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Mplus Discussion > Categorical Data Modeling >
 Laura posted on Thursday, March 25, 2004 - 12:18 pm
I'm conducting a multi-group path analysis in which the model has a categorical dependent variable that is both influenced by and influences another observed dependent variable. Although I should be relying on Theta parameterization for this model, as delta is the default, I'm not entirely sure what changes I should be making in my model command to use theta parameterization. Any suggestions would be greatly appreciated. Thank you!
 Linda K. Muthen posted on Thursday, March 25, 2004 - 3:03 pm
 Laura posted on Thursday, March 25, 2004 - 3:15 pm
Fantastic! Thanks so much!
 Jason Bond posted on Monday, January 30, 2012 - 5:24 pm
With 10, 4-category indicators of a single factor (with its variance, phi, fixed to 1) in CFA using the default delta parameterization with MI(3.84) specified, model fit appears adequate and no parameters appear in the MI section. When I switch to theta, the MI section indicates a number of residual covariances that should be included along with several residual variances with MI values of 999. However, as I am interested in the indirect effects of the factor indicators on another variable, I need to use theta. Does such output indicate this is not advisable? Thanks.
 Bengt O. Muthen posted on Monday, January 30, 2012 - 8:33 pm
If you use the Output option

modindices (all 3.84)

you should see significant MIs also for the Delta parameterization. "All" means that all parameter arrays are investigated, in particular off-diagonal elements of Theta in this case. If you don't see this, send the 2 outputs to Support.

999 means that the MI could not be computed, so ignore.

If you have large, significant, and substantively meaningful MIs, you probably want to sort out that model misspecification first before you start using the factor indictors as predictors.
 Jason Bond posted on Thursday, February 02, 2012 - 10:31 am
Referring to the same model above, and recoding the categorical factor indicators above down to 3 instead of 4 categories, when using both the latent factor and direct effects of a categorical factor indicator to simultaneously predict another 3-category the factor indicator, now also a predictor, used as a continuous variable in its original observed metric when serving as a covariate (i.e., with values of 1, 2, and 3) or is a predicted version of the continuous latent y*_j (ala notation in Web note #4) used? Also, is it possible to obtain or reconstruct, for each case i, the predicted values y* for categorical outcomes (i.e., I would like Tech10-type output for non-mixture models). Thanks.
 Linda K. Muthen posted on Friday, February 03, 2012 - 9:02 am
With weighted least squares, when the categorical variable is a covariate, it is treated as the latent response variable.

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