# 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?

## 1 Answer

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.

• 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? – bashity Dec 21 '20 at 20:55
• 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! – bashity Dec 21 '20 at 23:52
• @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. – Erwan Dec 22 '20 at 8:27
• 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! – bashity Dec 22 '20 at 16:00