Since there is no three-level EFA option, can you recommend an analytical approach that I could use with MPlus 7? I looked at the ICC's for level 2 and level 3 in my data set, and they are usually between .15 - .21 for all the outcomes. So, it indicates I should really have a three-level EFA.
So, would you recommend doing a two-level EFA (ignoring either the second level or the third level)? Then, should I do a three-level CFA based on the results for the two-level EFA?
Alternatively, I could move directly to a three-level CFA and try several different models. Thanks for any help!
So, I have 14 consecutive days of data nested within 98 individuals nested within 49 dyads. Based on the manual, I should use a two-level model.
By using Type = Complex Twolevel, am I then accounting for both the individual and dyad level clustering in my EFA? If not, what is that command doing?
My ultimate goal is to find the factor structure for several daily-level variables that takes into account the nested nature of the data. So, can the output of a multilevel EFA potentially produce a different factor structure at each level (i.e. time, individual, and dyad)?
In addition, I read thru the user's guide and examples for CH 4 & 9, but I am still not sure if I am coding this multilevel EFA correctly. First, am I coding the three levels correctly (or two levels in your program)? Second, did I choose the correct EFA options to account for these three levels? See below for code.
TITLE: EFA with continuous and count factor indicators
I would treat this as a multivariate rather than a multilevel model. This means the data would be in wide format rather than long format. The non-independence of observations is then handled by multivariate analysis. The modeling is more flexible allowing more parameters for each dyad member.
I have a follow-up question about this. We are evaluating a measure of therapist feelings after psychotherapy sessions, and the level 1 data consists of repeated measurements over sessions with some patients having only a few sessions while some have over one hundred. Level 2 consists of 200 patients, and level 3 is about 100 therapists. I thought the idea of using a two level EFA while controlling for therapist differences using TYPE=COMPLEX TWOLEVEL that Bengt mentioned would be perfect since we will use the measure on a patient level in later analyses (and thus we are not interested in the factor solution for the therapist level). However, I wonder if there is a problem that there are so many therapists who see only one patient (the mean number of patients per therapist is about 1.8)?
Also, I wonder how to interpret the level 1 factor solution? Level 2 is reasonably clear, it should be the way different therapist feelings cluster together across patients, after adjusting for therapist differences. But I'm not sure about how to interpret the factor solution for the repeated measurements? Does it have something to do with factor stability over time, after adjusting for differences between patients?
A quick follow-up question: Is it possible to estimate an EFA with Type = Complex Twolevel using categorical dependent variables (i.e. ordinal level with a scale from 0-4)? It doesn't seem to work when I try WLSMV?
I'm thinking of alternatives where I can use WLSMV. I thought I'd use only one session (thereby skipping the repeated measures level) and estimate a two level model with the therapist level (level two) estimated as an unstructured covariance matrix (since I don't think the data is enough to estimate a separate factor model for level 2, since many therapists only see one patient). But then I realized that model fit criteria probably look too good when I have an unstructured level 2 model? Especially the CFI, but I guess the Chi-square test will also look too good?
I also thought of using a one-level factor model with level two as Complex. Perhaps this is best, but since I chose only one session I got a warning that standard errors may be biased if I used the Useobservations command. When I instead used the Subpopulation command (as recommended in this warning), I got an error that in one of the categories the response was zero for all observations (and the model was not estimated).
Do you have any recommendations in this situation? Thank you very much for your help!
Thinking a bit further, I may be able to specify the above into two questions:
1. Am I right that when estimating a saturated between-level model in addition to the within-part of the model (the one I am interested in), the inclusion of a part of the model with perfect fit between model-implied and observed covariance matrices will bias the Chi-square test of overall model fit toward non-significance compared to if the within part of the model had been somehow tested "on its own"? If not, this may be our preferred approach.
2. Does it matter that the standard errors may be biased when estimating a model using Type = Complex for a subpopulation using the "Useobservations" command, if we are not really interested in the significance of the parameters but in their values (i.e. size of factor loadings) only?
I can't comment on all the issues since some touch on more general analysis strategies better suited for a general discussion list like Multilevelnet, but here are a couple of quick Mplus-related comments.
Note that 2-level analysis can be done using WLSMV.
Don't worry about using the Subpopulation command - it would seldom change results in a noticeable way.
It is fine to use a saturated between-level model but it also uses more parameters than are typically needed - often a 1-factor model is sufficient on between.
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