Inequality constraints with Mplus
Message/Author
 Kou Murayama posted on Sunday, October 14, 2007 - 1:45 pm
I try to test an ordering hypothesis within a correlation matrix with Mplus. Especially, I want to see whether a given correlation matrix fits the simplex structure.

To accomplish this, I put inequality constraints between correlations (or covariances) in Model Constraints to see whether correlation decreases as one moves away from the main diagonal. We use 6 variables. So there are 85 inequality constraints between correlations. No other constraints are imposed.

However, the output says "NO CONVERGENCE. SERIOUS PROBLEMS IN ITERATIONS." Changing the starting values does not help.

Would you tell me how to test this kind of ordering hypothesis with Mplus? I know Joreskog's (1970) formulation is another way to test the simplex structure. But I prefer to use this ordering constraints for some reason.
 Linda K. Muthen posted on Sunday, October 14, 2007 - 2:50 pm
Does the model converge without the constraints? That would be the first thing I would check. If it does and it is the addition of the constraints that causes the problems, you need to send your input, data, ouptut, and license number to support@statmodel.com.
 Kou Murayama posted on Sunday, October 14, 2007 - 4:39 pm
Thank you very much! Because the model without these constraints is default model (no constraints are imposed on the correlation matrix), it converged with perfect fit. I found that the model converges when the number of variables is smaller. I will send e-mail to the address after I try few more times.

Besides this convergence issue, I got another problem. Because inequality constraints do not increase degrees of freedom (i.e., the model has 0 degrees of freedom regardless of the constraints), I cannot test whether the inequality constraints (for a correlation matrix) are reasonable or not. Would you tell me how to resolve this issue?