There was some discussion (on t'other place) about interactions (moderations) being hard to detect, which puzzled me. So I did some Rmd simulations, which I think suggest this may be an over-generalised concern. Have a look, and please correct me where wrong. www.mrc-cbu.cam.ac.uk/personal/rik... - ThreadSky

rhens.bsky.social • 507 days ago

There was some discussion (on t'other place) about interactions (moderations) being hard to detect, which puzzled me. So I did some Rmd simulations, which I think suggest this may be an over-generalised concern. Have a look, and please correct me where wrong. https://www.mrc-cbu.cam.ac.uk/personal/rik.henson/personal/PowerForInteractions.html

Comments

jaquent.bsky.social•477 days ago

Did you see this? https://statmodeling.stat.columbia.edu/2023/11/09/you-need-16-times-the-sample-size-to-estimate-an-interaction-than-to-estimate-a-main-effect-explained/

rhens.bsky.social•474 days ago

I don’t think every statement there is true - I’d like to find out what is wrong with my simulations, which suggest such statements about low power for interactions are dangerously simplistic

jmsp.bsky.social•507 days ago

If you split by X, for example, as the main effect of X increases, the lines will shift away from each other vertically. As the main effect of Y increases, both lines will tilt by the same amount. But if the main effects of X and Y are 0, the pattern will always be an X.

jmsp.bsky.social•507 days ago

Specifically, the interaction effect alone is always a cross-over. All other patterns result from graphing both the interaction and ‘main effects’.

rhens.bsky.social•506 days ago

Thanks for your comments Jeff. Agree absolutely about all interaction contrasts being cross-overs - that sentence about different types of interaction related to other arguments I have come across, which I think boil down to effect size.

jmsp.bsky.social•506 days ago

Effect size of the interaction or the main effects?

jmsp.bsky.social•507 days ago

My second thought was about your comment on ordinal vs. cross-over interactions. I realize these are common ways of describing ‘interaction effects’, but that’s confounding the actual interaction effect with the combined effects of the variables going into the interaction (i.e., X, Y, & XY).

jmsp.bsky.social•507 days ago

I’ve also been confused why people are so down on interactions. Thanks for doing this! I had a couple of small thoughts after reading your post.

jmsp.bsky.social•507 days ago

First, I know it’s common to mean center X & Z before multiplying them, but the test of the interaction is unaffected by this, because the partialed product term is identical either way. This can be seen by creating product terms both ways and partialing the respective main effect terms from each.

jmsp.bsky.social•507 days ago

Also, mean centering doesn’t remove the correlation entirely. There is a way to completely remove the correlation if you really want to: partial X & Y from XY.

rhens.bsky.social•506 days ago

Absolutely- that should be apparent later in the Rmd where I introduce correlation beyond mean correction. Then I think your point about partial correlation relates to my final demo about sequential sum of squares? You can partial main effects from interaction, but you need a priori reason for this

jmsp.bsky.social•506 days ago

Absolutely - I definitely wasn’t suggesting that we should partial main effects from the product term all the time - just that it does a better job of reducing the collinearity between the interaction and the main effects.

jmsp.bsky.social•506 days ago

One thing I’m curious about is what determines how much mean centering reduces the correlation b/t the product term & main effects, b/c it can vary a lot. I briefly tried figuring this out (ie avoided real work), but no luck. I’d guess it’s some aspect of the multivariate distribution b/t X & Y?

rhens.bsky.social•506 days ago

…ie a priori reason to assign common variance to main effects

jmsp.bsky.social•506 days ago

Don’t you always want to assign common variance to the main effects, given that the interaction is not the product term itself, but the product with main effects partialed out (Cohen 1978, Psych Bull)? So any shared variance shouldn’t belong to the interaction.

jmsp.bsky.social•506 days ago

Also, mean centering essentially reduces colinearity by assigning shared variance to main effects (although not perfectly).

rhens.bsky.social•505 days ago

Thanks I didn’t know the Cohen paper so will have a read. My intuition is still that one should not explicitly orthogonalise (partial) interactions with respect to main effects. I accept that mean-correction is an example of this but we rarely care about means of regressors in MLR

rhens.bsky.social•507 days ago

PS ...and the R markdown available here: https://www.mrc-cbu.cam.ac.uk/personal/rik.henson/personal/PowerForInteractions.Rmd

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