Dear Erik,
Do you want to know how to create weighted statistics from tract level data ? I use PUMS data to create a model (loglinear) from a multivariate table based on PUMS variables at the PUMA level . I then adjust the model based on various marginal tables from the tract level ACS tables (synthetic estimate). (reference Discrete Multivariate Analysis - Theory and Practice, Bishop, Fienberg Holland (Find a reference on Small Area Estimation - synthetic estimates) This would allow you to get tract level statistics for the ALICE estimate You can then combine tracts to get county level estimates using the ALICE formula estimate. I would need to hear more about how the ALICE estimate is constructed. This analysis can be done in R using the survey and mipfp packages.
All this allows you to get estimates for counties that have PUMA "components' that span multiple counties. This requires a fair amount of code and the estimates need to go through a "quality check" process to make sure that you don't make an error in your program.
Your suggestion to take population weighted linear combination is a "quick and dirty" way to do this. However the parts of the PUMAS that intersect/cross the county boundary need to be relatively homogeneous across the county boundary. The only way to test this assumption is to get tract level estimates as above. The estimates above adjust for covariates from the marginal ACS tables.
Dave
PS if someone has an easier way to do this -- give us a shout out.
I just looked at reference: file:///home/dorer/Downloads/2020ALICE_Methodology_FINAL.pdf it only mentions ACS 1 year tables:
B18101 SEX BY AGE BY DISABILITY STATUS
B18106 SEX BY AGE BY SELF-CARE DIFFICULTY
in the references.
They also mention using medicare BLS IRS etc data but this data doesn't go down to the tract level.
As a minimum I adjust for the 3-way marginal age x sex x race. It looks like they add Disability status and Self-Care difficulty but not race (a big problem when you are looking at poverty statistics).
In any case the "methodology" has no statistical references and does not give the model that they are using.
I checked out some of the PhD members on the Advisory Committee and the PhD's on the author list and there are no statisticians. I would email them and ask for their statistical methods.