Hello, I did an exploratory factor analysis in SPSS which suggested 4 clear factors. One factor in particular has four items with factor loadings all greater than .79. However, when I plug these items in to CFA in MPlus, only two items have high factor loadings (>0.83) and the two others are low (<0.36). Can you explain this? Thanks.
The 4-factor SPSS analysis determined the loadings for the 4 items by not only the correlations among the 4 items but also by their correlations with other items. If you redo the SPSS analysis with only those 4 items you probably get more similar results to the CFA. Assuming that you are using estimators that are the same or similar.
If you treat the items as continuous (the Mplus default) and use the ML estimator in both programs, the loadings are going to be exactly the same since CFA with 1 factor is the same as EFA with 1 factor. So something else is going on that I can't see. Note also that when you do the CFA and want the results in the same metric as the EFA, fix the factor variance at 1 and free the first factor loading.
A 1-factor CFA with some large and some small loadings does not invalidate the hypothesis of a single factor. That should instead be determined by the chi-square test of model fit.
I don't know if SPSS can handle categorical items. You can't compare results from one program treating the items as continuous and therefore using a linear factor model with results from another program treating the items as categorical and therefore using a non-linear (probit/logit) factor model.
You will be fine using WLSMV in Mplus treating the items as categorical.
I've got a dataset with 23 items (rated 1-7 scale). I've run an EFA in SPSS (prinicipal axis factoring, varimax rotation, 2 factors extracted) and found that 2 factors accounted for well over half the variance in the dataset and the loadings of the items make perfect theoretical sense.
When I got to test the model in CFA (2 factor model), the fit indices (CMIN, RMSEA, CFI, NFI, etc.) are all really bad. I am wondering if you might be able to help me understand what might be happening (or point me to an article that could)?
Your SPSS EFA does not give you standard errors of the rotated factor loadings and therefore does not give you information about significant cross-loadings which when fixed at zero in CFA causes misfit. Mplus EFA will give you this information.
You also don't have to impose the strong structure of the CFA - for more on that I suggest that you read about the new idea of "ESEM":
Marsh, H.W., Muthén, B., Asparouhov, A., Lüdtke, O., Robitzsch, A., Morin, A.J.S., & Trautwein, U. (2009). Exploratory Structural Equation Modeling, Integrating CFA and EFA: Application to Students’ Evaluations of University Teaching. Forthcoming in Structural Equation Modeling.
and also the Asparouhov-Muthen article both on the Mplus web site at
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Daniel Lee posted on Tuesday, March 24, 2015 - 12:21 pm
Hi Dr. Muthen,
I have a very short 4-item scale and would like to run an EFA and CFA for 1 and 2 factor solution.
I know that a 2 factor solution is a saturated model (that's the limit). I tried running the CFA of the 2-factor solution and it worked just fine. However, when running a two-factor solution with EFA, mplus indicated that too many factors were requested. Can you briefly tell me why a CFA can be conducted, but not an EFA for the 2-factor solution of a 4-item scale?
The are many more parameters in an EFA than a CFA. See the Topic 1 course handout and video on the website where this is discussed. Slide 104 gives the formula for the number of factors that can be extracted for a given number of variables.
Daniel Lee posted on Wednesday, March 25, 2015 - 7:36 am