Main effects and/versus Interactions

[Messu Melu]

Hi all,

I have four vars:
outcome coded as 0 "no" 1 "yes"
race coded as 1 "asian" 2 "latin" 3 "black" 4 "white"
region_res coded as 1 "South" 2 "West" 3 "Midwest" 4 "Northeast"
rural coded as 0 "no" 1 "yes"
The dataset is coplex survey data; thus, I svyset and ran logistic regressions with region-race interactions as follows.

svy: logit outcome ib3.race##ib3.region_res i.rural, or

	Linearized
outcome	Odds Ratio	P>t
race
1	0.50
2	0.24	***
4	0.34	***
region_res
1	0.30	*
2	1.67	*
4	0.43	***
race#region_res
1 1	4.90
1 2	0.22
1 4	0.73
2 1	10.26	**
2 2	2.43
2 4	2.15	*
4 1	4.66
4 2	1.58
4 4	5.00	***
1.rural	0.06	***
_cons	14.52	***

However, I then thought that residing in a specific region and having a specific racial background are discrete characteristics for each observation that I could not get the whole point of including the main effects of region and race in the regression analysis. So, I excluded the main effects got the following output.

svy: logit outcome ib3.race#ib3.region_res i.rural, or

	Linearized
outcome	Odds Ratio	P>t
race#region_res
1 1	0.74
1 2	0.19	***
1 3	0.50
1 4	0.16	***
2 1	0.74
2 2	0.96
2 3	0.24	***
2 4	0.22	***
3 1	0.30	*
3 2	1.67
3 4	0.43	***
4 1	0.49
4 2	0.91
4 3	0.34	***
4 4	0.73
1.rural	0.06	***
_cons	14.52	***

MY QUESTION:
Am I right with my second point, 'partial factorial'? I'm just wondering if this may affect the analysis.

Thank you!

I use Stata15.1/SE version

[Clyde Schechter]

You can do this either way. You just have to be sure you know how to interpret whichever way you do. I would say that the best way to interpret these results is to use the -margins- command, as it will give you the right results either way and you don't have to worry that you've done it wrong.

[Messu Melu]

Thank you very much Clyde, for you fast response! This is very helpful! Sure, I will use margins to interpret. However, I could not find any examplary literature for interpreting two interacting variables with four categories each. Am I right if I just compare each interaction with reference groups the way I can do for two interacting binary variables?

[Clyde Schechter]

Yes. When you have variables with multiple levels and you use the single # interaction operator, it is as if you had a single variable representing all 16 combinations of race and region and then entered that into the model as i.combination_race_region_variable. One category will be omitted as the reference, and each of the other categories gives an odds ratio relative to that omitted category.

If you follow that up with -margins race#region- you will get output for all 16 combinations showing their predicted probabilities--which for most people is probably easier to grasp than a series of odds ratios.

[Messu Melu]

Thank you very much once again, dear Clyde!

[Messu Melu]

I found these UCLA annotations helpful as well.

https://stats.idre.ucla.edu/stata/fa...n-interaction/