I'm relatively new to Mplus. I would like to know when (and why) to list or not list variables in the %BETWEEN% section along with a regression in which those variables are already included as predictors. Here is the relevant part of some code:
VARIABLE: NAMES = ...; USEVARIABLES = ...; MISSING ARE ALL (-999); CLUSTER = SubScen;
ANALYSIS: TYPE = TWOLEVEL;
MODEL: %WITHIN% Pref ON Distort PrevPref; %BETWEEN% Distort; PrevPref; Pref ON Distort PrevPref;
The results of this code depend on whether the variables Distort and PrevPref are listed under %BETWEEN%. For example, when they are listed, the coefficient for Distort in the between regression is 1.658, p=.090. But when that line is omitted, the coefficient is 0.378, p=.824. The former output includes the variances of the two variables at both levels and the latent means at the between level, but the latter does not. I'm wondering whether the latent centering isn't happening when the variable are not listed. Why would that be?
I have most often seen models without such variables listed (e.g., in UG 9.1), but I've also seen models with several such variables listed (e.g., in slides for cross-classified path analysis).
%BETWEEN% Distort; PrevPref; Pref ON Distort PrevPref;
you estimate the variances of those 2 latent covariates. But make sure to also estimate their covariance so it isn't fixed at zero (check the output) because that could be a mis-specification that would explain your different results.
Typically, you mention covariate variances when you want to handle missing data on the covariates. See chapter 10 of our new book.
Thank you for the quick reply. You are correct that adding the covariance (at either the between level or at both levels) eliminated the difference in the results. The results were very similar to those from the simpler model that did not ask for the variances at all. (I confess that I'm not exactly sure why, though.)
On a related point, do you have an example in which cluster centering is done with GROUPMEAN in the DEFINE section (as in 9.2) and in which the cluster means are also computed with CLUSTER_MEAN in the DEFINE section? That seems like a logical thing to do, but the examples seem to have the cluster means already computed. When I try this with my own data, I get problems with matrix inversion and convergence. I understand that latent centering may be preferred, but I'm trying to learn and understand, so that I trust my output.