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I know there are similar questions on here, but I can't quite find an answer that covers all of what I need. I am running multiple regression in r with two predictor variables and sometimes an interaction term e.g.:

model1 = lm(Measure1 ~ Variable 1 + Variable 2)
model2 = lm(Measure1 ~ Variable 1 + Variable 2 + Variable2:Variable 3)

I am first wondering, what is the best way to calculate the effect size specifically of variable 2 in both instances. I know because the second formula includes an interaction I can't necessarily use the standard coefficient values, and I'd like to get the effect size in a consistent way between the two formulas. Also, if it's important, the DV is continuous, but the variables are dummy coded variables (e.g. on/off a drug and gender). Along these lines, is there a good way to determine when I should use an interaction in the equation when I have many dependent variables I want to look at? Creating a plot of each manually doesn't seem like the most efficient way to do so…

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If you include an interaction term, then "the" effect no longer exists. Instead you have multiple effects: one for each level of the other variable with which you created the interaction. This is the very point of including interactions, so there is no way around it.

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  • $\begingroup$ So then when including an interaction term there is no way to report the effect size? $\endgroup$ – Brandy Riedel Sep 18 '14 at 19:41
  • $\begingroup$ no, that is not what I said. There are now multiple effect sizes, so you need to find a way to report them all. If these are two binary variables you can just report them, if they are continuous variables you need to think about graphs. $\endgroup$ – Maarten Buis Sep 18 '14 at 19:48
  • $\begingroup$ Okay, I see. What is the best measure to use as the effect in this type of analysis? From my understanding I can't use the coefficient values… (I'm using r specifically) $\endgroup$ – Brandy Riedel Sep 18 '14 at 19:56
  • $\begingroup$ To repeat, there is no "the" effect when including an interaction; there are many, and you need to report all of them. So if you want to report one effect size you should not include an interaction. Alternatively, if you need an interaction, you need to report multiple effect sizes. It is one or the other. You cannot have an interaction and report only one effect size. $\endgroup$ – Maarten Buis Sep 19 '14 at 8:09
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    $\begingroup$ Yes, I understand there would be an effect for each independent variable used (including interaction variables). I was just trying to figure out the best methodology to calculate this. For instance, Cohen's d vs. partial R-squared, and how I can do so using the R program. I am going with partial R-squared, but if you have any input on this let me know. $\endgroup$ – Brandy Riedel Sep 22 '14 at 22:29

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