I have two questions regarding the centering approach used in DSEM for the lagged variable and the level-1 covariates respectively. (1) From my understanding, the latent centering approach is used for the variable with the autoregressive parameter by default. So in the following syntax, we use the raw (uncentered) data for y. Is this correct (in Mplus V8.0)? (2) Is latent centering approach also available for level-1 covariate x, which has variability on both within-person and between-person levels? If so, how do we specify it? Or do we have to use the group-mean center approach for x as follow?
I'm using Mplus 8.0 for DSEM analysis. Does it mean that in 8.0, the observed group-mean centering approach needs to be used for covariate X to get accurate estimates for within-person and between-person effects?
You can use the observed centering approach if the cluster sizes is more than 100, but generally you should try to move to 8.2, not just because of the latent centering but also because you might want to use the RDSEM method instead and include auto-correlation for the covariate as well. See the first three papers http://statmodel.com/TimeSeries.shtml
I am currently familiarizing myself with DSEM and have a question on the meaning of the intercept when using the latent covariate approach to centering.
The model is simple: the dependent variable y (occasions nested in persons) is regressed on the time varying predictor variable x. The Mplus code is
VARIABLE: NAMES = id y x; USEVARIABLES = y x ; WITHIN = ; BETWEEN = ; CLUSTER = id; ANALYSIS: TYPE = TWOLEVEL RANDOM; ESTIMATOR = BAYES; PROCESSORS = 2; BITERATIONS = (2000); MODEL: %WITHIN% s | y on x; %BETWEEN% y on x; x; [x]; y; [y]; s; [s]; y with s;
The estimated intercept for y is very different from the intercept of a similar model in which I use the observed group mean centering approach as described in Asparouhov & Muthen (2018). Instead, the intercept seems to be reflect a value for x = 0. The estimated slope, instead, is quite similar to the slope of the group mean centering approach. That is, the latent mean centering approach seems to center the Level-1 predictor x around the latent means of x (similar to what happens in group mean centering), but the Level-2 part of x does not seem to be centered. Is my observation correct or am I doing something wrong here / misunderstand something? What exactly is happening here?
Correct. The Level-2 part of x is not centered. Centering on Level-2 is not as important as centering on Level-1. Centering on Level-2 is nothing more than subtracting a constant from a variable, i.e., it is a simple model reparameterization / change of scale. You can add DEFINE: CENTER x (GRANDMEAN); if you want it centered.