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I wish to fit a model in which one latent variable is regressed on 2 other latent variables and their interaction (plus an observed covariate, gender). The indicators for each factor are measured on a 5 point, ordinal scale. I fitted the model treating the indicators as continuous using MLR. I then fitted the model treating the indicators as CATEGORICAL, also using MLR. Can you recommend any diagnostic procedures to determine which set of analysis is most appropriate? 


If your variables are ordinal, the most appropriate way to treat them is as categorical variables. If your 5 point variables do not have strong floor or ceiling effects, you can probably treat them as continuous will little ill effect. 


Thank you very much. 

Guillermo posted on Friday, January 23, 2015  3:53 am



Dear Dr. Muthen: I have a CFA with 4point ordinal indicators (not strong floor or ceiling effects). When I treat them as categorical using WLSMV, I get the warning message 'THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE', and the results are somewhat incoherent. However, when I treat them as continuous using ML and MLM, the model runs perfectly and the results are as expected. Is it OK using ML or MLM in a case like this, or is there any way to deal with the nonpositive definite matrix? Thank you so much in advance. 


The data you analyze are different when you treat the variables as categorical versus continuous. A more accurate comparison would be to use the CATEGORICAL option and ML. I would want to understand why treating them most appropriately has a problem. If you want help with this, send the output and your license number to support@statmodel.com. 

Guillermo posted on Friday, January 23, 2015  6:37 am



I understand that when using ML with the CATEGORICAL option, ML estimation is applied to the polychoric correlation matrix. Is this correct? Would it be any better using MLM? 


No, this is not true. WLSMV uses a tetrachoric/polychoric correlation matrix as statistics for model estimation. ML and MLM, all maximum likelihood estimators use individual data. 

Guillermo posted on Friday, January 23, 2015  6:58 am



Thank you so much for the clarification. I will try using CATEGORICAL with ML. 

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