Centering: implicitly done or not? PreviousNext
Mplus Discussion > Multilevel Data/Complex Sample >
 Jemima posted on Monday, September 08, 2014 - 8:13 am

I am using the 7.0 version of Mplus. In light of my current analyses I have a question concerning the centering of data in Mplus. To investigate a multilevel mediation model, I have defined my model on the within and between level. It is a simple, mediation model in which two predictors relate to three mediators, in turn linking to a dependent variable. One of my paper's referees asks me to look at the interaction between the two predictors. I wonder whether I can simply define a new variable (which is obtained by multiplying both variables)? In other words, is the centering already done by defining the model on both levels, or do I still have to center my data before computing the interaction term. And if so, should I center these data on the group or grand mean? (note that my research question is situated on the within-person level, but that my model is defined on both levels to be as complete as possible).

I hope my question is clear, your help is really welcome.

Thanks in advance!
 Linda K. Muthen posted on Monday, September 08, 2014 - 9:52 am
Observed variables are not centered unless you center them. Center them using grand mean centering and then create the interaction term.
 Daniel Kopala-Sibley posted on Sunday, September 04, 2016 - 9:37 am

I also have a simple multilevel model. Each subject has 3 observations over time for each of several variables. I understand that if none of these are specified as within variables, but are included on both the %between and %within lines in Type=twolevel, MPlus will implicitly decompose these raw scores into between/means versus within subject fluctuations (ie such that scores represent deviations at each time point from each person's own average score)?

If that is accurate, how would this be different from manually creating between subject mean scores and time-varying within-subject deviation scores (ie raw score minus the mean score), the specifying which variables are between and which are within, and including each on the respective between vs within paths using type=TWOLEVEL? Finally, if this latter approach is appropriate, I understand I would have to use the mean of the dependent variable on the %between line, but for the dependent variable on the %Within line, would I use the raw score or the deviation score I created?

While these approaches seem conceptually similar to me, they produce wildly different results and use a different number of observations.

Thanks so much,

 Bengt O. Muthen posted on Sunday, September 04, 2016 - 11:29 am
These issues are discussed in the paper:

Lüdtke, O., Marsh, H.W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: A new, more reliable approach to group-level effects in contextual studies. Psychological Methods, 13, 203-229.
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