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Thread: multicollinearity of interaction term in binary logistic regression

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    multicollinearity of interaction term in binary logistic regression




    Hello,

    I would like to conduct a Binary Logistic Regression Analysis with a regression model containing
    • a nominal 0/1-dummy variable (D)
    • a grand mean centered metric variable (M)
    • as well as their interaction term of aforementioned two variables (D*M)

    as independent / predictor variables.

    Now I am “accused” by my thesis advisor that my model is said to comprise multicollinearity, because the interaction term D*M is always equal to either D or M, e.g.:
    • if D=0 then D * M = 0 and hence = D
    • if D=1 then D * M = M

    The occurrence rate of D=0 is 3/4, and the same for D=1 is 1/4.

    Consequently, an eyeball-check already suggests that variable D and interaction term D*M as well as M and D*M might be somewhat correlated.

    However, I have tested the multicollinearity of the model (both with and without other variables included) by means of tolerance (TOL) and variance inflation factor (VIF) and as a result found no multicollinearity whatsoever.

    Nevertheless my advisor persists multicollinearity is present in the model, without hinting at an approach to solve the problem.

    I suppose, there are millions of logistic regression models containing an interaction between a dummy and metric variable, without anybody ever objecting. I mean, it is obviously in the “nature of the beast” that D and M are to some level correlated with D*M, right?

    Can someone please tell me what I have overseen or - perhaps even more important – give some advice to outargue this problem with my advisor?

    Many thanks for your help in advance.

    Greetings,
    Anna

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    Re: multicollinearity of interaction term in binary logistic regression

    I am not sure of the logic here. To being with multicolinearity [MC} does not deal with correlation between two of the predictor variables, but the correlation between all of them at once [so you don't analyze bivariate correlations for MC]. It wouldn't be suprising to me if MC existed with an interaction term which by definition contains two or more of the other predictors. I find it hard to believe you found no multicolinearity at all, I assume you mean that the MC was within the levels that are considered acceptable for the VIF and Tolerance test. If you did then MC is not a problem. You can find any text on MC and cite this [perhaps this is what you advisor is asking for]. Or you might consult John Fox's books on regression which in general downplay the importance of MC.

    Centering the predictors, which I have seen applied in non-linear models with quadratic or cubic terms, but apparently may work with interaction as well, might be of value. But this seems a waste when your test show MC is not an issue.

    You might look at this.

    http://www.mlrv.ua.edu/2009/vol35_1/...cke_rproof.pdf
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: multicollinearity of interaction term in binary logistic regression


    This might be worth reading from a wiser poster than I.

    http://www.talkstats.com/showthread....ll=1#post90052

    Of course this makes me wonder even more why you found no significant MC.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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