Number of free parameters - WLSMV PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Kristof posted on Saturday, September 23, 2017 - 3:12 am
Dear SEM Experts,

Consider a very simple example (z1-z2 are latent variables, a1-a6 are manifest variables):

z1 BY a1 a2 a3;
z2 BY a4 a5 a6;
z2 ON z1;

Acc. to information reported by MPlus number of free parameters is 26, as there are 19 thresholds (3*5+4*1).

Number of non-redundant elements in the correlation matrix is 6*7/2=21.

How to check identifiability of WLSMV models using t rule test (Bollen 1989)? I guess we should not take into account thresholds. Hence, do we have 7 free parameters for t-rule test? I mean, 4 factor loadings, 1 path coefficient, 1 latent variable variance and 1 residual variance?

The same problem I have with calculating degrees of freedom for both chi-square tests of model fit which are reported by MPlus for structural equation models estimated by WLSMV. However, answer for the first question will clarify the second question a bit.

Thank you in advance.
 Bengt O. Muthen posted on Saturday, September 23, 2017 - 3:54 pm
You can ignore the thresholds because that part of the model is just-identified. for categorical outcomes (which I assume they are all categorical given your thresholds statement), there are 6*5/2 = 15 free parameters in H1 for these 6 variables (or put differently, 15 correlations). As you say, there are 7 parameters apart from the thresholds. So there should be 15-7 = 8 df.
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