Interaction: ## versus * - OR are different

[Lisseth Aliaga]

Dear Statalist:
I have some queations

METHOD ONE: I created the following interaction variables using *. Where c1=no disease, c2=cancer c3=mental disease c4=other disease. Giving1= not caregiving, giving2=caregiving

NO CAREGIVING AND DISEASES
gen nocaregiving_nodisease= giving1*c1
gen nocaregiving_cancer= giving1*c2
gen nocaregiving_mental= giving1*c3
gen nocaregiving_other= giving1*c4

CAREGIVING AND DISEASES
gen caregiving_nodisease= giving2*c1
gen caregiving_cancer= giving2*c2
gen caregiving_mental= giving2*c3
gen caregiving_other= giving2*c4

The dependant variable es k6cat which is binary

Then proceed with the following command for logistic regression

logit k6cat nocaregiving_cancer nocaregiving_mental nocaregiving_other caregiving_nodisease caregiving_cancer caregiving_mental caregiving_other caregiverdisease caregiving sex agecat2 agecat3 agecat4 e2 e3 job setaiexpbyninsu_cat, or nolog

note: caregiverdisease omitted because of collinearity
note: caregiving omitted because of collinearity

Logistic regression Number of obs = 879,674
LR chi2(15) = 25077.54
Prob > chi2 = 0.0000
Log likelihood = -512669.93 Pseudo R2 = 0.0239

--------------------------------------------------------------------------------------
k6cat | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
---------------------+----------------------------------------------------------------
nocaregiving_cancer | 2.166334 .0488408 34.29 0.000 2.072692 2.264206
nocaregiving_mental | 5.87672 .0993783 104.73 0.000 5.685135 6.074762
nocaregiving_other | 1.427238 .0075137 67.57 0.000 1.412587 1.442041
caregiving_nodisease | 1.415696 .0518512 9.49 0.000 1.317631 1.521059
caregiving_cancer | 3.454236 .6844809 6.26 0.000 2.342505 5.093585
caregiving_mental | 8.505128 1.54574 11.78 0.000 5.95637 12.14451
caregiving_other | 2.182677 .0617268 27.60 0.000 2.064987 2.307075
caregiverdisease | 1 (omitted)
caregiving | 1 (omitted)
sex | 1.220351 .0060654 40.07 0.000 1.208521 1.232297
agecat2 | .5647246 .003999 -80.69 0.000 .5569409 .5726171
agecat3 | .6406081 .005502 -51.85 0.000 .6299146 .651483
agecat4 | .8240018 .0098324 -16.22 0.000 .8049542 .8435001
e2 | .9156378 .0056034 -14.40 0.000 .904721 .9266864
e3 | .8764097 .0060818 -19.01 0.000 .8645704 .8884112
job | 1.194357 .0071747 29.57 0.000 1.180377 1.208502
setaiexpbyninsu_cat | .9502311 .0046335 -10.47 0.000 .9411928 .9593561
_cons | .2517346 .0032518 -106.78 0.000 .2454411 .2581894


METHOD 2: using ## with the "original variables". Where Caregiverdisease; 0= no disease, 1=cancer, 2=mental disease, 3=other disease. Caregiving; 0= not caregiving, 1=caregiving

logistic k6cat i.caregiverdisease##i.caregiving sex agecat2 agecat3 agecat4 e2 e3 job setaiexpbyninsu_cat, allbaselevels

Logistic regression Number of obs = 879,674
LR chi2(15) = 25077.54
Prob > chi2 = 0.0000
Log likelihood = -512669.93 Pseudo R2 = 0.0239

---------------------------------------------------------------------------------------------
k6cat | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
caregiverdisease |
0 | 1 (base)
1 | 2.166334 .0488408 34.29 0.000 2.072692 2.264206
2 | 5.87672 .0993783 104.73 0.000 5.685135 6.074762
3 | 1.427238 .0075137 67.57 0.000 1.412587 1.442041
|
caregiving |
0 | 1 (base)
1 | 1.415696 .0518512 9.49 0.000 1.317631 1.521059
|
caregiverdisease#caregiving |
0 0 | 1 (base)
0 1 | 1 (base)
1 0 | 1 (base)
1 1 | 1.126307 .2282772 0.59 0.557 .7570724 1.675623
2 0 | 1 (base)
2 1 | 1.022294 .1902165 0.12 0.906 .7098954 1.472169
3 0 | 1 (base)
3 1 | 1.080247 .0498851 1.67 0.095 .9867683 1.182582
|
sex | 1.220351 .0060654 40.07 0.000 1.208521 1.232297
agecat2 | .5647246 .003999 -80.69 0.000 .5569409 .5726171
agecat3 | .6406081 .005502 -51.85 0.000 .6299146 .651483
agecat4 | .8240018 .0098324 -16.22 0.000 .8049542 .8435001
e2 | .9156378 .0056034 -14.40 0.000 .904721 .9266864
e3 | .8764097 .0060818 -19.01 0.000 .8645704 .8884112
job | 1.194357 .0071747 29.57 0.000 1.180377 1.208502
setaiexpbyninsu_cat | .9502311 .0046335 -10.47 0.000 .9411928 .9593561
_cons | .2517346 .0032518 -106.78 0.000 .2454411 .2581894

***************************
As you can see the OR values in the first method nocaregiving_cancer, nocaregiving_mental, nocaregiving_other, caregiving_nodisease, are the same with 1,2, 3 from caregiverdisease and 1 in caregiving. The other OR values from the first method caregiving_cancer, caregiving_mental, caregiving_other; and second method: caregiverdisease#caregiving 11 2 1 31 are different.

Is there any explanation for these differences in OR? I think these should be equal.

Thank you for your attention,

[FernandoRios]

Hi Lisset
The reason why the coefficients are different is because both methods are "omitting" different variables during the regression.
In your fist example, Stata is producing all interactions, skipping the base values. In the second, it produces coefficients for base values skipping some of the interactions.
HTH

[Lisseth Aliaga]

Fernando. Thank you for your answer. I understand.
I was trying to replicate the same with a different dataset and the values in the first and second examples were very similar. That is why I was trigerred.

Regards