I think you can compute Wald test, but a better option may be to run the whole data together by including interaction terms using the dummy of the group in the model?
where b1 is the coefficient from the 1st logit, b2 is the corresponding coefficient from the 2nd logit. For logit, this will be z-statistics, not t, I think(?)
I still think running the model with interaction term is a better approach.
I think you need to use command window since you need to compute yourself, for example, if g is your group variable with 0 for one of the subgroup and 1 for the others,
* run 1st logit
logit y x if g==0
* record b and SE2
mat B1=e(b)
mat V1=e(V)
* run 2nd logit
logit y x if g==1
* record b and SE2
mat B2=e(b)
mat V2=e(V)
to test the difference of coefficient for x, we compute the p-value
local p=2*(1-normprob(abs(B1[1,1]-B2[1,1])/sqrt(V1[1,1]+V2[1,1])))
di `p'
if using menu, under data->create or change data->other variable creation commands->interaction expansion
then depend on if the other variables are continuous, if continuous, select I.varname1*varname3, select the variable for 健康组/非健康组 in the categorical variable, and the x (continuous) variable in continuous variable selection, click ok. It will generate new variables named start with _I
Then run the logit reg by include all the new variables named as _I in addition to the variables you already used with robust SE
It will be easy to use command window as (if you do logit Y on x by group):