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I have a short question regarding interaction variables:

  1. In a logit regression with 2 independent dichotomous variables (A and B), both variables are significant. By including the interaction (AxB) in the regression, B becomes insignificant. Is the high (0.6) and significant correlation between (AxB) and B the reason for this? And in conclusion, has B a significant influence on the dependent variable or not?

  2. By including demographics and their interaction variables, all initial significant variables become insignificant (enter method). Is it smarter to simply use the stepwise forward method? By doing so, the initial significant variables remain significant. However, all new added varialbes are not included in the model.

Thanks a lot in advance for your help.

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  • $\begingroup$ Welcome to the site. I removed your signature because the site adds it automatically $\endgroup$ – Peter Flom - Reinstate Monica Feb 20 '13 at 12:08
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Regarding your first question - without seeing the data, I don't think we can say for sure what is going on, but certainly the relation between two independent variables can have the sort of effect you portray. However, in the presence of an interaction your question "does B have a significant effect?" is not strictly answerable; an interaction means that the effect of B on the dependent variable is different at different levels of A.

Regarding your second question: No, stepwise is usually not a good way to select variables for a model.

More generally: You should add the interaction if you think it is important, rather than significant and, if you include an interaction, you should include (except in very unusual circumstances) the main effects (here, A and B) that go into that interaction.

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    $\begingroup$ Well said Peter. Interpretation of "main effects" is not usually fruitful in the presence in interactions. One can form hypotheses or estimands of interest and then test or estimate those. These can be stated in terms of comparisons that are meaningful to the researcher. For example: Is there a difference between A=1 and A=0 for either level of B (a 2 d.f. test)? Is there a difference between A=1 and A=0 when B=0 (1 d.f. test)? $\endgroup$ – Frank Harrell Feb 20 '13 at 12:47
  • $\begingroup$ Thanks Frank. I used to think that it was never a good idea to include interactions without the main effects, but David Rindskopf published some interesting papers on cases where it is good to do this. $\endgroup$ – Peter Flom - Reinstate Monica Feb 20 '13 at 13:04
  • $\begingroup$ The argument would have to be very convincing before I would entertain fitting a model that does not satisfy the hierarchy principle. $\endgroup$ – Frank Harrell Feb 20 '13 at 19:07
  • $\begingroup$ If you're curious here is a link to one of David Rindskopf's articles. I read it long ago, but I do know David and he is a smart guy. $\endgroup$ – Peter Flom - Reinstate Monica Feb 20 '13 at 23:36
  • $\begingroup$ Looks pretty interesting Peter. I would rather use special after-the-fit contrasts than his approach though. $\endgroup$ – Frank Harrell Feb 21 '13 at 3:44

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