Grand-mean centering, cluster-mean centering, and cluster means

[@Nioco2]

Thank you! That helped me to understand the concept.

[@mronkko]

You are welcome

[@mehmetkaya4330]

Thank you! Nice explanation!

[@sabrinapannier-diehl7981]

Can it be that you're mixing something up at about 9:40? You're saying that Y01 is the contextual effect but on the screen it says Y10...

[@summertummer2394]

@@mronkko At 9:35 you also say that Gamma 01 is always the within effect, and I think that may be an error also. Will Gamma 10 (within effect) be the same in both equations or will it change? As in will the standardized coefficient for Gamma 10 (within effect) be the same for both equations or will it change?

[@VioletSClover]

THANK YOU SO MUCH

[@mronkko]

You are welcome.

[@anmolpardeshi3138]

5:28 : that (cluster centering) gives us the between effects BUT 6:22 this method eliminates between cluster effects - - contradiction?

[@mronkko]

At 5:28 I talk about the cluster means, not cluster mean centering.

[@anmolpardeshi3138]

@@mronkko thanks; great video :)

[@work4development]

To have interpretable intercepts and cross level interactions, we should also center level-two variables, right? The question is the "x-bar_HOURS_j" (average working hours per individual - contextual or between effect) should also be centered around the grand mean?

[@work4development]

In addition to centering, Gelman also recommends to divide by two standard deviations, so all effects are comparable with dummies variables. Thus, perhaps, we should grand-mean and divide by two standard deviations first, and after that, group mean, if the case. Sounds right? (ok graphs will be "wrong" and interpretation of substantive effects is harder, but if the idea is to get clearer and comparable estimates....)

[@aviejaypaul6568]

Dear Sir, I have a query here. Because the population average is difficult to justify, does that mean that we should not attempt to interpret the slope in case of a grand mean data set? Is there any other way to make this interpretation?

[@mronkko]

The answer really depends on the research question and data. Sometimes the PA effect is the only thing you can estimate. For example if you have just one observation for each unit (i.e no multilevel data). This is not really related to grand mean centering. I do not think grand mean centering is useful at all and personally I never grand mean center my data. We discuss this a bit in our paper on the random effects assumption. journals.sagepub.com/doi/10.1177/1094428119877457