An identifiability issue in the EM al... PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 Anonymous posted on Wednesday, January 12, 2005 - 1:59 pm
It may take a while to explain the problem. The question is related to Muthen and Shedden (1999) in Biometrics. Estimates from M-step in equations (29) through (32) should be equivalent to MLE estimates from a multivariate linear regression model, right? Take equation (3) as an example. Is it right to use posterior expectation of eta and c in the linear regression to get estimates? The issue is that the posterior of eta is a weighted mean of Psi^{-1}(A*c+Gamma.eta*x) and Lambda.y'Theta^{-1}y, and I have an estimate of Psi so close to a singular matrix that makes the weighted mean closer and closer to A*c+Gamma.eta*x as EM goes on and Theta^{-1} has no effect to pull the weighted mean away from the collinearity.

This is probably a problem of identifiability. I would like to put constraints on the model (Lambda.y is already fixed as suggested by the paper). Apparently, that's not enough. In fact this makes Theta^{-1} having even less impact on the weighted mean because of the discrepency of the outcome and the covariates in equation (2). What should I do to balance the posterior expectation of eta so that Psi does not converge to a singular matrix?

Many thanks.
 BMuthen posted on Wednesday, January 12, 2005 - 4:41 pm
The problem may have to do with the model causing psi to be singular. You should try this out in Mplus to explore why psi would be singular. If it is not singular in Mplus, then you may have a programming error.
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