Margins "option continuous implied because a factor with only one level was specified in option dydx()"

[Gabor Mugge]

Hi,

I am running the following simulation of a probit estimation:

clear all
set obs 1000000
set seed 134

* categorical variable with 3 levels
gen cat=mod(_n, 3)+1

* generating latent LHS variable, with only cat==3 having a significant effect
gen y_l=rnormal(0,.1)
replace y_l=y_l+1 if cat==3

* generating LHS variable
gen y=rbinomial(1, normal(y_l))

* estimation
probit y 3bn.cat
margins, dydx(*)

For margins, Stata gives me the following output:

. margins, dydx(*)
note: option continuous implied because a factor with only one level was specified in option dydx().

Conditional marginal effects                         Number of obs = 1,000,000
Model VCE: OIM

Expression: Pr(y), predict()
dy/dx wrt:  3.cat

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       3.cat |   .3461805    .000876   395.17   0.000     .3444635    .3478975
------------------------------------------------------------------------------

Could someone please explain to me why it makes sense (from an econometric perspective) that "option continuous implied because a factor with only one level was specified in option dydx()"?
I can imagine calculating discrete marginal effects as:

probit y 3bn.cat
local bcat=_b[3bn.cat]
local bcons=_b[_cons]

* evaluating CDF at cat == 3 vs at cat == some base value 
quietly forval i=2/3{
        preserve 
        replace cat=`i'
     * evaluated normal pdf() for each observation in the training sample
        gen cdf_eval=normal(`bcat'*3bn.cat+`bcons')
     * the marginal effect of the given variable for each observation 
        su cdf_eval
        if `i'==2 {
                local at_0=r(mean)
        }
        if `i'==3 {
                local at_1=r(mean)
        }
        restore 
}
* taking the difference of these 
local discrete_marginal_effect=`at_1'-`at_0'
    
di "`discrete_marginal_effect'"

For this the output is: .34095.

Thank you!

[George Ford]

 * estimation
probit y 3b.cat
margins, dydx(*)

[Gabor Mugge]

Hi George,

Thank you very much for your response.
I think you may not have sent the full message, however. Could you please share your full answer if you intended to write one?

Thank you again,
Gabor

[George Ford]

run the code I posted and see if it gives you the result you want. using 3bn eliminates the base, causing your dichotomous problem.