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I've read a number of the other discussions I can find on here about lower order items and interaction terms in regression but either my statistical incompetence is preventing from seeing it or I could not find a clear answer to the specific question I have. Any help would be very much appreciated!

I have a regression model in which I use sex and a personality trait to predict a separate outcome. Both sex and the personality trait do predict the outcome variable. However, there is a clear interaction: the personality trait is only predictive of the outcome in men. In men the association is very clear, whereas it is completely insignificant in women. Hence, there is an interaction, and this is supported by a significant R2 change when you add the interaction term to the model. When you add the interaction term, both sex and the trait alone become insignificant, so the main effects are no longer meaningful.

My aim is not to predict new data but to understand the phenomenon I'm observing and it is clear that you would say 'if you are male, then this trait predicts this outcome, but not if you are female'. However, I am obliged to report a regression equation. Should I still include the coefficients for the main effects in the equation even though they are now non-significant and so, it seems to me, shouldn't be included in a model to predict the outcome? If I should only include the interaction term in the equation, then should I also report the actual regression model as just including the interaction term, without the lower order trait and sex predictors, given that they go straight to insignificance when the interaction is included?

Again, any help would be much appreciated, and apologies if this is answered in the other threads about lower order terms but I just did not understand it!

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  • $\begingroup$ I understand that very similar questions have been asked before but they seem to either be about one where the main effects, or at least one main effect, remains significant and in the answers I do not see it clearly stated whether one should or should not include the non-significant main effects in a regression equation. I would be very happy if you can point me to an answer that has answered this question in a way that is understandable to someone who is not well versed in statistics (which I understand must be a little frustrating if the answers seem entirely clear to you) $\endgroup$
    – Jamie
    Feb 20, 2018 at 13:41

1 Answer 1

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Including the interaction but not the main effects in a model

I think this should answer what you have asked. Apologies if you have already viewed it.

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  • $\begingroup$ Thanks, I did look through this thread before asking but could not find a clear answer to my question. I apologise if it is very clear to you but I did not find the answers there to offer any clarity at my level of understanding. $\endgroup$
    – Jamie
    Feb 20, 2018 at 13:46
  • $\begingroup$ The answer there I thought was quite good. Essentially it says that if you have significance in your interaction term but not in your "lower order" terms then it must be due to variance and is likely an error of the data. Yes, you should be including the "lower order" terms unless you have a very good, theoretical reason for not doing so. $\endgroup$ Feb 20, 2018 at 14:27
  • $\begingroup$ Thanks for your response Stuart. I'm not sure I agree that significance in an interaction but not in the lower order items must be an error of the data though - is there a statistical reason for why this must be? I can think of a multitude of cases where variables only have any effect when in combination with another variable. $\endgroup$
    – Jamie
    Feb 21, 2018 at 19:27
  • $\begingroup$ I believe the person was speaking from experience. Like I said, if you have a theoretical reason for not doing so, then by all means, go ahead. $\endgroup$ Feb 21, 2018 at 20:01
  • $\begingroup$ Okay - thanks for your responses Stuart - much appreciated! $\endgroup$
    – Jamie
    Feb 23, 2018 at 11:56

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