Sooooooo happy for you!!!!! 🥹 🎉🎉👏🏼

I love working with grad students. I love it even more when they try to take forward steps despite uncertainty/confusion. Uncertainty/confusion is not just a part of learning or a sign of one’s early career stage, it’s a part of science. It does not go away.

Interesting - I wonder if it will have any real impact.

I also hate it when they redo your figures. Multiple times I’ve minimized useless black (i.e., background) space around brain images, only to have the journal add black space in, so that now it’s 70% useless space and the actual data part is relatively smaller and thus lower resolution.

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

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.

Effect size of the interaction or the main effects?

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?

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.

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.

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

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).

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.

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.

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.

Probably lots of zeros or other repeated values - unzipped each matrix entry is represented individually in memory, but (g)zipped it finds patterns (e.g., lots of zeros in a row) and saves the pattern descriptions, which are much smaller

Thanks for the shout-out! For those who are interested, you can learn more about Reviewer Zero at our website, follow us at @reviewerzero.bsky.social and read our recent paper!

www.reviewerzero.net/home
pubmed.ncbi.nlm.nih.gov/37676130/