Computing Hierarchical Omega in bi-fa...
Message/Author
 Itzik posted on Thursday, March 05, 2015 - 5:43 am
Dear Drs.
I have conducted a bi-factor geomin efa, with 3 factors. I wanted to ask you how can I use the output to calculate hierarchical omega coefficient(for the general factor).
It is my understanding that the formula is something like this:
(squared sum of unstandardized loadings on G)/(squared sum of unstandardized loadings on G + squared sum of unstandardized loadings on S1 + squared sum of unstandardized loadings on S2 + error variance for this item).
Is that correct? can I use the 'estimated residual variances' seen in the output as the error for the item?

Many Thanks,
Itzik.
 Bengt O. Muthen posted on Thursday, March 05, 2015 - 9:10 am
Yes on both; this seems correct.
 Itzik posted on Friday, March 06, 2015 - 1:40 am
Thanks!

Does it matter that the rotation was non orthogonal? Can I still count on factor loadings to do the calculation? and if not - how can I do it?

Thanks again.
 Bengt O. Muthen posted on Friday, March 06, 2015 - 8:02 am
The rotation should be orthogonal, otherwise you have to include covariance terms among the factors in computing the total variance in the denominator.
 Itzik posted on Saturday, March 07, 2015 - 1:10 am
I see.
Where can I find the covariance terms among factors in the output? Do I have to also calculate their squared sum?

Thanks!
Itzik.
 Itzik posted on Saturday, March 07, 2015 - 2:58 am
Let me be more specific - in the oblique rotation, the correlation between the two specific factors is -0.169. The program does not provide correlation with the general factor. Can I use this correlation to caclulate the covariance and add it to the denominator?

And one last question, if its okay - when adding the residual variances to the denominator - should I calculate the squared sum of variances as given, or should I calculate the squared sum of the square root of residual variances?

Thanks!
 Bengt O. Muthen posted on Saturday, March 07, 2015 - 2:07 pm
so if you have

y = b*G + b1*S1+b2*S2 + e,

with a non-zero covariance between the S1, S2 factors, then the variance is

V(y) = b^2*V(G)+ b1^2*V(S1)+b2^*V(S2)+2*b1*b2*Cov(S1, S2)+ V(e).

No square root.
 Itzik posted on Sunday, March 08, 2015 - 6:19 am
Ok. I think another approach would help me more. I can simply calculate the denominator by summing the correlation/covariance matrix, right?
So the only question is whether I should use the correlation or covariance matrix? In any case - how can I ask Mplus to produce the matrices used for the EFA (geomin bi-factor efa with WSLMV estimator).

Thanks!
 Bengt O. Muthen posted on Sunday, March 08, 2015 - 9:29 am
That will only be an approximation since the model-estimated variance may not fit the observed-variable variance exactly.

EFA uses a correlation matrix.
 Itzik posted on Monday, March 09, 2015 - 12:22 am
I'm sorry for my troubles understanding, but I need a method to calculate the denominator which is the total variance in standardized units (as the actual V(x) is in unstandardized units, being close to the sum of the covariance matrix). So how can I get an output of the correlation matrix which is used by the WSLMV estimator?
Alternatively, how can I use the formula you wrote above, to calculate the variance based on standardized loadings?

Thanks!
Itzik
 Bengt O. Muthen posted on Monday, March 09, 2015 - 6:29 pm
When a correlation matrix is analyzed, your estimates are already in a metric of V(x)=1.
 Marc Goodrich posted on Thursday, May 12, 2016 - 12:39 pm
Drs. Muthen,

I am using bi-factor CFA models for a recent analysis and need to compute omega, omegaH and omegaS. In this thread a user posted about using the unstandardized factor loadings to compute omega coefficients, but other examples I have seen all use standardized loadings in the computation (e.g., Reise, Bonifay, & Haviland, 2012; Gignac, 2014; Watkins, 2013).

Thanks!

Marc Goodrich
 Bengt O. Muthen posted on Thursday, May 12, 2016 - 7:05 pm
Using the unstandardized is correct but perhaps you get the same result using standardized.
 Daniel Lee posted on Tuesday, June 06, 2017 - 12:56 pm
Hi Dr. Muthen,

In a Bifactor CFA model (of an anxiety scale), if the OmegaHS was .87 for the general factor and ranged from .01 -.06 (across 4 subtypes), ECV was close to .80, and the percent of uncontaminated correlation was close to 100, does that suggest that the scale is unidimensional and that I should interpret it as such?

If this scale is truly unidimensional, why might the model fit for the one-factor model be so poor (e.g., RMSEA > .15)? Also items loaded well on subtype factors (factor loading > .3) even after loading on the general factor, which further confuses me as to whether this scale is uni- or multidimensional.

As always, thank you for sharing your knowledge and wisdom!
 Bengt O. Muthen posted on Tuesday, June 06, 2017 - 6:14 pm
These general analysis questions are suitable for SEMNET.