How to compute marginal estimate of interaction term in probit model with ##?

[Tanima Ahmed]

Dear Statalist,

I am not being able to compute the marginal probit estimates when I run the probit model with the interaction term using ## command. Example: I am running a model:
probit nn female##i.provider_group_nonwkda
where I have provider_group_nonwkda = 0,1,2 and female=0,1

The probit estimate I get is:
----------------------------------------------------------------------------------------
nn | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
1.female | -.3815376 .0112263 -33.99 0.000 -.4035407 -.3595345
|
provider_group_nonwkda |
Weekly | .076711 .0325869 2.35 0.019 .012842 .1405801
Daily | -.4846047 .0477395 -10.15 0.000 -.5781725 -.3910369
|
female#|
provider_group_nonwkda |
1#Weekly | .0726932 .0409042 1.78 0.076 -.0074775 .1528639
1#Daily | .2651311 .0594447 4.46 0.000 .1486216 .3816407
|
_cons | .595262 .0085057 69.98 0.000 .5785912 .6119328
----------------------------------------------------------------------------------------

But after the log odd estimates I want to compute the margin of 1#weekly and 1#Daily. I used the margin command: margin, dydx(*) but I am not getting any results. I only get the marginal estimates of female and i.provider_group_nonwkda as below:
----------------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
1.female | -.1339451 .0038084 -35.17 0.000 -.1414095 -.1264807
|
provider_group_nonwkda |
Weekly | .0428335 .0069229 6.19 0.000 .0292648 .0564021
Daily | -.1284197 .0114771 -11.19 0.000 -.1509143 -.1059251
----------------------------------------------------------------------------------------


I can only compute the marginal estimate of 1#weekly and 1#Daily if I run probit explicitly by using the dummy interaction of female with provider groups like:
probit nn female i.provider_group_nonwkda female_weeklycom female_daily

The probit estimate is:
----------------------------------------------------------------------------------------
nn | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
provider_group_nonwkda |
Weekly | .076711 .0325869 2.35 0.019 .012842 .1405801
Daily | -.4846047 .0477395 -10.15 0.000 -.5781725 -.3910369
|
female | -.3815376 .0112263 -33.99 0.000 -.4035407 -.3595345
female_weeklycom | .0726932 .0409042 1.78 0.076 -.0074775 .1528639
female_daily | .2651311 .0594447 4.46 0.000 .1486216 .3816407
_cons | .595262 .0085057 69.98 0.000 .5785912 .6119328
---------------------------------------------------------------------------------------


The marginal estimates with: margins, dydx(female i.provider_group_nonwkda female_weeklycom female_daily) or margins, dydx(*) is:
----------------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
provider_group_nonwkda |
Weekly | .0274973 .0115214 2.39 0.017 .0049158 .0500788
Daily | -.1862453 .0185577 -10.04 0.000 -.2226178 -.1498728
|
female | -.139162 .0039807 -34.96 0.000 -.146964 -.13136
female_weeklycom | .0265141 .0149181 1.78 0.076 -.0027248 .055753
female_daily | .0967039 .021672 4.46 0.000 .0542276 .1391802
----------------------------------------------------------------------------------------


My question is , how to get the same marginal estimates using the interaction (##) in the model. I cannot run the second model because I am mainly interested to run a simultaneous model with cmp:
cmp (provider_group_nonwkda = female##parents_not_here) (nn = female##i.provider_group_nonwkda), ind(5 4)


Can anyone please help me with the margin command to compute marginal estimates after cmp or probit using ## in the model? Because after cmp the command below does not work:
margins, dydx(female##i.provider_group_nonwkda) predict(pr eq(nn))

I need to know the marginal estimates of 1#weekly and 1#Daily for my research.

Thanks in advance.

[Clyde Schechter]

My question is , how to get the same marginal estimates using the interaction (##) in the model.

You can't, they don't exist. When you have an interaction model, you can estimate marginal effects of each of the interacted variables separately, either averaged, or conditional on specific values of the other. But the interaction term itself has no marginal effect. There is simply no such thing. It's like asking what color an idea is (hat tip N. Chomsky). That's why -margins- doesn't compute them.

As you have discovered, if you create your own product variable and use that without factor-variable, you can trick -margins- into calculating a "marginal effect" for that variable. But the result you are getting is not the marginal effect of anything; it is just a meaningless number that corresponds to nothing in the real world.

[Tanima Ahmed]

Ok, you are right. Got that now. Thank you so much for the quick
reply.