Interpreting a regressor in probit model

[Parul Gupta]

I am running a probit model to assess the determinants of private tutoring participation. One of the regressors I'm using is the teacher attendance ratio at school. The hypothesis is that higher teacher attendance should be correlated with lower tutoring.

My concern is regarding the interpretation of the coefficient of this variable. Naturally, in probit models, the coefficient itself doesn't have a meaning, and one needs to calculate the marginal effect. Should I use the dydx option with margins? What would be the interpretation of this variable which is measured as a ratio?

A similar question is posted here https://www.statalist.org/forums/for...tory-variables
However, it doesn't entirely resolve my doubt.

[Joseph Coveney]

Naturally, in probit models, the coefficient itself doesn't have a meaning, and one needs to calculate the marginal effect.

If your hypothesis is that higher teacher attendance correlates with lower tutoring participation, then wouldn't a negative regression coefficient, itself, indicate that regardless of whether the explanatory variable is measured as a ratio?

[Parul Gupta]

Right, the sign does indicate the negative correlation. But I would also like to interpret the magnitude. Suppose the estimated marginal effect is
-0.000192. Can I say that a 1% increase in teacher attendance reduces the probability of tuition participation by 0.019 percentage points?

[Joseph Coveney]

Can I say that a 1% increase in teacher attendance reduces the probability of tuition participation by 0.019 percentage points?

Others on the list do that sort of thing all of the time, but the distortion strikes me as a difficult-to-justify simplification to attempt to quantitatively express a relationship that's fundamentally nonlinear as if it were linear, in terms of some kind of average partial effect or whatever it's called.

It seems to me to be more defensible to either leave it in its original estimation metric (educate your audience if it has a problem with nonlinear functional relationships; draw a picture) or as predictions at representative values of the explanatory value (see my reply to your other post for an example).

[Jeff Wooldridge]

Parul: Is your teacher attendance variable measured as percent of days showing up? So something like 93.5? Then of the APE is -0.000192 this means that a one percentage point (not one percent) increase in the attendance rate lowers the probability of having a tutor by 0.000192 -- about 0.019 percentage points, as you said. Not a huge effect.

[Parul Gupta]

Professor Wooldridge, I've constructed the variable by dividing the number of teachers present in school on the day of the survey by total number of teachers. So, yes, I'm interpreting it as the percent of days a given teacher shows up, for example, 85 percent (this is data for India, where teacher absenteeism is high, hence this interpretation). Should I use 0.85 or 85? How will the interpretation change if I use 0.85 instead of 85?