I am working on a dataset of 41 items on Likert scale supposed to represent three latent variables (an independent(28), mediating(5), and dependent one(8)). I collected 450 responses and performed an EFA on it as a first step to conduct CFA and SEM. The results of the EFA revealed 7 factors having eigenvalues greater than one, with the items of the independent as well as the mediating variables are loading on the same factor. In addition, 3 items of the dependent variable loaded on the second factor and three other items loaded on a third factor. How could I deal with this situation, given that I will not be able to combine the independent and the mediating variables together in a single variable, because the three variables are already placed in the research title. Thank you.
Hello Tarek,
If there is no extant research on this specific set of 41 variables to indicate structure, then, based on your EFA, it sounds as if you'll need to either re-specify your research questions to reflect a very different structure than proposed, or be prepared to modify the variable set so as to conform to a three-factor solution which reliably separates IV, mediator, and DV.
However, before abandoning all hope for the current data set, please note a couple of points:
1. In general, the eigenvalue > 1 criterion is not the best method for an initial guess at the number of latent variables/factors to extract. Parallel analysis tends to work better, judging from simulation studies published.
2. You didn't indicate how you treated the data (ordinal strength scores, not interval strength scores), the method of extraction used, the rotation scheme used, or criterion for declaring variable-factor affiliation. These choices can make a difference.
3. It is possible that a CFA, with the proposed 3-factor solution, may be a better starting point for the analysis., and could show adequate model-data fit.
4. Finally, cross-loadings do not necessarily flag variables as flawed, especially when correlated factors exist in the structure. Not all real-world data fit Thurstone's "simple structure" ideal, in which a variable has a near-perfect loading on one factor, and zero or near-zero loadings on all others.
Good luck with your work.
Thanks Dr. Morse. That was really helpful. I tried performing maximum likelihood instead of principal component and according to eigenvalues rule, the items of the M variable is now loading on another factor different from that of the IV. But I have another question: why the items of some factors showed negative factor loadings though they are in the same direction of the items the other factors? Thank you Dr.
Hello again Tarek,
Then, it sounds as if the item/variable set needs more work. Minimally, some of the variables likely need to be discarded or modified and more data collected.
As for why some items have apparently reversed estimated loadings compared to "peer" items, you might find it helpful to do de-briefing sessions with respondents, to find out how they were interpreting the respective items while completing the questionnaire. This assumes you've done all the obvious checks and adjustments for item polarity/valence.
Good luck with your work.
Thanks Dr. Morse. I performed CFA using Amos and deleted 12 items out of the 41 original ones and covariate the errors of other items, and have reached a good model fit. The number of items now is 29 with 450 responses. Do you think the number of deleted items is more than what is acceptable? And do I still need to collect more responses?
Hello Tarek,
Since you've modified the model, based on your data set, the concern is that of having arrived at an overfitted model. The ideal approach would be to collect additional data to assure that the modified model continues to perform satisfactorily in accounting for the observed relationships in a validation sample.
However, one can find published instances in which the validation step does not appear.
Good luck with your work.
Thanks Dr.Morse. your answers added a lot to my understanding of CFA and SEM
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