Standardized coefficients in multilevel-models to compare predictor influence

Suppose I conducted an experience sampling study and set up a multi-level regression, in which episodic well-being (LVL-1) is predicted by episodic flow (LVL-1) and episodic loneliness (LVL-1) (measurement occasions nested in participants; both LVL-1 predictors flow and loneliness with random slope).

I am interested in whether flow and loneliness are associated with well-being and for which predictor the association is higher. Based on the recommendations of Enders and Togfighi (2007; https://psycnet.apa.org/doiLanding?doi=10.1037%2F1082-989X.12.2.121), I group-mean centered the two LVL-1 predictors. Both are significant, positive predictors of well-being. But now I'm faced with the problem that I can't compare the height of the association of the predictors with well-being. I suppose that to do that I'd have to scale them using z-values instead (using scale() function)? But then I fear that the model will not be calculated correctly anymore. Or is the group-mean centering in case of LVL-1 predictors only done to make the intercept more meaningful (which in this case would be secondary)?

Kindest Regards, Dominik

I'm late to respond but maybe this is useful to some readers.

In my understanding, you can get standardized regression coefficients for a multilevel regression using the standardize_parameters function from the sjstats package in R, you just need to specify method="pseudo".

So if you have a model, say:

m <- lmer(outcome ~ (var1|id)+var1, data=data)

library(sjstats)

effectsize::standardize_parameters(m, method="pseudo")


This method calculates the standardized coefficients according to within-cluster variance (in your case, within-participant variance), and is recommended for multilevel models (Hoffman, 2015, p. 342)

Hoffman, L. (2015). Longitudinal Analysis: Modeling Within-Person Fluctuation and Change. Routledge.

I currently don't have access to the paper but I assume that it proposes "group-mean-centering" to account for (unobserved) group-differences that may be correlated with your regressors. That would be called "within transformation" in some literatures, sometimes it's called the fixed-effects-estimator.

What's important for making the estimated effect of regressors comparable is their variance/standard deviation - their mean only affects the estimated intercept. You can easily check that yourself by adding some number to a regressor (-> the intercept changes) vs. multiplying the variable by a number (-> the estimated slope parameter changes accordingly).

Bottom line: You can make your regressors comparable by

• using the scale()function or
• dividing by the respective standard deviations (shouldn't make a difference)

After that, you can do your "group-mean-centering". It doesn't do anything to the standard deviation but removes mean differences across groups.