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I have four explanatory variables and one independent response Y. Three of the explanatory variables (X1, X2, X3) are just measured in the experiments. However, the forth one is computed using a function where I am using variables X1 and X2, hence it is not independent of them. I want to use GLM to model Y as a function of X1, X2, X3, X4. More importantly I want to know if any of those four variables are more "important" in modeling Y. Hence I have to include all of them in my model.

I was wondering if that dependency between X4 and X1, X2 causes any problem when I am using GLM?

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  • $\begingroup$ It causes problems when attempting to read causality from the coefficients, but doesn't cause problems in terms of the actual fitting. $\endgroup$
    – user2879934
    Commented May 9, 2017 at 21:15
  • $\begingroup$ Thanks for the answer. Can you please elaborate a little more. And how one can read causality from the coefficients. I would appreciate it if you can give me some references. $\endgroup$
    – Mina
    Commented May 9, 2017 at 21:48

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It depends on the function used to compute X4 and the value of X1, X2, and X3.

Suppose X1 is continue variable, for example, age, you may know that we can add square term of X1 (X1*X1) and X1 together into GLM as coviarates. So if your X1, X2 and X3 are continue variables and that function is non-linear (linear means something like X4 = 3*X1+X2+5*X3), then putting four Xs into the same model has no problem (given X1, X2 and X3 have no problem themselves).

If somehow the collinearity happens, generally statistical software will tell you this situation.

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