Variance decomposition when using %wi...
Message/Author
 Student 09 posted on Thursday, June 18, 2009 - 3:04 am
Hi

when declaring covariates as %within%, does this mean that these covariates are (a) automatically group-mean centered or
(b) treated as uncentered ?

Further, assume one intends to model the main effects of individual-level covariates x1 and x2 (measured on the within level) on y. All variables show substantial ICCs.

For x1, the interest is really on both its within- and between group variance components (thus this variable is not declared as %within%).

The major purpose of x2, however, is to account for differences in the population composition of the different groups.Accordingly, one decides to grand-mean center x2, without decomposing its within- and between-group variance.

Question #c: Can I achieve a grand-mean centered x2 using the centering = grandmean command and then declaring x2 to be a %within% variable?

Many thanks!
 Linda K. Muthen posted on Thursday, June 18, 2009 - 8:57 am
Variables are centered only if the CENTERING option is used.

Question #c: Yes.
 Student 09 posted on Friday, June 19, 2009 - 9:47 am
Hi Linda

but if I grandmean-center a within-level covariate x2 and then tell Mplus that x2 operates on the %within%-level, can the between-group fraction of x2 still partial out between-group variation in the dependent variable y?

This is the background for my question:

I would like to control for compositional differences between groups via grandmean centering (rather than group-mean centering) of several variables (x2-x10) in order to avoid to have to include the group means of all these variables in the analyses.

By contrast, because the theoretical interest is really on the within and between effects of x1 on y, I keep the Mplus default group-mean centering for x1.

 Bengt O. Muthen posted on Friday, June 19, 2009 - 11:18 am
Yes, you can estimate between-cluster variation in y even when an x variable is grand-mean centered.
 Bengt O. Muthen posted on Friday, June 19, 2009 - 11:29 am
To study centering issues, you may also want to look at

Enders, C.K. & Tofighi, D. (2007). Centering predictor variables in cross-sectional
multilevel models: A new look at an old Issue. Psychological
Methods, 12, 121-138.