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I have the following model:

logistic regression:

outcome ~ b1*age + b2*smoker + b3*age:smoker

smoker has two levels: non-smoker, smoker
age is a continuous variable

likelihood ratio test shows the interaction term is insignificant

How should I interpret b1?

interpret b1:

The effect of one unit change in age on outcome (log adds), controlling for effect of smoking status (keep smoking status constant).

another way to interpret b1:

The effect of one unit change in age on outcome for non-smoker (non-smoker is the base level, in this case, smoker==0)

I'm a little confused. There interpretation does not seems to be the same... Can anyone clarify me on this? Thanks a lot.

zesla
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  • https://stats.stackexchange.com/questions/380222/interpretation-of-different-logistic-regression-models-to-test-hypotheses/380294#380294 – Huy Pham Dec 19 '18 at 19:44
  • The second interpretation is correct. When the interaction between age and gender exists, there is no common effect of age, so the first interpretation is meaningless. – user158565 Dec 19 '18 at 21:45
  • I tested the interaction. The interaction is insignificant. So how should I interpret that? which one is right. @user158565 – zesla Dec 19 '18 at 22:10
  • It depends on the model. Even the interaction is not significant, but you insist to keep it in the model, then the second interpretation is correct. If you refit the model by excluding the insignificant interaction, then first explanation is correct. – user158565 Dec 19 '18 at 22:27
  • @Huy Pham thank for that link. I updated my question. I understand not to interpret main effect when interaction is present. In my case, the interaction is insignificant. There are two way to interpret b1. Need advice which one is right? – zesla Dec 19 '18 at 22:30
  • @user158565 could you elaborate more and put it in answer? thanks a lot. why I should use two different interpretation depending on whether I leave the insignificant interaction term in the model? Also, if I leave out the interaction term and rebuild the model, why I cannot use the second interpretation? – zesla Dec 19 '18 at 22:37
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    Your question implicitly changes the model halfway through. Either your model is the one you gave or it is the one without the interaction. It cannot simultaneously be both. Which one do you want to interpret? Answers to both have been given elsewhere on this site. – whuber Dec 19 '18 at 22:39
  • @whuber Ok, I leave the insignificant interaction in the model. why the first way is not right. Can you explain? – zesla Dec 19 '18 at 22:47
  • Because you fail to mention you are also controlling for the interaction. You are describing the model without interaction, not the first. – whuber Dec 19 '18 at 23:23

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