How to interpret margins in percentage points when the independent variable is a percentage?

[Laiy Kho]

I have 2 research questions, dependent variable of 1st question is a binary variable and I use logit regression to estimate it on STATA. The dependent variable of second research question is in percentage (proportional variable, between 0 and 1 including 0 and 1). I use fractional response regression on Stata. In both research questions, my key explanatory variable X is expressed in percentage. I am a bit confused and need help in interpreting the coefficient.

I have read that if both dependent and independent variable is expressed in percentage, then we can interpret the coefficient as percentage point. I estimated the margins after fractional regression using margins dydx command, if the coefficient is -0.5, then we interpret it as with one percentage point increase in X, Y decreases by 0.5 percentage points. Am I correct?

Secondly, in the case of logit regression, where dependent variable is a binary variable 0 or 1, I am predicting likelihood of an event. So, 1 = if event occurs and 0 otherwise. I am interested in interpreting the margins in percentage points. I estimated the margins after logit regression using margins dydx command. The coefficient for X (margin output) is -0.88. How do I interpret this coefficient? Is it correct to say with a percentage point increase in X, the likelihood of event reduces by 0.88 percentage points? I am confused if it is to be interpreted as 88 percentage points or 0.88 percentage points? Can someone explain this in simple terms?

Thank you

[George Ford]

Assuming X is always on the unit interval:

A one-pp change would be 0.005 in the first case and 0.0088 in the second.

can also run both model using regress. The coef should be very similar to your margins results and you'd interpret like OLS (dY = dX, where dX is 0.01).

Say mean of X = 0.5. Another option to clarify is:

margins, at(x = (0.50 0.51))

But note that the margins are not equal across all values of X.

try,

margins, at(x = (0(0.01)1))
marginsplot

clear
set obs 1000

g x = runiform()

g y = 0.4+0.3*x+rnormal(0,.1)
g yb = rbinomial(1,y)

summ y yb x

reg y x
margins, at(x = (0.5 0.51)) post
di e(b)[1,2] - e(b)[1,1]

fracreg logit y x
margins, dydx(x)
margins, at(x = (0.5 0.51)) post
di e(b)[1,2] - e(b)[1,1]

reg yb x
margins, at(x = (0.5 0.51)) post
di e(b)[1,2] - e(b)[1,1]

logit yb x
margins , dydx(x)
margins, at(x = (0.5 0.51)) post
di e(b)[1,2] - e(b)[1,1]

logit yb x
margins, at(x = (0(0.01)1)) post
marginsplot

[Laiy Kho]

But note that the margins are not equal across all values of X.

Thank you for clarifying. I estimated margins as following

logit y x
margins, dydx( x ) post

When I do not specify at what level of variable x, what is the meaning of the results? Does stata automatically use any level of x in providing margins with the above command?

I am not particularly interested in finding the margin at a certain value of x, I just want to know as the value of x increases, what is the impact on y. Is the above command sufficient for this purpose?

Also just to confirm,

A one-pp change would be 0.005 in the first case

In the first case (fractional regression), both dependent variable and explanatory variable is in percentage (%). Would it be wrong to interpret as "with one percentage point increase in X, Y decreases by 0.5 percentage points" ?

I am interested in interpreting the impact of X on Y for both results in percentage points.

Accordingly for the second result (logit),

A one-pp change would be 0.005 in the first case and 0.0088 in the second.

Here you are interpreting the impact of X on Y as percentage right? Essentially, with one percentage pointincrease in X the likelihood of event reduces by 0.88%, right?

Here X is a variable expressed in %, and Y is binary variable.

Is there any way to unify the scale of impact, as such with one percentage point increase in X, the likelihood of event reduce by _____ percentage points?

Appreciate your help, thank you!

[George Ford]

A one-unit change is a 100pp change. Use the "at" version and you can compute it.

dydx will give you the result at the mean of X or the mean effect of X as observed (depending on what you ask for).

the "at" option will give you exactly what you want without having to scale it.

[Nick Cox]

Cross-posted at https://stats.stackexchange.com/ques...-variable-is-a

Please note our policy on cross-posting, which is that you are asked to tell us about it. https://www.statalist.org/forums/help#crossposting