I did EFA on a set of Likert Scale data.
I got 3 factors based on parallel analysis.
Factor 1 - 15 items
Factor 2 - 5 items
Factor 3 - 3 items
Didi CFA and got good fit.
Is it possible to reduce the number of factors to say 4 or 5?
I tried reducing it, did cronbach's alpha ..before was like 0.93, after is 0.92-ish
BTW, factor loadings of all 14 of the 15 items are also quite high - 0.69 to 0.92
I'm trying to reduce the number because in SEM, the 15 items is a lot of freeparameters resulting in identification issues.
If you have suggestions, let me know. Thanks!
It is actually better to have more, rather than fewer, items in CFA/SEM, as long as the items are "good" indicators of their factors. Identification is actually improved with more items, and so are other things. See
Marsh, H. W., Hau, K. T., Balla, J. R., & Grayson, D. (1998). Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research, 33(2), 181-220.
Although you have more parameters with more items, you also have more pieces of information (covariances) to estimate parameters from and hence more degrees of freedom.
Thanks Christian.
However, that was my initial understanding also. But Stata oftem time give a message after fitting a model ....
"you have X number of parameters more than your data can support"..
Plus I am probably running into sample size issues (only 266) and this translates to around max of 26 free parameters...adding more items will be a double-edged in my case...
I have a 2nd order latent factor model and I fitted it just fine. But I would like to add more observed variables (other than the Likert items) and I can only add two more maximum before running problems.
If you really have too many items given the sample size, you might consider item parceling strategies to retain all items (but combine them into fewer latent variable indicators/sum scores). See:
Article To Parcel or Not to Parcel: Exploring the Question, Weighing...
Little, T. D., Cunningham, W. A., Shahar, G., & Widaman, K. F. (2002). To parcel or not to parcel: Exploring the question, weighing the merits. Structural Equation Modeling, 9(2), 151-173.
Starting on p. 165, the authors describe different parceling techniques. The paper also contains a thorough discussion of the pros and cons of the item parceling approach in general.
See also:
Little, T. D., Rhemtulla, M., Gibson, K., & Schoemann, A. M. (2013). Why the items versus parcels controversy needn’t be one. Psychological Methods, 18(3), 285-300.
Little, T. D., Rioux, C., Odejimi, O. A., & Stickley, Z. L. (2022). Parceling in structural equation modeling: A comprehensive introduction for developmental scientists. Elements in Research Methods for Developmental Science.
Thanks for your suggestion Christian! I will try this and hope to have some good results. Trying SEM for the first time is both difficult and fulfilling. I'm happy there are online communities willing to help out.
Update:
I read of the topic of item parceling and IMO it is a good way forward for me. The I get the basic idea but I would like to ask how specifically it is implemented?
Literature says "sum or avrerage of factor loading(?) are used to represent a parcel"...--> How is this done in real application?
Is my understanding below correct?
1. Group the items into parcels (I read several ways to to this)
2. Run the necessary analysis (e.g. CFA) for each parcel just to make sure it has good fit
After this is where I am lost
3. Sum or average sa loading of items in eacg parcel. Use it at observed variable for the latent construct
(Is predict not involved?)
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