Centering default in Type=twolevel PreviousNext
Mplus Discussion > Multilevel Data/Complex Sample >
 Student 09 posted on Saturday, August 06, 2011 - 4:13 am

I am not entirely clear about the Mplus centering default in twolevel regression analyses.

(1) On the one hand, page 242 shows the familiar decomposition xij = xwij + xbj.

(2)On the other hand, the %within% and %between% parts are described as level 1/level 2 equivalents just as in other multilevel programs.

According to (1), I would expect that covariates at the %within%-level are by defautl treated as group-mean centred

According to (2),I would expect that covariates at the %within%-level are by default treated as uncentred.

Which perspective is correct?
Many thanks for your response!
 Bengt O. Muthen posted on Saturday, August 06, 2011 - 9:10 am
If you want what other multilevel programs do, put x on the within list:

within = x;

Then it is uncentered, unless you use a centering option.

Regarding (1), x is not on the within list but a latent within and a latent between part of x is created by Mplus, and, as you say, the (latent) within part is group-centered.
 Patchara Popaitoon posted on Sunday, August 21, 2011 - 5:12 am
Dear Bengt,

In the case that I used data ceterning option to run the multilevel analysis, what would be a more appropriate specification for the multilevel construct? In my model I have employee attitude as the multilevel construct wherein leadership practices influence employee attitudes which in turn impact on the group level performance:
leaderhip practices --> employee attitudes --> performance outcomes at group level

I am using the data centering method and specifying the model such that employee attiude (Attitude1-Attitude6) is not listed in both within and between variables. I also have a command of 'Centering = Grandmean (Attitude1-Attitude6)' Is that correct?

 Bengt O. Muthen posted on Monday, August 22, 2011 - 8:02 am
Let me assume that "leadership practices" is a level 2 variable just like "performance at group level". To model the two arrows you show, "employee attitudes" would have to refer to a level 2 construct, and the arrows correspond to regressions on level 2. Here, the attitude indicators are not listed on the Within or Between lists. Grandmean centering or not of those attitude indicators doesn't matter.
 Patchara Popaitoon posted on Monday, August 22, 2011 - 11:06 am
Dear Bengt,

Sorry I was not clear about the leadership construct. In my study, 'leadership practices' is the individual level construct which is assumed to have influenced on 'employee attitudes' at the individual level. This attitudinal effect is hypothesized to have aggregate effect on performance outcomes at group level.

The 'employee attitudes' is used in both the individual and unit level analysis and hence, it is not listed on the Within or Between lists.

Given this model specification, do I need to have a command line of 'Grandmean centering' for attitude1-attitude6 variables?

Also, I would like to know the implication of using data centering method on the multilevel model analysis. Would the result be more robust if I don't center data and specify some controls in the model instead?

 Bengt O. Muthen posted on Monday, August 22, 2011 - 5:13 pm
You still don't need to center the attitude variables.

To learn about centering methods and the interpretation of the model, see the Raudenbush-Bryk (2002) multilevel book, e.g. the discussion around page 140.
 Patchara Popaitoon posted on Tuesday, August 23, 2011 - 5:18 am
 Christoph Weber posted on Friday, May 25, 2012 - 4:22 am
Dear Dr. Muthen,
I have a question regarding example 9.1.

Does the second option (model constraints) allow the interpretation of within and between effects (X within, X between and W)?


Christoph Weber
 Linda K. Muthen posted on Friday, May 25, 2012 - 11:27 am
MODEL CONSTRAINT creates a contextual effect. The reference where this is described is given in the user's guide.
 Michelle Baldanza posted on Saturday, March 16, 2013 - 2:10 pm
Dear Dr. Muthen,

I am attempting to conduct a multi-level analysis looking at children nested within classrooms.

My outcome is Peer sociability.

On level 1 I am looking at child age, poverty status, and proportion of time spent in large group activity settings.

At level two I am looking at particular teacher strategies of management/routines and facilitation of cognition.

My question is about centering.
When I use the grand mean centering command my means become zero or are out of range.

Before centering command:
Age= 4.13
Poverty= 1.10
Large Group=0.25

After Command

Sociability= -0.02 (variable 1-7 scale)
Age= 0.00
Poverty= -0.003
Large Group= 0.00

I am very confused by this. Without adding the centering command are the means of my level 1 variables already centered by default? I am clearly missing something. Please help! I cannot interpret my results with means of zero.
 Linda K. Muthen posted on Saturday, March 16, 2013 - 2:57 pm
Grand mean centering makes the means zero. There is no centering done if you don't ask for it.
 Tessa posted on Tuesday, November 13, 2018 - 11:51 pm
Dear Prof. Muthen,

I am analyzing a cross-level interaction in Mplus, but am not sure whether I should use a centering option.
I study how individual victimization (level1) x school-average victimization (level2) affect depression. My script is:

WITHIN = vict_ind;
BETWEEN = vict_sch;

integration = montecarlo;
TYPE = twolevel random;

s | dep ON vict_ind;
s ON vict_sch ;
dep on vict_sch;

Does this require a group-mean centering command of within-level predictors (vict_ind) or is that not needed? It substantially affects my results.
Thanks in advance! Best, Tessa
 Bengt O. Muthen posted on Wednesday, November 14, 2018 - 4:47 pm
Yes, you want to group-mean center the within-level predictor. Better still is to use latent variable centering which with random slope is available using the Bayes estimator. See the new article on our website which explains the advantages of latent variable centering:

Asparouhov, T. & Muthén, B. (2018). Latent variable centering of predictors and mediators in multilevel and time-series models. Structural Equation Modeling: A Multidisciplinary Journal, DOI: 10.1080/10705511.2018.1511375 (Download scripts).

In this way, the vict_sch variable is also latent.
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