciated! Thank you!

Stas Kolenikov over 8 years ago

Since state isn't a stage of selection in ACS (all of the first stage stratification and PSU selection happens at the level wa-a-ay finer than states), you don't have to bother with the scaling issues discussed by Pfeffermann et. al. 1998, say. You can just give the states unit weights.

If you really want to fiddle with the weights to see what alternative specifications could be, then, following Pfeffermann's suggestion, you could produce weights scaled to the effective sample size ( egen sum_wgt = total( perwt ), by(state); egen sum_wgt2 = total( perwt*perwt ), by(state); gen effn_wt = perwt*sum_wgt / sum_wgt2 ). Then you can also entertain allocating the lost weight to the states (gen fake_state_weight = sum_wgt2 / sum_wgt ) so that the total mass in fake_state_weight*effn_wt stays constant.

So in the end, you can run and compare four models, at least:
1. ignore weights whatsoever;
2. level-1 weight = ACS perwt, level-2 weight = 1
3. level-1 weight = effective sample size weight, level-2 weight = 1
4. level-1 weight = effective sample size weight, level-2 weight = fake_state_weight

You can wave hands and come up with relations between weights and outcomes and explanatory variables that would justify any of the four models. In reality, we don't know which one is right.
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