I am planning to do a multilevel repeated measures analysis with Mplus and am currently reading up on the literature. So far, I have been working with MLwiN. Now one difference in modeling between Mplus and MLwiN that I spotted was the explicit between and within component of Level 1 predictor variables in Mplus.
My question would be whether this distinction of between-within components is neccesary and if so how I can compute this between-component of a predictor variable.
To me this sounds like a centering issue, so I would merely center Level 1 variables around their group mean and Level 2 variables around their grand mean (as I do with MLwiN) and ignore the aforementioned between and within component. As far as I know this can be done with Mplus as well...
I would be grateful if you could assist me with this.
If you want to do what MLwiN does, you specify the within predictor x as a Within=x variable and create a between counterpart xm using Define as
xm = cluster_mean (x);
where you declare xm as Between = xm;
The advantage of the latent variable decomposition of x that can be done in Mplus is detailed in the paper on our website:
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.
This latent variable decomposition can not be used with random slopes.