Harry Garst posted on Tuesday, December 10, 2013 - 6:54 am
I am surprised that there was no warning in the output of Mplus that the between covariance matrix was not positive definite. One of the eigenvalues was negative. I fitted a TWOLEVEL model using the WLSMV estimator and ordinal variables (CATEGORICAL ARE option). I thought the matrix should be positive definite or have I missed something?
With the weighted least squares the estimation of the unrestricted within and between variance covariance matrices is estimated on a bivariate basis, i.e., the within and the between correlation is estimated separately for each pair of variables. That often causes the total variance covariance matrix to be not positive definite, however, that does not hinder the estimation of the structural model. The same issue also occurs for single level models with the weighted least square estimation.