Three way interactions and multicollinearity

[nashrf]

Dear Colleague,

Would you be kind to advise whether muticollinearity (VIF > 10) between one of the main effects and its products terms with other main effects is a cause of concern?

In my (three way interaction) model there exists multicollinearity (even after centering and standardization) between one of the main effects (x) and its two way (x*y) and three way (xyz) product terms with other main effects. All the main effects are continuous. However, the issue is resolved if I use main effects (x; y; z) and two way interaction terms (xy; xz; yz) OR main effects and three way interaction term (xyz) separately. If I understand correctly main effects, their two way interaction terms, and three way interaction terms must be used simultaneously to estimate the model and plot the interaction effects.If that is the case, then is multicollinearity, as described above, a cause of concern? If so, how can one handle it?

My data is based on observation of 345 firms over the period of 2007 to 2009.

Highly appreciate any suggestion or reference to address the issue of multicollinearity in three way interaction model.

Best,

Naeem

[Maarten Buis]

Typically, you must include the lower level interaction terms. There are exceptions, but multicolinearity is not one of the acceptable reasons.

If two variables are strongly correlated then it will be hard to disentangle those variables. As a consequence the standard errors tend to be large. This is unfortunate, but a correct representation of the state of your data. So multicolinearity is something to be aware of, but not something you can do anything about after the data is collected.

[nashrf]

Thanks Maarten. I guess I can estimate models with all the variables. Kindly do refer me to a published source which I could quote to satisfy the reviewers.

Best,

Naeem

[Joseph Coveney]

Do you anticipate a referee's requiring your keeping only main effects and three-way interaction terms in your model as a condition of acceptance?