Should I keep Insignificant interaction term in the model?

[Laiy Kho]

Hello,

I employed an OLS regression with one unique independent variable and several control variables. From the control variables, I created two interaction terms based on rationale and one based on another study. However, when I ran the regression, one of the interaction term turned to be insignificant. I followed it up with linktest, and the test result indicated that there are no specification error at 10% significance level as the p-value was 0.001. Should I keep this insignificant interaction term in my model? After removing this term, my model seems to have specification errors as the linktest is rejected. What is the correct thing to do in this case?

[Richard Williams]

The bigger question is whether you should include insignificant terms, period. You should be careful about including dubious terms in a model just to see what happens, as adding extraneous terms can inflate standard errors. See

https://www3.nd.edu/~rwilliam/stats2/l41.pdf

Put another way, there is a penalty for including junk in a model. Don't toss in anything and everything just because you think there is a wild chance something you haven't thought about may be important.

On the other hand, just because a term is insignificant does not mean it doesn't belong in the model. It may just be that you don't have enough statistical power to accurately estimate its effect. Further, in this case, it appears that the model may be mis-specified without the interaction term.

I'd probably run it both with and without. Unless it appears that an extraneous term is driving up other standard errors, I would probably leave it in.

[Carlo Lazzaro]

Laiy:
as an aside to Richard's helpful guidance:
1) as per FAQ, please share via CODE delimiters what you typed and what Stata gave you back. Thanks;
2) I'm also not cler with your statement "there are no specification error at 10% significance level as the p-value was 0.001" If, for ant reason, you went;

. linktest, level(90)

you should make it explicit in your post, as -level(90)- is not the standard. In addition, was the same option used in -regress-, too?
3) the .linktest- outcome tells you that, with a bit of genealization, your model is correctly specified. Therefore, you are cleared to proceed to your next waypoint, being that a research report or else.

[Laiy Kho]

Thank you both for your response.

Carlo:

Here are my results for the linktest:

LoanRate	Coefficient	Std. err.	t	P>t	[95% conf.	interval]
_hat	1.045663	.013813	75.70	0.000	1.01859	1.072736
_hatsq	-.1478771	.0446686	-3.31	0.001	-.2354261	-.0603282
_cons	-.0034602	.001051	-3.29	0.001	-.0055202	-.0014002

I interpreted this result as there are no specification errors at 10% significance level. Is my inference incorrect?

[Carlo Lazzaro]

Laiy:
as far as I can see, your significant threshold is 5%.
Your -linktest- CI is a 2-way 95% one, leaving 2.5% in each tail of the sample distribution of the coefficients.