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I have one dependent variable C and four independent variables:

  • S
  • SD
  • TPA
  • VPT

The correlation matrix between them is the following

    TPA     VPT      S
TPA -       -       -
VPT -0.37   -       -
S   0.04    0.00    -
SD  0.05    -0.04   0.01

TPAand VPT have a moderate negative linear relationship.

Now I want to create a regression model:

C ~ S + SD + VPT + TPA

Does it makes sense to consider the correlation between VPT and TPA in the model? If so, what should I add to it to consider the correlation?

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I think this question goes to two issues: Collinearity and interactions/mediation.

Collinearity is a problem in regression. However, it is best assessed with condition indexes, not correlation matrices. If you are using R you can get these in the perturb package; if you are using SAS you can get them with the /collin option. Although I said that correlations aren't the best way to look at collinearity, I don't think this will be a problem here.

There is nothing to add to the model to "consider the correlation". However, when IVs are correlated, they can mediate each other, so you may want to compare models with both terms to ones with only one; then, you may be able to say that one IV mediates the other.

Also, IVs may have interactions, which is something to add to the model, but even uncorrelated variables can interact.

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  • $\begingroup$ Thank you for your answer. Is there a library to check if to check if IVs mediate each other? Or is the only way to find out by comparing different models? $\endgroup$
    – ustroetz
    Apr 16 '14 at 13:30
  • $\begingroup$ As far as I know, you have to compare the models - that's what any package would do, anyway $\endgroup$
    – Peter Flom
    Apr 16 '14 at 21:05
  • $\begingroup$ Do you have an example, @PeterFlom, of when uncorrelated variables can interact? $\endgroup$
    – Erosennin
    Feb 9 '17 at 8:28
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    $\begingroup$ @Erosennin Yes. In predicting HIV risk, there is an interaction between sex (male, female, other) and sexuality (gay, straight, other). Another is that, in predicting income, there is an interaction between race and sex (the gap between blacks and whites is much larger for men than for women). $\endgroup$
    – Peter Flom
    Feb 10 '17 at 13:20

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