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I am having some trouble with the literature on the correct model specification for my question.

Here is the setup: I have a multilevel model with a variety of variables at level 1 and a single level 2 variable. I am examining interactions between both level 1 variables and cross interactions between the level 2 variable and other level one variables.

Here is an example: X = level 1 variable D = level 1 variable Z = level 2 variable

The model I want is Y = X + D + Z + XD + XZ Therefore, I have interactions between two level 1 variables (X and D), as well as a cross-level interaction (X and Z)

This is where I am having trouble figuring out the correct centering in the model. Where do I group-mean center and grand-mean center? What about the centering for the main effect terms? Also, should I be including any random slopes?

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  • $\begingroup$ Always include a random slope for a level 1 variable that is involved in a cross-level interaction. Not doing so is anti-conservative in the sense that the resulting p-value will be too small - see Hesig & Schaefer (2019) at doi.org/10.1093/esr/jcy053. $\endgroup$
    – Erik Ruzek
    Commented Sep 16, 2022 at 19:00
  • $\begingroup$ In terms of centering, there are many threads on this on CV. For example, see stats.stackexchange.com/questions/403693/… $\endgroup$
    – Erik Ruzek
    Commented Sep 16, 2022 at 19:01
  • $\begingroup$ Hi @ErikRuzek. Thanks for the information. I have seen that literature regarding including the random slopes for the cross level interactions. I guess my key question is then, should I center all level 1 variables within group and interact those centered variables with both the level 1 variable and level 2 variable? Then, allow random slopes for the centered level 1 variables? $\endgroup$
    – bzh
    Commented Sep 19, 2022 at 13:07
  • $\begingroup$ I think centering within group makes a lot of sense for the variable involved with the cross-level interaction and it cannot hurt to center the other level 1 variables within group. For that second group of variables, you could also leave them uncentered and enter their group means in the model for the intercept. $\endgroup$
    – Erik Ruzek
    Commented Sep 19, 2022 at 13:41

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