0
$\begingroup$

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?

$\endgroup$
0
$\begingroup$

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.

$\endgroup$
4
  • $\begingroup$ Hi Erwan - absolutely, I agree. I am making a major assumption based on the relationship between the variables. Is there any relevant literature on this topic you might suggest? $\endgroup$ – bashity Dec 21 '20 at 20:55
  • $\begingroup$ Fair enough! I was thinking the areas like 'Small Area Estimation' or 'Imputation', but I think you're right. I need to demonstrate that it is a reasonable assumption in my data. I know of some fine-grained analogous sources where I might be able to do so. Thanks! $\endgroup$ – bashity Dec 21 '20 at 23:52
  • $\begingroup$ @bashity I don't know small area estimation but imputation is for the case where you have partial data with missing values, so you would need at least some data at the fine-grained level. $\endgroup$ – Erwan Dec 22 '20 at 8:27
  • $\begingroup$ no problem! I took your advice and conducted a test of the proposed linear relationship that is based on the population proportion. I then identified some 'true' fine-grained dataset that had a very similar (if not the same) variable. The estimated quantity and 'true' data so far demonstrate a very strong relationship (cor 0.94, absolute difference quite small). It's still has a ton of assumptions, but I'm going to scale this check to as much data as possible. Thank you a ton - yours was an excellent suggestion! $\endgroup$ – bashity Dec 22 '20 at 16:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.