# Should group mean centring impact results of a multilevel mediation?

I'm currently writing up results from a multilevel model of my study and have come across an issue and was hoping for your help. Essentially, when running my mediation model using lmer and mediation package I get the expected results using raw data. However, I then read that I'm supposed to group-mean centre predictor variables. After running the same model with group-mean centred predictor variables, the whole results appear somewhat messed up and I cannot figure out why. I have attached a copy of the raw model and the centred model below if anyone could take a look and give me some feedback please.

Output Based on Overall Averages Across Groups (uncentred)

Estimate 95% CI Lower 95% CI Upper p-value
ACME            0.20065      0.11393         0.30  <2e-16 ***
ADE             0.00527     -0.12834         0.14  0.9448
Total Effect    0.20592      0.08931         0.32  0.0012 **
Prop. Mediated  0.97478      0.49820         2.32  0.0012 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Output Based on Overall Averages Across Groups

Estimate 95% CI Lower 95% CI Upper p-value
ACME             0.2328       0.1396         0.34  <2e-16 ***
ADE             -0.0859      -0.2472         0.08   0.294
Total Effect     0.1469      -0.0122         0.30   0.068 .
Prop. Mediated   1.5113      -4.5800         9.93   0.068 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


I understand that output of the models, and the fact that the indirect effect is still significant is what's important, but I don't understand why it impacts the total effect so much. Can the size of the seperate groups be having an impact on this?

Has anyone else had issues with this?

Thanks!

• At what level of your data hierarchy are you interested in testing mediation? In the multilevel world, people talk about 2-1-1 or 1-1-1 mediation models, corresponding to the level at which, respectively, the main predictor, mediator, and outcome are measured. Feb 8 '20 at 1:56
• @erik I'm actually interested in just accounting for the nesting of data (athletes) within teams. so it's actually a 1-1-1 mediation accounting for nesting. So what I've done in each seperate lmer function is set team as a random intercept `apath <- lmer(pnts ~ ccb + (1|team), data=...) Feb 10 '20 at 19:47

## 1 Answer

I'm not familiar with multilevel mediation per se, but in general group-mean centering results in a different model fit, because the parameters for the centered predictors give the within-group effect, which is distinct from the uncentered case. Grand-mean centering will change the intercepts, but not the overall model fit.

In general, you would have to expect that given the constituent parts of the analysis are changed by group-mean centering, the mediation analysis will change too.

• thanks for this.After some more reading and understanding of it I see it makes sense that the group-mean centring changes the results to an extent. However, when I use the raw data, or grandmean centred one I get a singular fit message for one of my seperate mediations, which I didn't pick up on until now. Are there circumstances where reporting random effects as 0000 with a SD of 000 is ok? Feb 10 '20 at 19:54
• That sounds a lot like a problem with your data/model to me. I wouldn't trust a variance estimate of exactly zero for a random effect - that's essentially just a fixed effect - maybe check that you're not misspecifying something in the model. Feb 11 '20 at 2:49