Comparing custom contrasts when interaction is not significant

[Kastchei]

Hello, everyone!

I have a model that incorporates race as (Whites vs other) and ethnicity as (Hispanic vs not).  The PI wants to look at non-Hispanic Whites vs all others as a contrast.  This is easily enough done by including the interaction in the model and writing:

lSMestimate race2*hispanic2 'All Others vs. Non-Hispanic White'  1 -3
                                                                 1  1 / divisor = 3;

It turns out that this interaction is very not significant (Type 3 p = 0.70).  I realize that the interaction staying in the model while not significant is not likely to affect my results much.  But if I did want to remove the interaction from the model and rerun, could I still do the same comparison: non-Hispanic Whites vs all others?  I've written this code, and it's estimable, but my hunch is that theoretically, the model can no longer say anything about a combination of the two groups, even though I technically can form the estimates and compare their difference.

*estimate 'Hispanic Non-White'            intercept 1 race2  0  1 hispanic2  1  0;
*estimate 'Non-Hispanic Non-White'        intercept 1 race2  0  1 hispanic2  0  1;
*estimate 'Hispanic White'                intercept 1 race2  1  0 hispanic2  1  0;

 estimate 'Avg. of All Others'            intercept 3 race2  1  2 hispanic2  2  1 (divisor = 3),
          'Non-Hispanic White'            intercept 1 race2  1  0 hispanic2  0  1,
          'Avg. of All Others vs. Non-Hispanic White' race2 -2  2 hispanic2  2 -2 (divisor = 3);

This does give an answer in the same ballpark as the model with the interaction, which might be expected since the interaction was not significant.

My reason for asking is because my real model has 8 racial groups and 3 ethnicity groups, and running the model with an interaction is not possible (quasi-complete separation in logistic).  I dichotomized race and ethnicity to get an answer to the study question, but I am just curious if I could have kept the full responses, omitted the interaction, and still answer the question.  The answer I get when I do that is very different from either of the dichotomized answers above.  I want to understand if that difference is likely because what I did is invalid or if keeping all the detail about the other racial and ethnic categories might really have changed the result a lot.

Warm regards,

Michael

[StatDave · Accepted solution]

I don't see anything wrong with your approach, but keep in mind that if you make that comparison in the model that omits the interaction, the effect of White is assumed by the model to be totally unaffected by ethnicity even if there is some small, but insignificant effect of ethnicity. BTW, you might find it more intuitive to create a single variable that has a unique value for each combination of race and ethnicity and use that in place of race, ethnicity and their interaction. That would allow you to use the LSMESTIMATE statement to write the comparison(s) of interest.

[Kastchei]

Thank you!  And duh!  I don't know why I just didn't make a combined variable.  It's so obvious now, haha.