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I am conducting a CFA using categorical (binary) variables (54 items) using WLSMV. I am attempting to evaluate the fit of 3 different models: Model 1 consists of a general factor. Model 2 is a twofactor model (based on item format: MC versus studentproduced response items) Model 3 is a fourfactor model based on content areas. My questions pertain to conducting a Chisquare difference test between Models 1 & 2 and Models 1 & 3: 1) I tried to use the command "DIFFTEST", but received an error message indicating that my "models were not nested." Is there another method I can use to compare model fit? 2) I am unclear as to why my models are not nested. It seems as though both Model 2 and Model 3 would be nested in Model 1 (separately). I am using all 54 items in all three models. Please advise. Jennifer 


Model 1 is nested in models 2 and 3. You may have your setup backwards. You should run model 1 last. If you are doing this and still having problems, send your input, data, output, and license number to support@statmodel.com. 


I am using DIFFTEST with WLMSV to compare the goodness of fit of 3 models based on 17 categorical items. (There are some theoretical reasons for comparing these different models.) In the first model the 17 all load on 1 factor; in the second model, 9 items are on 1 factor and 8 on a second. In the third model, also with 2 factors, 7 of the original 9 load on the first factor while the remaining 2 of Factor 1 now load on the second factor in addition to the 7 already specified in the second model. Is there any way I can compare the Goodness of fit between the second and third models since the message I get is that these are not nested. Can I use the difference between the two Chisquare difference measures, the first from comparing Models 1 and 2 and the second from comparing Models 1 and 3 as a further Chisquare difference measure? Thanks Ruth 


Your second and third models are not nested so using a difference test to compare their fit is not appropriate. 

Sanja Franic posted on Wednesday, November 18, 2009  5:26 am



I cannot use the "difftest" option in MPlus when also using the "model constraint" option. Is there any other way to calculate the chisquare difference, given that I am using the WLSMV estimator? Thanks, Sanja 

Sanja Franic posted on Wednesday, November 18, 2009  6:05 am



I think I just found the answer to my own question. I use WLSM instead of WLSMV and use the scaling correction factors I get in the output to perform a shisq difference test. 


Dear Professors Muthen, I have a secondorder latent variable in CFA, and I would like to see if the thirdorder latent factor is a better alternative of the construct. Both secondorder factor and the thirdorder alternative have the same number of 34 ordinal indicators, so I am using WLSMV. The only difference is whether a 2nd or a 3rdorder construct is used. Hence I would like to ask if the DIFFTEST is appropriate in this situation? Or should I simply compare values of fit indices of both models and select a better fitting one? Thank you Alex 


We would need to see the 2 models to be able to say  you can send to Support along with your license number. Or ask on SEMNET. 


Dear Drs. Muthen, I am conducting a CFA testing the following models of ordinal data using WLSMV estimation: 1. 3 correlated factors 2. 3 correlated factors plus a general factor 3. 3 orthogonal factors plus a general factor I am trying to compare models 2 and 3 with model 1 using difftest. The difftest for model 1 vs. model 2 runs successfully; however, for model 1 vs. model 3, I get the error: THE CHISQUARE COMPUTATION COULD NOT BE COMPLETED BECAUSE OF A SINGULAR MATRIX. I have conducted the difference test of model 1 vs. model 3 by running model 3 (orthogonal bifactor) with the save command: SAVEDATA: difftest is orthbifacdiff.dat; then running model 1 (correlated factors) with the following analysis command: ANALYSIS: ESTIMATOR=WLSMV; DIFFTEST=orthbifacdiff.dat; The orthogonal bifactor and 3 correlated factors models both ran without issues previously. I would be grateful for any suggestions you have about how I may be able to address this. Thank you in advance. 


That message may appear due to nonnested models. First check that your models are nested. See the new option NESTED as described in the paper on our website under Papers, SEM, especially Section 4.2: Asparouhov, T. & Muthén, B. (2018). Nesting and equivalence testing in Mplus. Technical Report. May 16, 2018. (Download scripts). 


Thank you, Dr. Muthen. I have now been able to resolve the issue. I appreciate your help! 

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