Standardized coefficients in multilevel-models to compare predictor influence

Question

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)?

Thank you in advance for any advice.

Kindest Regards, Dominik

Answer 1

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.

Answer 2

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.