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I'm working on an analysis with another person. First we did a logistic regression with study group and variable X. They were both significant. Then we added the interaction between study group and X only the study group and the interaction were significant. Actually, there are 3 groups and only one of the groups and one of the group*X interactions is significant.

I am having a hard time to convince this person that we should not present the odds ratios for X from the first analysis that do not account for this interaction. This person thinks that we can show the results of the first analysis AND then the second analysis. I think this is misleading and will confuse people.

I am not the best at explaining things (as you can tell), so any help with how to argue my point would be appreciated.

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I agree that it could cause confusion to present two fitted models, especially since it appears that one of them may not fit the data very well. You can tell by comparing the deviance or some other fit statistics for the two models to see if adding the interaction makes an important difference overall.

The reason the significance of the effects changes is because there is multicollinearity. The interaction effects are doing a better job of explaining some of the effects that previously were explained by $X$ alone. This could happen, for example, if $X$ Is important for one group but not the others. Without the interaction, we are fitting an average X trend to the groups, which could be significant by virtue of the one group where it is significant. I'm not saying that's exactly what is happening, just that that is one plausible scenario.

What you can do to explain the one model is to PLOT the fitted lines for each group! Then you can see what the model is describing. You could even go a step further and apply the inverse logit to these lines to show the estimated probability for each group, versus X.

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Showing both models is fairly common in some disciplines. In those disciplines showing only the model with the interactions can cause confusion, rather than the other way around. So I don't think your client is necessarily wrong.

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The interaction means the effect to X in the response Y is different in the categories defined by the Group variable. Sometime it is useful to do a stratified analysis, by Groups, where you analysis the effect of X in Y in each group. You should see the effects are different. You could present these stratified analysis and show the P-value of the interaction for justify the stratification.

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