Simr power for interaction: how to set the effect size for interactions? I want to calculate power for an interaction (two categorical variables, each with two levels). I'm using the simr package. I'm able to calculate the observed power, but now I would like to modify the effect size. I know that I cannot set the effect size for the overall interaction, but I need to either modify the main effects or set the effect for each combination of the two variables involved. The issue is that, whichever of these two solutions, I don't know how to choose the new values. I would just play around and see ho the power and interaction effect size change, but, for some reason, the powerSim function doesn't calculate the effect size (instead says: Test: unknown test). Does anybody have any suggestion?
 A: An interaction between two binary factors $x_1$ and $x_2$ is a double difference.   If the $x$'s had values of 0 and 1, and letting 00 01 10 11 denote all the $x$ combinations, the interaction effect corresponds to parameters for (01 - 00) - (11 - 10).  We don't usually expect qualitative interactions, i.e., different signs for 01 - 00 as for 11 - 10.  It is reasonable to set a interaction effect size not to miss, for the purpose of a power calculation, as (01 - 00) / 2, i.e., the interaction effect being half the main effect.  In the best possible case of equal cell sizes for 00 01 10 11 you'll need $16 \times$ the sample size for the interaction effect that you need for the main effect.  See this by Andrew Gelman.
A: As far as I know, powerSim uses slope differences. This is an effect size but not a standardized one. So of course, powerSim doesn't calculate the effect size in a standardized way - it uses your observed slope differences (depending on the contrast you have used in your model) to calculate power. If you want to manipulate the effect size, just use the fixef-function to change them (e.g. fixef(model)[c("effect1", "effect2")] <- c(somevalue_x, somevalue_x).
