EFA with ordinal complex data
Message/Author
 Anonymous posted on Monday, June 27, 2005 - 11:15 am
Hello,
I'm hoping to ascertain whether Mplus supports estimation of a multilevel EFA with ordinal and hierarchically nested (complex) data. Thank you.
 Linda K. Muthen posted on Tuesday, June 28, 2005 - 7:55 am
No, Mplus does not support multilevel EFA unless you do an EFA model in a CFA framework.
 Alison Riddle posted on Thursday, November 29, 2007 - 7:51 am
Can you please explain a bit more what you mean by doing an EFA model in a CFA framework?

I am working with complex survey data with binary outcomes and I would like to undertake a multilevel EFA. What are my options in MPlus?

Cheers,
Alison
 Linda K. Muthen posted on Thursday, November 29, 2007 - 8:05 am
Mplus Version 5 has multilevel EFA. See Examples 4.5 and 4.6 in the Mplus Version 5 User's Guide which is on the website.
 EFried posted on Thursday, June 07, 2012 - 7:57 pm
We are running ordinal EFA and CFA using WLSMV estimator to see how many factors to extract.
N in this sample =550.

In >15 samples we looked at, we found either 1 or 2 factor solution, fit indices for both solutions being close to good, eigenvalue for third factor <.4 and bad fit.

This sample proves problematic, however.

EFA 1-3:
STANDARD ERRORS COULD NOT BE COMPUTED.
PROBLEM OCCURRED IN EXPLORATORY FACTOR ANALYSIS WITH 3 FACTOR(S).
THE CONDITION NUMBER OF THE ROTATED SOLUTION IS 0.162D-11.
THE OPTIMAL ROTATION IS NOT SUFFICIENTLY IDENTIFIED. CHANGING THE ROTATION METHOD MAY RESOLVE THIS PROBLEM.

Eigenvalue for third factor >1 so we're interested to extract it.

CFA:
Testing 1 through 3 factor solutions with CFA shows abysmal fit indices, and this warning in 2 and 3 factor solution:

WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IS NOT POSITIVE DEFINITE.
THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR AN OBSERVED
VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO OBSERVED
VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO OBSERVED VARIABLES.
PROBLEM INVOLVING VARIABLE PHQ4.

Could you speculate what could cause this?

Thank you!
 EFried posted on Friday, June 08, 2012 - 7:02 am
(I forgot to mention that the questionnaire has 9 items, each item ranging from 0 to 3).
 Linda K. Muthen posted on Friday, June 08, 2012 - 11:27 am
Regarding the EFA, you could try changing the rotation method as is suggested.

Regarding the CFA, ask for the standardized solution where you can see if you have a negative residual variance for phq4. I suspect that is the problem.
 EFried posted on Friday, June 08, 2012 - 7:46 pm
Thank you Linda. Using quartimin in EFA I get the error message that variance for PHQ4 is negative.

Using promax the EFA runs, but the results are bogus. I tried CATPCA in SPSS and checked the data twice (frequencies), there are no problems in the data, and N~500 should also be ok. Again, on the other 15 datasets both the EFA and CFA syntax in MPLUS worked very well.

You are right about the negative residual variance in the CFA. Could you recommend a way to solve this?
PHQ4 Undefined 0.22316E+01 -1.232

It's way to large to just fix it to zero. Using a 1 factor solution doesn't fit at all (4 out of 9 items don't even load significantly on the one factor in that case), that's why we're trying to extract 2 or 3 factors.

Thank you for the support
 Bengt O. Muthen posted on Friday, June 08, 2012 - 8:29 pm
To constrain residual variances to be positive in EFA, you can use ESEM, label the residual variances, and use Model Constraint to require each to be >0. That, however, may mask an important misspecification such as using too many factors or omitting correlated residuals (which can also be included in ESEM). The ESEM EFA is specified like

f1-f2 BY y1-y10 (*1);

for the example of 2 factors.
 EFried posted on Sunday, June 10, 2012 - 7:01 am
Thank you Bengt.

The item that seems to cause the issue is very negatively skewed:

Item4
Category 1 0.027 14.000
Category 2 0.180 94.000
Category 3 0.235 123.000
Category 4 0.558 292.000

Maybe that could cause the problem?

I don't feel comfortable constraining a residual variance of over -1.2 to zero.

Is there any other solution (after trying different estimators)? Or does it mean the data are not ... fit for running EFA in MPLUS on them? Are there alternatives?

I'm confused because I never had trouble with EFA in MPLUS before.
 Bengt O. Muthen posted on Sunday, June 10, 2012 - 3:46 pm
A factor model does not fit all data sets. A large negative residual variance can be an indication of that. You can try to tweak the model in several ways:

- add residual correlations (for both EFA and CFA; judging by modindices)

- treat variables differently, such as treating your Item 4 as categorical
 EFried posted on Tuesday, June 12, 2012 - 6:17 pm
Thank you Bengt. The variables are all categorical, and I tried cross loadings for the difficult items and allowing residuals to covary, to no avail.

I also tried orthogonal rotations, just in case. Seems the data are simply not properly 'factorizable'.

Thanks!
 Francisco Argueta-Ortiz posted on Friday, September 12, 2014 - 10:49 am
Good afternoon Dr Muthen,

I am writing

I have 12 items of a scale that we measured 3 times. I am trying to run longitudinal factor analysis to see how the loadings are common over the time, invariance of the factor loadings and common factors. It is example 4.5 from the manual.

I would like to know if you could explain me or help me find a place to understand:
1. Which variable should I use as clustering variable: participant ID or timepoint?
2. Understanding better the within and between factors.

Thank you very much!
 Bengt O. Muthen posted on Friday, September 12, 2014 - 6:00 pm
Because you have only 3 times, I don't think you should do 2-level FA, but instead wide format CFA. So you will have 3*12 variables.
 Francisco Argueta-Ortiz posted on Tuesday, September 16, 2014 - 6:06 am
Thank you Dr. Muthen for your response!

I tried to run before the EFA at 2 time points with wide format (Example 5.26). When I run the syntax with t1 data, I get the message “No Convergence… The residual covariance matrix (theta) is not positive definite”. When I run the analysis with t2 and t3 data, I have no issues.

I would like to know if you could help me setting up this analysis.

Thanks
 Linda K. Muthen posted on Tuesday, September 16, 2014 - 7:30 am