Message/Author
 Jim Shaw posted on Wednesday, June 20, 2007 - 8:07 am
I am attempting to fit the following hierarchical model:

Y = X and X = Z

where

Y is an observed continuous variable;
X is a continuous latent variable with ordinal indicators x1, x2, x3; and
Z is a continuous latent variable with ordinal indicators z1, z2, z3.

I want to derive an estimate of the indirect effect of z1 (z2, z3) on Y. By analogy, if X and Z were observed variables, then I would regress Y on X and X on Z and multiply the path coefficients to derive the indirect effects.

Further, since z1 (z2, z3) are ordinal (categorical), I would like to estimate separate coefficients for each category save the base category. In other words, if z1 has 4 levels, then I would like to generate 3 separate coefficients for z1.

I can output the indirect effect of Z on Y. However, treating z1 (z2, z3) as ordinal indicators yields a single coefficient for each. Would I be able to derive multiple coefficients for these indicators by treating them as nominal? I don't think Mplus allows nominal indicators to be used for continuous latent variables.
 Linda K. Muthen posted on Wednesday, June 20, 2007 - 9:10 am
You could turn the ordinal indicators into a set of dummy variables.
 Jim Shaw posted on Wednesday, June 20, 2007 - 1:12 pm
I tried to use dummy variables for z1 (z2, z3) as indicators for Z. For example, z11, z12, z13 for z1, which has 4 levels. However, this resulted in an error message that the covariance matrix was not positive definite, and no standard errors were produced.

I then tried to fix the loadings of some of the dummy variables (e.g., z11, z21) at 1.0. This resulted in a lack of convergence.
 Linda K. Muthen posted on Wednesday, June 20, 2007 - 5:42 pm
I would need to see what you are actually doing. Please send your input, data, output, and license number to support@statmodel.com.