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I am curious to know what kind of independence model is used to generate the CFI for the following model. TYPE = TWOLEVEL EFA 3 UW UB; Note in the model described above that the betweenlevel model is unstructured (i.e., df = 0). According to Hox (2002) and Ryu and West (2009) the perfect fit of the unstructured betweenlevel model may affect the value of the comparative fit index (CFI) if the baseline independence model is in fact a within and between level independence model. This problem can be addressed by estimating an alternative multilevel partial independence model that consists of a unstructured betweenlevel model with a withinlevel independence model. The chisquare value from this new baseline partial independence model may then be used to manually calculate the CFI for the 3 factor withinlevel EFA shown above in a way that is not influenced by the perfect fit of the saturated betweenlevel model. Is this the method that has been used to calculate the CFI in Mplus for multilevel EFA in those instances where one level is specified as being unstructured, and if this is not the method used what method is? 


For TWOLEVEL EFA the baseline model is the model of means, between variances, and within variances. 


Can I ask a followup question here? Is it possible in Mplus to estimate the "partially saturated independence model" that Ryu and West (2009) describes using for calculating the modified CFI for this type of model? Thank you very much! Fredrik Falkenström 


You could specify that model and compute CFI by hand. There is not option to change the baseline model. 


Hello, Dr. Muthen indicated that an analyst can directly estimate the partiallysaturated independence model and manually carry out the levelspecific fit calculation for CFI from Ryu & West. I have attempted this approach and encountered a result that was not intuitive. To perform the withinlevel fit calculation, I directly specify a partiallysaturated withinlevel independence model. %between% Item1 with Item2  Item5 ; Item2 with Item3  Item5 ; Item3 with Item4  Item5 ; Item4 with Item5; Item1; Item2; Item3; Item4; Item5; %within% Have I properly estimated this partiallysaturated independence model in MPlus? With this code I obtain the following output: ChiSquare Test of Model Fit Value 34008.044* Degrees of Freedom 10 ChiSquare Test of Model Fit for the Baseline Model Value 26623.515 Degrees of Freedom 20 My concern is that the ChiSquare value has increased in this partiallysaturated model compared to the original baseline model. I would have expected the partiallysaturated model to provide better fit to the H1 Unrestricted model than the original baseline model since the betweenlevel is saturated. My initial thought is that because the items are specified as categorical, the withinlevel independence model is not being properly specified in MPlus. Thank you very much! Benjamin Brumley 


I assume you are using 2level WLSMV. One can’t count on WLSMV chisquare values being ordered in line with the restrictiveness, although this large difference is a bit strange. Try WLSM. If that doesn't change matters, send relevant files and license number to Support. 


Hi Dr. Muthen, Thank you for the suggestion. Yes, it is a twolevel model with the WLSMV estimator. I reran the model using WLSM and the results look more reasonable to me. ChiSquare Test of Model Fit Value 50799.673* Degrees of Freedom 10 ChiSquare Test of Model Fit for the Baseline Model Value 50934.805 Degrees of Freedom 20 If we use this solution, I am assuming we would also need to rerun our 'target' models using the WLSM estimator as well? Thank you again for your help. 


Note that there is nothing wrong with using the WLSMV results. DIFFTESTing gives the right conclusions. 


I notice that DIFFTEST is not available for TYPE = TWOLEVEL. Something for the Mplus 7.4 wish list perhaps. 


Perhaps later. Not for 7.4. 


Hi Dr. Muthen, I wanted to followup on your response. I was trying to obtain the chisquare for the partialindependence model to perform the levelspecific fit evaluation for CFI (Ryu & West, 2009). I am assuming I have specified the model appropriately in MPlus. The twolevel WLSMV estimator produces a partiallysaturated model chisquare that is larger than the original baseline model test. This is my finding across three different data sets. You indicated that there is nothing wrong with the results and that DIFFTESTing gives the right conclusions. However, DIFFTEST cannot be done in type=twolevel. My question is, can we trust this partiallysaturated model chisquare for performing the recalculations of the CFI? I have found I can replicate the original MPlus fit indices using the original baseline model chisquare through the calculations in Ryu & West (2009). So the logic seems to stand in the regular way. My feeling though is that I should not trust this partiallysaturated chisquare result even though the original CFI calculations seem to be straightforward. Thank you very much, Benjamin Brumley 


Why not use WLSM here? 

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