Hi all, and thanks in advance for any responses.

I'm estimating the following model: mlogit enroll_method ses_index2 i.race2 physical2 emotion2 i.enroll_site enroll_age i.period, vce(robust), where enroll_method is one of six contraceptive methods selected at enrollment in a study and ses_index2 is a composite index with continuous values.

For each enroll_method, I have run the margins command to get the predicted probability at the 10th and 90th percentile values of the ses_index2:
margins, at(ses_index2=(1 6)) predict(outcome(2))

For this example I get the following results:

Predictive margins Number of obs = 12,316
Model VCE : Robust

Expression : Pr(enroll_method==2), predict(outcome(2))

1._at : ses_index2 = 1

2._at : ses_index2 = 6

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | .1607696 .004946 32.50 0.000 .1510756 .1704636
2 | .114489 .0061308 18.67 0.000 .102473 .1265051
------------------------------------------------------------------------------


I now want to test whether .1607696 is significantly different than .114489, but am having trouble finding sufficient documentation to do this on (1) a continuous independent variable and (2) for different values of the same independent variable.

Any and all advice would be deeply appreciated!
Best,
Kelsey