marginal effect of interaction term in glm (predictnl )

[Federica Di Marcantonio]

I am trying to calculate the marginal effect of an interaction term of a glm model, fam (bin) link (logit).
The marginal effect, p-value and se of the interaction term obtained with this command :

 margins, dydx(*)

are equal to -0.0638* (se=0.0288)
If I get correctly what is discussed and explained here :
https://www.stata.com/support/faqs/s...-interactions/
I should calculate the marginal effect of my interaction term as follow:

sysuse auto, clear
(1978 Automobile Data)

 set seed 12345
 generate dum=uniform()>0.5
 table dum

----------------------
       dum |      Freq.
----------+-----------
         0 |         37
         1 |         37
----------------------

generate td=turn*dum
probit foreign turn dum td, nolog

Probit estimates                                  Number of obs   =         74
                                                   LR chi2(3)      =      40.64
                                                   Prob > chi2     =     0.0000
Log likelihood = -24.712342                       Pseudo R2       =     0.4512

------------------------------------------------------------------------------
      foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         turn |  -.4162473   .1256398    -3.31   0.001    -.6624968   -.1699978
          dum |  -6.545885    5.52614    -1.18   0.236    -17.37692    4.285149
           td |   .1644299   .1498474     1.10   0.273    -.1292656    .4581253
        _cons |   15.41459   4.641172     3.32   0.001     6.318063    24.51112
------------------------------------------------------------------------------

quietly summarize turn if e(sample)
local meantur= r(mean) . quietly summarize dum if e(sample)
local meandum = r(mean)
 local xb _b[turn]*`meantur' + _b[dum]*`meandum' + _b[td]*`meantur'*`meandum' + _b[_cons]
predictnl dydt = normalden(`xb')*(_b[turn] + _b[td]*`meandum') in 1, se(set)


list dydt set in 1

   +----------------------+
   |      dydt        set |
   |----------------------|
1. | -.0725871   .0163552 |
   +----------------------+


 local xb1 _b[turn]*`meantur' + _b[dum]*1 + _b[td]*`meantur'*1 + _b[_cons]
 local xb0 _b[turn]*`meantur' + _b[dum]*0+ _b[td]*`meantur'*0 + _b[_cons]
 predictnl dydd = normal(`xb1')-normal(`xb0') in 1, se(sed)


 list dydd sed in 1

   +----------------------+
   |      dydd        sed |
   |----------------------|
1. | -.0057505   .1292351 |
   +----------------------+

predictnl dyddt =normalden(`xb1')*(_b[turn] + _b[td]) - normalden(`xb0')*(_b[turn]) in 1, se(sedt)


list dyddt sedt in 1

   +---------------------+
   |    dyddt       sedt |
   |---------------------|
1. | .0378494   .0348098 |
   +---------------------+

In order to get the p-value I have tried the follow:

predictnl dyddt =normalden(`xb1')*(_b[turn] + _b[td]) - normalden(`xb0')*(_b[turn]) in 1, se(sedt) p(pval)

Is that correct?
Can anyone clarify how I can calculate the p-value?

Thanks
Federica

[Richard Williams]

Unless you are using an ancient version of Stata, you are relying on an ancient FAQ. You should use factor variable notation instead of computing interactions yourself. And, at least the way Stata does things, there is no such thing as the marginal effect of an interaction term. See

https://www3.nd.edu/~rwilliam/stats3/Margins01.pdf

https://www.stata.com/statalist/arch.../msg00293.html