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I have data involving 3 key variables (predictors), 2 of them being randomly assigned treatment conditions, and the other denoting the sample (A vs. B). I am finding it easier to present the results doing 2 regressions each with a two-way interaction, but just wanted to check if there's any statistical difference/issue with doing that vs. putting them all in one regression and doing a 3 way interaction.

Thank you!

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The issues are the same as when comparing subsets vs. a single two way interaction: You don't get parameter estimates, p values, etc. for the difference in the two subsets, but you would get these with the interaction.

Here, it's all just one level "up" - you don't get parameter estimates for the differences between the two models, each of which has a two way interaction. How big is the three way interaction? What's its standard error? P value? etc.

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