When only one variable in a multilevel model is of interest (all of the other variables are treated as nuisance parameters), and we wish to estimate between- and within-effects, should we only center the variable of interest for interpretability? Or should we still center all other variables and just omit reporting their associated model output? (Keeping things simple here and not referring to the type of centering, what level the other variables are at, etc. to focus specifically on my question of whether we center only the substantive variable of interest or all variables included in the model).
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1$\begingroup$ Hey, I think it depends a bit on the random effect structure of your model (i.e., whether you model random slopes for the covariates or not), because person mean centering of the Level 1 predictors affects this structure. In most applications I know of, people center all variables at the respective person means (Level 1 predictors) or the grand mean (Level 2 predictors). Best, Stefan $\endgroup$– StefanCommented Jun 25 at 14:50
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