# Thread: multicollinearity of interaction term in binary logistic regression

1. ## 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

2. ## The Following User Says Thank You to anna_84 For This Useful Post:

hlsmith (01-06-2015)

3. ## 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

4. ## Re: multicollinearity of interaction term in binary logistic regression

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

Of course this makes me wonder even more why you found no significant MC.

 Tweet

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts