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I've got regional level data and I want to impute said data on a county level strata (smaller strata with respect to the regional strata). I know I can do that if I have a series of variables on the county level that I can use as proxys to determine their "share" according to their size.

For example, in a region that has two countys, if county 1 has a size of 40 and county 2 has a size of 60 on a proxy variable, I can guess that they get 40% and 60% of the regional value that I'm looking to impute.

Is this the best approach? Are there any models that deals with this issue? If there is a model, is there a way to know a goodness of fit to such model (how precise are my guesses)?

Thank you!

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