Choosing dyex or dydx for fracreg?

[Tarjei W. Havneraas]

I am working on a fractional response model where the outcome, y, is a fraction and the predictor, x, is a fraction as well. Both variables mainly have values <.1. Ideally, I want to apply margins to get the percentage point increase in the response, given a one percentage point increase in the predictor. Realistically, I know margins will provide an approximation to a change in y given a one unit change as x is not discrete. My code is:

fracreg probit y x
margins, dyex(*)
margins, dydx(*)

As far as I know, dydx(*) gives the change in percentage point while dyex(*) gives the change in percentage (see e.g., this Stata post). However, this example of fracreg seem to be interpreting dyex as a percentage point change. Which one is correct?

In my case, the mean response value is low, at around .02. What puzzles me is that dydx gives a *considerably* higher estimate than dyex. While dydx provide a value of .3, dyex gives a value of .01. An increase of 30 percentage points would hardly make sense, while a 1 percentage point increase is sensible. Moreover, graphical inspections of the variables does not seem to support the large percentage point change implied by dydx. Intuitively, I would expect an absolute change in percentage points to be lower than a relative percent change, at least in the data I am working with.

I have spent quite some time looking at Stata documentation and googling without a confident conclusion on dydx and dyex, so any input on interpretation would be appreciated.

[Fei Wang]

In you case, -dydx- directly gives what you want. For example, -dydx- provides a value of 0.3, implying that one percentage point increase in x is related to a 0.3 percentage point increase in y. The 0.01 from -dyex- means one percent increase in x is associated with a 0.01 percentage point increase in y. Given that the mean of x is somewhere between 0 and 1 and closer to 0 according to your description, one percent increase in x would be far smaller than one percentage point increase in x, and it would be natural to observe a far smaller number from -dyex- than -dydx-

[Tarjei W. Havneraas]

Thanks for your reply, Fei Wang! For clarification,

-dydx- provides a value of 0.3, implying that one percentage point increase in x is related to a 0.3 percentage point increase in y.

The output for -dydx- is 0.3. As both x and y are fractions, they must be multiplied by 100 to interpret as a percentage, so the -dydx- result is then implying that a one percentage point increase in x is associated with a 30 percentage point increase in y, right? I may of course misunderstand this.

[Fei Wang]

No, you don't need to rescale 0.3. The 0.3 from -dydx- means one unit increase in x is associated with 0.3 unit increase in y. One unit increase represents 100 percentage points increase for both x and y. So 0.3 means 100 percentage points increase in x is associated with 30 percentage points increase in y, which is equivalent to that one percentage point increase in x is associated with 0.3 percentage point increase in y.

[Tarjei W. Havneraas]

Ok, that breakdown was helpful. I was not aware that the one unit increase refers to a full 100 percentage point increase here; I thought of it as the change in y given a .01 increase in x. I believe this was my source of confusion. Thanks for clearing this up for me!

[Mienke Knipe]

Thanks Tarjei W. Havneraas for highlighting this issue and Fei Wang for your guidance. I had a similar concern since the stata post and the youtube video (mentioned in your first post) (and ChatGPT might I add) gave contradictory advice. Tarjei W. Havneraas I'd appreciate a link to your publication on the work mentioned above.