I had 3 variables in my data as following;
1. HIV testing (y) --> coded 0 for no, 1 for yes
2. Gender (gender) --> coded 0 for Male, 1 for Female
3. Age group (agegr) --> coded 0 for <=25 yrs, 1 for >25 yrs.

I tried to find the factors associated with HIV testing.
I used the logistic model to identify factors and interaction term;

Case1: Model with main effect and interaction term

Code:
logit y i.gender i.agegr gender#agegr
predict y     // find probability in each covariate pattern
predict n, n     // identify covariate pattern
Case2: Model with only the main effect

Code:
logit y i.gender i.agegr
predict y2
predict n2, n
After I ran the commands already, I was wondering that why both cases had the same covariate pattern?
So, Case1 and Case2 had 4 patterns.
Gender Agegr Pattern no. (n)
0 0 1
0 1 2
1 1 3
1 1 4
In Case1, Why the program did not include an interaction term for covariate pattern?

Example;
In my imagination of Case1;
Should I have 16 patterns?
Gender Agegr Interaction of Gender and Agegr Pattern no.
0 0 0 (Gender=0, Agegr=0) 1
0 0 1 (Gender=0, Agegr=1) 2
0 0 2 (Gender=1, Agegr=0) 3
0 0 3 (Gender=1, Agege=1) 4
0 1 0 (Gender=0, Agegr=0) 5
0 1 1 (Gender=0, Agegr=1) 6
0 1 2 (Gender=1, Agegr=0) 7
0 1 3 (Gender=1, Agege=1) 8
1 0 0 (Gender=0, Agegr=0) 9
1 0 1 (Gender=0, Agegr=1) 10
1 0 2 (Gender=1, Agegr=0) 11
1 0 3 (Gender=1, Agege=1) 12
1 1 0 (Gender=0, Agegr=0) 13
1 1 1 (Gender=0, Agegr=1) 14
1 1 2 (Gender=1, Agegr=0) 15
1 1 3 (Gender=1, Agege=1) 16