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Using OLS, the starting aim of my analysis is to study how different types of credit card contracts affect the dependent variable (y: use of credit cards). I have generated three dummies (v1, v2, v3) to reflect each of those types. As this previous post recommends, the three dummies should be included in a unique model. Following this, my model would be:

y = a + b * v1 + c * v2 + d * v3 + control variables + e

So far so good. However, an essential part of my analysis is to use interaction terms to analyze how other variables might moderate the effect of the type of contract. When I do this, I start having troubles caused by multicollinearity.

Given this, should I perform different analyises for each contract? Is this were correct, should I do this since the beginning or when multicollinearity problems arise? Is there another way to proceed? Thanks in advance.

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madu
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  • What is the VIF? Have you tried centering the control variables before adding the interactions? – Chris Novak Mar 06 '15 at 13:35
  • You seem to have included *both* all the dummies *and* an intercept. They will be linearly dependent. You should either exclude the intercept of one of the dummies. Also, it seems to me that the post you are referring to deals with a different question. In your case having one equation instead of three (for each credit card type) will make $a$ and the coefficients in front of the control variables common for all credit card types. Meanwhile, you could let them differ if you had separate equations for each credit card type. It is up to you to choose the more relevant specification of the two. – Richard Hardy Mar 06 '15 at 13:44
  • Chris, when the basic variable of the interaction term is continuous, I have centered it. The value of the VIF depends on the concrete interaction term that I use (for some variables, in some specifications, it is 15.09). – madu Mar 06 '15 at 20:02
  • Richard, there is a fourth type of contract (sort of a mixed category), ie, there is no dummy trap. You are right: the post to which I referred does not deal with exactly the same problem. Nevertheless, it is related to my question in the following sense: if I do not split the dataset, is it "correct", in statistical terms, to use three equations instead of just one? Does it matter or is it irrelevant? – madu Mar 06 '15 at 20:15
  • @RichardHardy, I add this comment to be sure that you are notified that I have answered to your comments. I am sorry for not having added your user name directly in my answer. – madu Mar 06 '15 at 20:39
  • @ChrisNovak, I add this comment to be sure that you are notified that I have answered to your comments. I am sorry for not having added your user name directly in my answer – madu Mar 06 '15 at 20:40
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    Statistically there is no problem with either separate equations or a common equation. It matters more what you believe about the model specification. If you believe that the parameters in front of control variables are the same regardless of credit card type, one equation is the way to go. If you believe otherwise, use separate equations. Even though those are nuisance parameters (I guess you do not care about them from the subject-matter perspective), you would want the model to be well specified. – Richard Hardy Mar 06 '15 at 20:52
  • Thanks, @RichardHardy, for your quick answer. From a subject-matter perspective, control variables have a relevant but secondary role. Yes, what I want is a well-specified model. Indeed, I do not have a solid theoretical background to choose between one and three equations. But my intuition is that a separate analysis would be better: less noise, no multicollinearity, and simpler interpretations (even I get what you mentioned: the coefficients of the control variables can change). – madu Mar 06 '15 at 21:09
  • I do not want to encourage reckless behaviour, but if separate analysis has all these virtues, why not go for it... – Richard Hardy Mar 06 '15 at 21:25
  • I agree with @RichardHardy but this will make it hard for you to compare the relative effects of moderator across different credit card types. You could also try to reduce the number of parameters extracting principal components from the controlled variables. – Chris Novak Mar 09 '15 at 06:59

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