Yes you should.

As you stated, the interaction is not with the main exposure of interest, however, when running multiple regression models, you are claiming to consider several variables aiming to explain a specific outcome, which means you should include possible interaction between variables. Keep in mind that you must explain the interaction, since from time to time, there are mathematical interactions that have no clinical meaning.

To explain the interaction, you may have to run additional regression models with doomies variables of the combination among the interaction of the main regression model.

I hope you find this useful.

I agree.

In general the advice would be add any interaction that (a) makes sense from theory/understanding of how factors may interact and (b) if adding the interaction term improves the model fit. The explanation of an interaction is that the association between one covariate and the outcome is dependent upon the level of a 2nd covariate. For example if the association between age (covariate) and ischaemic heart disease (outcome) is different for men vs women (2nd covariate). From my understanding you should keep the original covariates also as independent effects as well as the interaction.

You say that there is not much change in the coefficient for association between exposure of interest and outcome. In this case the interaction is simply describing more of the variation in outcome that is not explained by the main exposure (i.e. you have a more complete model explaining the outcome).

Hope this helps

tim

I am generally not in favour of introducing interaction terms in a model, unless they are pre-specified. This because with (say) 5 independent variables, there are 20 possible interaction terms, and you end up with a bit of a fishing expedition! So, unless there is a good reason to suspect a significant interaction, I would be inclined not to include these terms.

This nice post captures the dillemma rather well

"we now recognize that there is some value to looking for interactions but of course, the more you look, the more likely to see spurious ones. The opposite is also true: the less you look, the less likely to see real ones"

see http://andrewgelman.com/2008/08/20/interactions/

I must admit I am a fan of looking but also testing on a hold out sample to see if you have been led astray by chance results- and I should do this more.

What I like about tree -based modesl is that thay are looking for non-linearity and intercations and use random cross-validation to see if the results generalize beyond the sample -see http://www.statmethods.net/advstats/cart.html

Of course, these tree- based models have much in common with AID models - automatic interaction detection ( and alternatives THAID, CHAID - https://www.statsoft.com/Textbook/CHAID-Analysis)

So - caveat emptor.

In a designed experiment, we will start with a "full model" and reduce it from there. This full model includes all quadratic terms, 2-way interactions and main effects.

If you want to run this type of a model on observational data set, you need to mean-center you variables. What will happen is that he significance of your interactions will change dramatically and the VIF among you variables will drop dramatically too.

When you are running a multiple regression, you need to look out for VIF among the terms in your model. VIF should be small. The general DOE idea is VIF under 10.00 is acceptable.

If you want to see how dramatic the results are, check out the last page of the attached paper.

You can run GLM in R, the explanation is in:

Crawley MJ. The R Book. In: Ltd. JWaS, ed. England., 2007.

Fernando

I do not see why the term interaction should be limited to categorical variables (ie Factors) - I regularly calculate them between continuous variables and between categorical and continuous variables. As always you have to take care with what you are doing and how you interpret the resuilts.

Andrew, really interesting paper for a person, like myself, in observational epidemiology. It seems to me that your method of mean-centering observational data will minimize spurious null findings, i.e. Beta-errors, but not so much spurious significant findings, i.e. alpha-errors, which may be more frequent as one increases the total number of tests. Am I misunderstanding?

Jessica,

I came at that data set from the point of view of an applied/industrial statistician. I looked for a method to minimize the VIF among the terms and see how that affected the model if I use the p-value method for excluding terms. I have no idea if the terms in my models "make sense" or actually belong in the model. That was more of an exercise to show how centering the data can have a huge impact on the models you can come up with.

I'm sure there are spurious terms that are significant from a statistical point of view. However, they should not be part of the model. To some extent, I would rather have an extra term in the model that does not belong than lose several terms that do belong. Centering the data gives us the best ability to see the truest effect of each term by minimizing the VIF among the different terms.

I'm not a big fan of deciding that if a term does not make sense, then it does not belong. To me, this seems like a source for further research. Telling the data what to do is usually a bad idea.

The scientists that were investigating the O-zone layer in Antarctica had enough data to prove the O-zone hole was both present and seasonal back in the 70's. The paper they published didn't get written until the 80's. The reason is, they decided a value below a certain amount is a bad data point. Therefore, any value below that concentration is invalid. When they looked at their data, they were missing 30%-50% of the data. If they decided to look at all of their data and that their data was real and their preconceived model was not, we would be about a decade ahead of where we are now.

Imagine where we would be now if every researcher decided to listen to their data instead of telling their data what to do. How further ahead would we be?

Michael, you should consider the specifics of your field. For example, in some fields it is plain statistics and p value estimation. However, in medicine, you have to look at clinical and statistical significane and conducting statistical tests should keep in view the literature and clinical implications. Interaction testing is a good way to address your question.

you must enter the interaction term in your model even if it appears to play a limited confounder role.