Fractional logistic regression equation

[Dean Isa]

Hi,
I have a dataset with strictly proportional data and all the variables used in my fractional regression are proportions. My question is more of a theoretical one - does the fracreg logit command still assume that my model is linear in its parameters? And if it is, how do I know which explanatory variable should be squared in my regression model? my data is an aggregate of binary responses globally and are random for the most part.
I mean the standard (PRATE I X) = B, + BzMRATE +.... etc equation - help would be hugely appreciated.

Edit:
Say i wanted to use a logit quasimaximum likelihood estimation as in the attached picture, how would i then write the equation?

[Jeff Wooldridge]

Dean: In that equation you can take G() to be the logistic function, which has an S-shape bounded below by zero and above by one. It is not a linear equation. If it were linear, you'd just use OLS and interpret the parameters has effects on PRATE. When G is logistic, use the margins command to get the average partial effects.

JW

[Dean Isa]

Dean: In that equation you can take G() to be the logistic function, which has an S-shape bounded below by zero and above by one. It is not a linear equation. If it were linear, you'd just use OLS and interpret the parameters has effects on PRATE. When G is logistic, use the margins command to get the average partial effects.

JW

Thank you for the reply - it was very helpful. Would that still apply if I was to use a beta regression instead of a fractional logit regression?

[Jeff Wooldridge]

Yes. The default for betareg is a logistic mean function.

betareg requires a full distributional assumption and does not apply when y takes on either zero or one.