Interpreting Two-Level EFA Model Test... PreviousNext
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 Stacey Farber posted on Tuesday, April 20, 2010 - 7:28 pm

I ran a two-level, EFA with categorical data. School id is used as the cluster variable.

The unrestricted within, 1 factor between has nice fit (CFI=.96, RMSEA=.04). The 4 factor within, unrestricted between has nice fit (CFI=.96,RMSEA=.05), and the four-factor solution seems to be most sensible with respect to interpretability and parsimony.

If I look at fit indices for a 4,1 model, however, results seem somewhat less certain (CFI=.92, RMSEA=.04).

Am I going about this in the correct manner? Also, can you recommend articles / manuscripts that might help me understand multilevel EFA?

Thank you in advance.
 Linda K. Muthen posted on Wednesday, April 21, 2010 - 9:00 am
It sounds like you have approached this correctly. I don't think CFI has been studied for this type of model so it is not clear if it behaves correctly here. A Monte Carlo simulation would be needed to study this. I also don't know of articles on multilevel EFA.
 Stacey Farber posted on Wednesday, April 21, 2010 - 4:56 pm
Thank you, Linda.

If I may follow-up with another question ... I noticed very high ICCs for a number of the variables used in my study (kindergarten reading language arts instruction), suggesting that schools or factors associated with the schools may heavily influence teacher instructional practice.

I was planning on regressing my EFA factors onto a number of school factors (between level) and teacher-specific factors (within level) to try to identify influencers of teacher practice.

Given your response above, I am wondering if something like this has been done. If so, might you be aware of examples to assist with my thinking? If not, would such an analysis be ill-advised at this point in time?

Again, many thanks.
 Linda K. Muthen posted on Thursday, April 22, 2010 - 8:43 am
You would need to move to a CFA framework to include covariates in the multilevel model. Covariates cannot be included in an EFA TWOLEVEL model.
 Stacey Farber posted on Saturday, April 24, 2010 - 11:22 am
Again, thank you, Linda.

Could you please tell me which fit statistics have been studied and deemed appropriate for a two-level, EFA with categorical items? If there are values (i.e., cutoffs) that suggest good fit, that would be great to know as well.

If there is documentation of this, I would appreciate the citation.

Again, many thanks!
 Linda K. Muthen posted on Saturday, April 24, 2010 - 11:52 am
I know of no such study or citation.
 Utkun Ozdil posted on Monday, March 07, 2011 - 5:08 am

I tried to run a two-level EFA with categorical data where class is the CLUSTER variable using the following syntax:
TITLE: Two-level EFA
DATA: FILE IS multiefa.dat;
VARIABLE: NAMES ARE class ques1-ques30;
CATEGORICAL ARE ques1-ques30;
However, the runtime of the analysis is taking more than half an hour and it never comes to an end...Is it normal that it takes too long with MPlus 6.1? Should I be patient or should I worry that something is not on the way?
I used the default estimator,, maybe WLS or WLSM would be more appropriate?

 Linda K. Muthen posted on Monday, March 07, 2011 - 6:56 am
Please send the input, data, and your license number to
 Utkun Ozdil posted on Monday, March 07, 2011 - 8:09 am

At last I reached an output but in the end of of 1,5 hours. May I send the input and data though?

1. I analyzed all the models crossed within 6 factors and observed that the unrestricted within solutions by between level factors always have the best fit indices (CFI/TLI). How can we interpret this? In other words, what is the essence in the "unrestricted solution"? Should we also go through the factor structures?

2. While interpreting a two-level EFA should we analyze all the models crossed at both levels and choose the best one; or should we focus on a specific one?

 Bengt O. Muthen posted on Monday, March 07, 2011 - 6:20 pm
Please send the input, data, and your license number to

1. In your case that means that even 6 within factors does not fit.

2. EFA is exploratory, so you should explore all models that you think are reasonable. Note that you typically have far fewer factors on between than on within. I have never seen as many as 6 between factors, typically only a few are needed.
 luk bruyneel posted on Friday, April 12, 2013 - 7:04 am
Hi Linda and Bengt. I read above that covariates cannot be included in an EFA twolevel model. Is this still the case? If so, is there a specific reason for this?
 Linda K. Muthen posted on Friday, April 12, 2013 - 9:02 am
TYPE=TWOLEVEL EFA does not use the MODEL command so covariates cannot be included. ESEM is not available for TYPE=TWOLEVEL but is available for TYPE=COMPLEX.
 Bilge Sanli posted on Wednesday, April 30, 2014 - 3:38 pm
Drs. Muthen and Muthen,

I am quite new to two-level factor analysis and the Mplus. Id like to adopt a two-level EFA approach in my research on different dimensions of conceptions of nationhood, and their contextual and individual predictors. My cluster variable would be countries, and my variables are all at the ordinal level of measurement. Id like to treat the factors I compute as dependent variables in a subsequent regression analysis wherein I regress them onto independent variables at both individual and contextual levels. My main question is: how can we incorporate within and between level factors as dependent variables in a follow-up multiple multilevel regression analysis? I read above that a two-level CFA is recommended if covariates are involved. However my research is exploratory in nature, and I am not testing a hypothesized factor structure. I am confused, therefore, as to how a CFA framework would fit my research purposes. Id appreciate if you could shed more light on how to use factors obtained through two-level factor analysis in further regression analysis. Thank you very much.
 Bengt O. Muthen posted on Wednesday, April 30, 2014 - 7:17 pm
If it is an exploratory analysis, you may want to follow the 2-level EFA with getting the 2-level factor scores and then in a second analysis use them as DVs in 2-level SEM.
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