AME from Multinomial model interpretation

[Melissa Garcia]

Can you confirm whether my interpretation of average marginal effects estimated from multinomial logistic regression model is correct?

use https://stats.idre.ucla.edu/stat/data/hsbdemo, clear
mlogit prog i.female i.ses read write
margins, dydx(*) post

The predicted probability of enrolling in a general program is -.040 lower for females than males.
The predicted probablity of enrolling in an academic program is .175 greater for those with high SES than low SES.
A one unit change in read score increases the predicted probablity of enrolling in a vocational program by .011

To confirm, AMEs will be available for each of the three dependent variable categories (program: general, academic, vocational)?

[Clyde Schechter]

[quote]The predicted probability of enrolling in a general program is -.040 lower for females than males.[quote]
I agree.

The predicted probablity of enrolling in an academic program is .175 greater for those with high SES than low SES.

I agree.

A one unit change in read score increases the predicted probablity of enrolling in a vocational program by .011

This one is wrong. The vocational program corresponds to _predict == 3. (See the explanations of the categories of _predict just above the -margins- output table.) So for the difference in predicted probabilities of enrolling in a vocational program you have to look in the row with _predict == 3, where you see not 0.11 but -.008 (to 3 decimal places). In addition to the number being incorrect, you are using causal language, which is not appropriate with results derived from observational data. So, I would say this as "For two people whose reading scores differ by 1 unit, the predicted probability of enrollment in a vocational school by the one with the higher score is 0.008 lower."

Finally, remember that these numbers are all estimates inferred from data. The data contains sampling error, and possibly non-sampling error as well. So any presentation of these results should also mention the uncertainty in these estimates, as reflect in the standard error or the confidence interval.

[Melissa Garcia]

Hi Clyde, thanks for the correction regarding interpreting the wrong coefficient and the clarification regarding using causal language!