

Number of free parameters  WLSMV 

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Kristof posted on Saturday, September 23, 2017  3:12 am



Dear SEM Experts, Consider a very simple example (z1z2 are latent variables, a1a6 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 nonredundant 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 trule 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 chisquare 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. 


You can ignore the thresholds because that part of the model is justidentified. 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 157 = 8 df. 

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