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This is a general question on logistic regression result reporting for a publication.

We have an example where two well correlated ($r=0.4, p=0.001$) blood parameters (blood parameter1 and blood parameter2) are associated with blood pressure in mixed sample of men and women, however, the effect is much stronger in women for blood `parameter1.

UNIANOVA analysis includes age, gender, and one of the two blood parameters at a time as covariates, and blood pressure as independent variable. Each analysis shows the blood parameters as significant, however, when including gender × blood parameter1, both the interaction term and blood parameter1 are significant. In women but not men blood parameter1 is highly correlated with blood pressure. The same interaction term using blood parameter2 (gender × blood parameter2) is not significant.

We are wondering whether for the publication of the data, we should include the table showing the interaction term where it is significant and not further include it/show it in the table where it isn't? I.e. show age, gender, blood parameter1, gender × blood parameter1 in one table and age, gender, blood parameter2, in the other? I would be grateful for an opinion. Alternatively, we could stratify the analysis for blood parameter1 by gender. The information seems to be the same, but it might be perceived in a different way.

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If I were the reviewer of that article and the two blood parameters are substantively related, then I would want to know why you included the interaction in one of the models and left it out in the other. I would have prefered to see the interaction term present in both models, and a discussion of why the authors think bloodparameter 1 works out differently for men and women and why no such difference was found for bloodparameter 2.

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  • $\begingroup$ Many thanks to you as well. The interaction term was initially included in both models for consistency. The reason for keeping it in one but not the other model would be that we found a correlation of the blood parameter1 with blood pressure in women but not men. No gender difference was found for the correlation of blood parameter2 and blood pressure. Is it, therefore, legitimate to remove the non-significant term from the model with blood parameter2 but keep it in the other model, or, should 'consistency' be the overriding consideration? $\endgroup$
    – user27666
    Jul 5, 2013 at 15:00
  • $\begingroup$ I cannot and will not give you a "statistical blessing". But, based on the (necessarily) very limited information I have about your problem, I would lean to consistency. $\endgroup$
    – Maarten Buis
    Jul 5, 2013 at 15:11
  • $\begingroup$ I have redone the analysis for the gender*blood parameter2 (call it bp2 from now on) and interestingly, including the interaction terms leaves all parameters non significant, without the interaction term bp2 is 0.008, including it is is 0.130. How would an interaction term have such an effect on the model? $\endgroup$
    – user27666
    Jul 5, 2013 at 16:58
  • $\begingroup$ I would not look at $p$-values that way. It now sounds like you consider them effect-sizes. If that is what you want, look at odds ratios (and ratios of odds ratios for the interaction term). As to your question: it is to be expected that the numbers change, as they mean different things. So to answer your question you'll just have to interpret your model correctly. I wrote a short tip on how to interpret interaction effects in models like logistic regression, which you can find here: maartenbuis.nl/publications/interactions.html . $\endgroup$
    – Maarten Buis
    Jul 9, 2013 at 10:02
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First of all, note that the stratification is not the exact same model as the one with the interaction term. The model with the interaction term requires all parameters except the one of blood parameter1 to be equal for both genders, while the stratified models allow all coefficients, including the intercept, to differ.

Furthermore, as @Maarten Buis has pointed out, do not omit the information that variables were included in a regression, even if you do not present their values, which in this case, for sake of comparibility, you should do. Furthermore, note that coefficient size and variance might still be of interest even if the coefficient is not significantly different from zero, as readers may be interested in why the coefficient is not significant, or want to extract information for a meta-study.

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  • $\begingroup$ Thanks very much for this answer, to clarify, once we found that the interaction term gender*blood parameter2 was not significant we removed it from the model, so nothing is concealed. The question was whether removing it from the model was justified. We found that women have much higher values for blood parameter1 and that it correlated with blood pressure in women, which is why an interaction term was included. There was no assumption a priori that there wold be any influence of gender, it was just a coincidental finding with respect to blood parameter1. $\endgroup$
    – user27666
    Jul 5, 2013 at 14:46
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    $\begingroup$ The pragmatic answer remains: if you have the interaction in one model, then people will ask you why it isn't in the other, and the best way to deal with that is to just include it and show that it is not significant. $\endgroup$
    – Maarten Buis
    Jul 5, 2013 at 15:00
  • $\begingroup$ I am worried about your statement that you don't conceal something when you don't show it. I suspect you think that "not significant" is equivalent to "not there". This would be wrong. Not significant just means "I cannot find it". On a more general level, by not showing the interaction you are concealing that you looked at it and chose not to show it. $\endgroup$
    – Maarten Buis
    Jul 5, 2013 at 15:04
  • $\begingroup$ Thanks again, 'not concealed' was to mean that I explain that I looked at it, it was not significant, and this is why I removed it. But I think I get your point. It does not hurt to show it in the table and to say since we observed it for one parameter, we checked it for the other... thanks again for your time!!! $\endgroup$
    – user27666
    Jul 5, 2013 at 15:51

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