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?
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.
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?
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.
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; VARIANCES = NOCHECK; VARIABLE: NAMES ARE class ques1-ques30; USEVARIABLES ARE class ques1- ques30; CATEGORICAL ARE ques1-ques30; CLUSTER IS class; ANALYSIS: TYPE = TWOLEVEL EFA 1 6 UW 1 6 UB; 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?
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?
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.