Two-Level Bi-Factor Confirmatory Fac...
Message/Author
 Benjamin Brumley posted on Wednesday, October 05, 2016 - 11:20 am
Hello Mplus team,

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;

!VARIANCES
Q1;
Q2;
Q3;
Q4;
Q5;
Q6;
Q7;
Q8;
Q9;
Q10;
Q11;
Q12;
Q13;
Q14;

%within%
F1W BY Q2 Q3 Q4 Q9 Q13;
F2W BY Q1 Q5 Q6 Q7 Q10 Q11 Q14;
GW BY Q1-Q14;

F1W@1;
F2W@1;
GW@1;

GW with F1W@0;
GW with F2W@0;
 Bengt O. Muthen posted on Wednesday, October 05, 2016 - 4:00 pm

F1w WITH f2w@0;

Note also that you can simplify your input

q1-q14 with q1-q14;

q1-q14;
 Benjamin Brumley posted on Thursday, October 06, 2016 - 8:58 am
Thank you for the response and simplying code!

Do the specific factors (f1w and f2w) have to be uncorrelated or is it just more typically modeled that way?
 Bengt O. Muthen posted on Thursday, October 06, 2016 - 10:31 am
The latter - in order to view them as "residual" factors.
 Benjamin Brumley posted on Tuesday, November 15, 2016 - 10:52 am
Dr. Muthen,

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?
 Bengt O. Muthen posted on Tuesday, November 15, 2016 - 5:32 pm
If the second level is saturated I would think that there is no contribution from that level to any of the fit indices.
 Katherine Barghaus posted on Friday, June 08, 2018 - 7:37 am
Hello,

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?
 Bengt O. Muthen posted on Friday, June 08, 2018 - 1:33 pm
You should not fix both the first loading and the factor variance.