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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. 

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