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 between-level model is unstructured (i.e., df = 0). According to Hox (2002) and Ryu and West (2009) the perfect fit of the unstructured between-level 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 between-level model with a within-level independence model. The chi-square value from this new baseline partial independence model may then be used to manually calculate the CFI for the 3 factor within-level EFA shown above in a way that is not influenced by the perfect fit of the saturated between-level 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?
Can I ask a follow-up 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?