About interaction y term in regression analysis

Hi, community!I found a question when practicing R.

Is the interaction term counted as an independent variable in a multiple linear regression analysis,with the other predictor variables are required to all be non-collinear? It is found that when an interaction term is added, there is 100% covariance with the other terms.

Is the Variance Inflation Factor (VIF) calculation in the presence of an interaction term the same as in the absence of an interaction term?

Maybe like this


Any help would be appreciated.

The interaction term does count as an independent variable and does have to be not perfectly collinear.

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Thank you for your help!
One more question, before I add interaction term in regression analysis, no collinear problem. When add, have. But the performance of regression is better.
So my question is there a resonable method to remove the collinear problem when add? Maybe centered data? What's more, there is no doubt that the interaction term would be correlated with the variable that make up it.
I am a little confused.

Some collinearity between variables is perfectly okay. In fact, that's the situation a multiple regression is built to handle. Centering makes no difference (except in very rare situations where there are computational problems).

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Yeah, if when add interaction term, the vif>10, before is <2. it means the add interaction is not good choice or error?

I don't see why the vif matters at all.

But you said above that there is 100% covariance. If this means there is perfect collinearity, then it does mean you can't include the interaction term. (Usually, it also means that the specification doesn't make any sense.)

You need to look at all of the factors that describe how well your model performs. You also need to develop an intuition for what change matters. The performance is better could refer to an adjusted R2, but it also matters if the improvement changes the R2 from 0.52 to 0.521 versus a change from 0.5 to 0.8. Without knowing the model and purpose one cannot say one is good and the other bad. Model fit plots are useful, as are plots of the residuals. The increase in VIF may be worth it if other features of the model improve, or the increase in VIF may be one indication of a general decline in model performance. There is no single metric that should be used to say "this model is good and that one is bad."

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Am seeking to capture potential interaction effects, I decided to include an interaction term between two predictor variables. Upon running the regression model, I encountered an error signaling perfect collinearity. The error message explicitly mentioned 100% covariance between the interaction term and one or more of the main effect terms, prompting concerns about the accuracy of the estimated coefficients.

The odds are that you've made a mistake in the specification. You might want to post the two predictor variables here using dput() to see if anyone can spot the problem.