I am attempting a two-level bi-factor confirmatory factor analysis. I have attempted to write some Mplus syntax to estimate a bi-factor model at the within level of a two-level model, fully saturating the between-level for model fit correction purposes. Could you confirm this is the proper way to specify the multilevel bi-factor in Mplus? Thank you!
ANALYSIS: TYPE IS TWOLEVEL; ESTIMATOR IS WLSMV;
Model: %between% !correlations Q1 WITH Q2; Q1 -Q2 WITH Q3; Q1 -Q3 WITH Q4; Q1 -Q4 WITH Q5; Q1 -Q5 WITH Q6; Q1 -Q6 WITH Q7; Q1 -Q7 WITH Q8; Q1 -Q8 WITH Q9; Q1 -Q9 WITH Q10; Q1 -Q10 WITH Q11; Q1 -Q11 WITH Q12; Q1 -Q12 WITH Q13; Q1 -Q13 WITH Q14;
To evaluate the fit of a two-level model like this where the level-1 is the only part of the model of interest (level-2 is saturated).... Should we only report the within-level SRMR provided by Mplus? My understanding is that the RMSEA, TLI and CFI reflect the fit at both levels and should be overly optimistic about model fit due to the perfect fit at level-2. Is that correct?
After reading this post I am curious if the bi-factor code is accurate since I believe it fixes both the first factor loading and the factor variances to 1. Is this the correct way to specify a bi-factor model at level-one of a multilevel confirmatory model?