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I'm trying to figure out how to interpret these results.

In my first regression, I include both of my two independent variables (IV1 and IV2) to predict a Dependent Variable (DV):

  • IV1 is significant
  • IV2 is significant

In my second regression, when I add the interaction term:

  • IV1 remains significant
  • IV2 is no longer significant
  • IV1*IV2 is not significant

This pattern occurs when the DV is coded as a dummy (in a logistic regression) and when it is a continuous variable (in a linear regression).

How do I interpret these results?

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When adding a term to a model causes another term to become nonsignificant, that means that the new term has some collinearity with the old one. The fact that the new term in this case is an interaction doesn't change the general nature of linear regression. In order for a term to gain significance it has to make a distinct contribution to the explanation of the Dependent Variable. If two terms carry the same information then neither will be significant even when that information is valuable.

My interpretation of your result is that IV2 does matter but the interaction IV1*IV2 looks a lot like IV2 and it doesn't add much information about the DV. I would expect a model selection criterion like AIC to tell you that model your first model is better than your second, but that the second model is better than one with IV1 alone.

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  • $\begingroup$ Thanks! You were correct. AIC indicated that my first model was better than the second. $\endgroup$
    – S. Kim
    Commented Nov 14, 2020 at 15:47

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