I am performing Factor analysis on a dataset with 16 variables and 22 observations. I realize the sample size is small but I am getting high factor loadings. The problem is that the correlation among variables under one factor is very high with correlation coefficients of more than 0.7. Also some of the variables under one factor are highly correlated with variables under another factor. I don't want to drop too many variables because they are important from the study aspect. I read that the correlation pattern among variables in case of small sample size is not reliable. If that is the case then can I go with the further analysis with the existing high correlation. Would there be a problem of multicollinearity?
Hello Sujata,
there is no multicolinearity involved--to the contrary: You would expect high correlations. Multicolinearity is an issue when you have high correlations amoung predictors in a regression model or SEM.
That having said, you really should not do anything with N=22 respondents...Collect more data.
HTH
--Holger
@Sujata Agreeing with @Holger I also endorse that multicollinearity doesn't seen to be an issue however, it would be too early to reach any conclusion given that sample is too low. Considering the case that loadings are appropriate and under right factors, the issue of high correlation among factors is also supposed to be sorted out with a larger data sample. Wishing you best for your research.
@sujata what about the communalities. Try to excluded variables with low communality.
1. I think the multicollinearity problem being referred to here is not high correlations among items, but a weighted average of some items being exactly another item. This is more common with small samples.
2. I presume you have beliefs about how some items are influenced by the same latent variables.
3. The sample is too small. Consider even a two-factor model and count how many loadings are estimated!
4. How did you decide on this sample size? What are the research questions that you have that lead you to doing an EFA?
Holger Steinmetz, Imran Anwar and Daniel Wright thank you for the insight in this topic. I am very grateful for all the responses.
I am working on the Punjab state of India which has only 22 districts and hence n is just 22. I am trying to develop an Index or scale for the districts of Punjab using factor analysis.
Abdulmuhsin S. Shihab since factor loadings are more than 0.5 that's why I didn't drop any variable but I will try doing it once again by dropping the variables with least communalities.
I have found another way of doing the analysis. Lets see whether it works or not.
Sujata Sujata
does that mean you have one participant from each of the 22 districts or do you have data from 22 districts with multiple participants from each one? If your N really is just 22 that is way too small to draw any meaningful conclusions from it.
Edit: Nevermind. I just read your question properly. Your sample size is too small.
Since your sample size is small (N = 22), I would recommend you go through the solutions put forward by van de Schoot and Miočević (2020). Here is the full citation.
van de Schoot, R., & Miočević, M. (Eds.). (2020). Small sample size solutions: A guide for applied researchers and practitioners. Routledge. https://www.routledge.com/Small-Sample-Size-Solutions-A-Guide-for-Applied-Researchers-and-Practitioners/Schoot-Miocevic/p/book/9780367222222#
Good luck,
Hello Sujata,
If you're using district-level data, and you have all of the relevant districts, then the correlations you have in hand are presumably the population parameters. So, at that level, sample size doesn't matter.
What does matter is, as Daniel Wright 's response indicates, what is the specific motivation for undertaking an EFA at this point? If the goal is to create some composite score which has utility for some purpose, then factoring, OLS regression, or some data mining method (such as lasso, among others) may offer viable paths for the generation of such a score. Of course, the specific purpose, and any relevant target/criterion variable associated with it would have to be declared and evaluated as well.
Perhaps a good place to start would be to look at correlations of the 16 variables with the target/criterion variable (as well as amongst themselves).
Apologies if I've misunderstood your query.
Good luck with your work.
Dead David Morse
may I trouble you for an explanation of your first statement? If there was indeed one respondent from each district, the total number would still only be N = 22. Why would sample size not matter in this instance? I am always eager to learn so thank you in advance for your reply.
Best
Marcel
Hello Marcel,
Sujata indicated that the variables were district-level, not person level. For example, if you quantify economic status as the median household income for a district, then presumably that variable is, for all practical purposes, the parameter for that district. Yes, even census data are often incomplete, but are as complete as one can practically attain in most instances.
If the variables were person/subject level, e.g., annual income, then I agree with you that one case per district would be an exceedingly poor sampling plan.
Finally, rumors of my death are greatly exaggerated, lol. (Re: your greeting)
Good luck with your work.
Hello David Morse
I can only apologise for the typo (what is worse: "Dead" or "Deer"?). This was most likely due to a severe lack of caffeine in the morning. Thank you for beeing a good sport and, more importantly, your explanation.
Best
Marcel
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