Regression with absorbing a large number of non-mutually exclusive categories (or dummies)

Hi,

I want to run a regression, controlling for a large number of categories, similar to what could be done with areg. The issues is, that each observation belongs to (exactly) two categories.

Option 1:

areg y x, absorb(category)
doesn't work because I can only have one category, but categories are not mutually exclusive

Option 2:

reghdfe y x, absorb(category1 category2)
doesn't work because it ignores that the effect of being in one category is by assumption the same, irrespective of whether it's listed in the variable "category1" or "categroy2"

Option 3:

create indicator dummies and:
reg: y x category_dummies*

doesn't work because of the size of the dataset. Also, I don't care about the dummy coefficients/fixed effects

Any hints on how I could achieve the computational efficiency of Options 1 and 2, while retaining the assumptions of Option 3 would be very much appreciated.

I.e. how can I tell regress to control for the fixed effects without computing them.


Cheers,

Simon