Methods of disaggregating data to smaller units? I have a relatively straightforward question that I know poses some difficult challenges.
Let's say I have a state-level rate of X. I would like to disaggregate the state-level rate to the county-level. I realize this is can be dangerous (ecological fallacy), but I have seen some studies use the technique with a set of assumptions.
For example, if I know that each county is a certain proportion of the entire state population, I could take that proportion and multiply it by the state-level rate of X to get an (incredibly) naive county-level rate of X.
I'm trying to find more information on ways to make this approach 'less' naive, but I can't seem to get any momentum. I've tried using the terms 'disaggregating' and 'weights', but I can't seem to tap into the right body of literature.
Does anyone know of any methods/body of work that have attempted to handle this problem?
From a statistical point of view this is impossible if one doesn't have any data at the fine-grained level. Any statistical inference must be based on a sample from which specific patterns can be observed.
If there is no data at the fine-grained level, any calculation is based on assumptions. For example one may assume that a variable is proportional to population (linear relation). But why not assume that the variable is a polynomial function of the temperature? Or that it is related to the prevalence of a particular gene? The main issue is that without any data there's no way to test any of these assumptions, so no there can be not reliable conclusion.