interaction term

[Jaeyong Yoo]

Hello,

I created an interaction term of two binary variables and added it to the model, using two different ways.

1. logit freq_move i.ace1_2 NbhdSupp_2021_d ace1_2#NbhdSupp_2021_d, nolog

I used "#" to create the interaction term.

The results are below:

freq_move	Coefficient	Std. err.	z	P>z	[95% conf.	interval]
1.ace1_2	1.037921	.0342157	30.33	0.000	.970859	1.104982
NbhdSupp_2021_d	-.2266996	.051156	-4.43	0.000	-.3269636	-.1264357
ace1_2#NbhdSupp_2021_d
0 1	-.0978577	.056232	-1.74	0.082	-.2080703	.0123549
1 1	0	(omitted)
_cons	-1.941679	.01769	-109.76	0.000	-1.976351	-1.907007

It seems the values "1" are omitted. So, I tried to create the interaction term manually like this: gen interaction2 = ace1_2 * NbhdSupp_2021_d

2. logit freq_move i.ace1_2 NbhdSupp_2021_d interaction2, nolog

Here are the results:

freq_move	Coefficient	Std. err.	z	P>z	[95% conf.	interval]
1.ace1_2	1.037921	.0342157	30.33	0.000	.970859	1.104982
NbhdSupp_2021_d	-.3245573	.0233473	-13.90	0.000	-.3703172	-.2787974
interaction2	.0978577	.056232	1.74	0.082	-.0123549	.2080703
_cons	-1.941679	.01769	-109.76	0.000	-1.976351	-1.907007

The sign of the interaction term is changed from negative to positive.

I think it is because the number of value "1" is small. (3.49%)

interaction
2	Freq.	Percent	Cum.
0	86,978	96.51	96.51
1	3,147	3.49	100.00
Total	90,125	100.00

In this case, how I interpret this result? Should I use a positive coefficient?

Thanks!

[Clyde Schechter]

Something is wrong here. You should not be seeing that 1 1 (omitted) in the first. It suggests that your data do not include the observations needed to support an interaction model. Run

tab ace1_2 NbhdSupp_2021_d

I suspect you will find that the ace1_2 = 1, NbhdSupp_2021_d = 1 will show a zero. If I am right about that, then you cannot do an interaction model here because of the absence of complete data for it.

If I am wrong, then the problem may have arisen because of the way you wrote your original model. You first show NbhdSupp_2021_d by itself, without a prefix, which leads Stata to think it is continuous. Then you also included it in an interaction term, again without a prefix, which leads Stata to think it is discrete. This sort of thing can get Stata very confused and produce inaccurate results, although I would more expect to see the problem pop up with -margins- than -logit-. Anyway, a better way to do this is actually:

logit freq_move i.ace1_2##i.NbhdSupp_2021_d // N.B. ##, not #
margins ace1_2#NbhdSupp_2021_d // N.B. #, not ##
margins ace1_2, dydx(NbhdSupp_2021_d)
margins NbhdSupp_2021_d, dydx(ace1_2)

But I emphasize that if that cell in the table I recommended you create above is, in fact, 0, no amount of recoding can fix it: you would need better data to proceed. You must have observations in all four cells of that table in order to fit an interaction model properly.

[Jaeyong Yoo]

Hello Clyde,

Thank you for your suggestion. I followed what you suggested.

 
 tab ace1_2 NbhdSupp_2021_d

NbhdSupp_2	ace1_2
021_d	0	1	Total
0	29,675	5,812	35,487
1	51,491	3,147	54,638
Total	81,166	8,959	90,125

It seems there are no problems of two variables. And then I ran this code below:

 
 logit freq_move i.ace1_2##i.NbhdSupp_2021_d // N.B. ##, not #

It works!

freq_move	Coefficient	Std. err.	z	P>z	[95% conf.	interval]
1.ace1_2	1.037921	.0342157	30.33	0.000	.970859	1.104982
1.NbhdSupp_2021_d	-.3245573	.0233473	-13.90	0.000	-.3703172	-.2787974
ace1_2#NbhdSupp_2021_d
1 1	.0978577	.056232	1.74	0.082	-.0123549	.2080703
_cons	-1.941679	.01769	-109.76	0.000	-1.976351	-1.907007

I found why 1 1 was omitted. I did not put "i" before NbhdSupp_2021_d.

When I ran this code again, I got the same results.

logit freq_move i.ace1_2 i.NbhdSupp_2021_d ace1_2#NbhdSupp_2021_d, nolog

Thank you so much for your help, Clyde.