I have data on about 25 subjects and 30 variables with about 20 missing values. The data is missing at random. What will be the best approach to perform factor analysis. How is factor analysis versus principal component analysis in such cases where some data is missing? Thanks in advance.
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$\begingroup$ You may not do FA on such a small sample, even without missing data. Especially that you have less subjects than variables (just cannot). To factor-analyze 30 variables you should have about 150 subjects if you expect results to be non-garbage. $\endgroup$– ttnphnsCommented Apr 4, 2015 at 8:17
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$\begingroup$ Thanks for this advice. So it may be better to simply do non-parameteric tests. Is any multivariate evaluation possible at all? The variables are mostly numeric (continuous). $\endgroup$– rnsoCommented Apr 4, 2015 at 8:21
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$\begingroup$ I don't think you can know that the data are missing at random. To know that, you have to know the values of the missing data, and if you know that, you don't have missing data. Perhaps they're assumed to be missing at random? $\endgroup$– Jeremy MilesCommented Apr 4, 2015 at 16:23
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$\begingroup$ Yes, of course I am assuming that the data is missing due to random lack of its recording in original documents. $\endgroup$– rnsoCommented Apr 4, 2015 at 16:34
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1 Answer
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In general, I agree with @ttnphns' comment in that you have to have a certain minimal number of cases per variable, with other metrics include loadings and number of variables per factor. This is addressed in the literature (i.e., MacCallum, Widaman, Zhang & Hong, 1999).
Having said that, this heuristic is not set in stone - people have different opinions on the topic and I ran across research that discusses conditions, when it is possible to obtain good results from factor analysis (FA) of small sample data sets ($N < 50$) and/or sample data sets with other questionable characteristics. In particular, aspects of applying FA to small sample data sets are discussed by Costello and Osborne (2005), de Winter, Dodou and Wieringa (2009) as well as Zhao (2009).
References
Costello, A. B., & Osborne, J. W. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research & Evaluation, 10(7). Retrieved from http://pareonline.net/pdf/v10n7.pdf
de Winter, J. C. F., Dodou, D., & Wieringa, P. A. (2009). Exploratory factor analysis with small sample sizes. Multivariate Behavioral Research, 44, 147–181. doi:10.1080/00273170902794206 Retrieved from http://www.3me.tudelft.nl/fileadmin/Faculteit/3mE/Over_de_faculteit/Afdelingen/BioMechanical_Engineering/Organisatie/Medewerkers/Winter/doc/exploratory_factor_analysis_with_small_sample_sizes.pdf
MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor analysis. Psychological Methods, 4(1), 84-99. Retrieved from http://people.musc.edu/~elg26/teaching/psstats1.2006/maccallumetal.pdf
Zhao, N. (2009). The minimum sample size in factor analysis. [Website] Retrieved from https://www.encorewiki.org/display/~nzhao/The+Minimum+Sample+Size+in+Factor+Analysis
answered Apr 4, 2015 at 9:06
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$\begingroup$ Thanks for your answer and references. I am reading them now. $\endgroup$– rnsoCommented Apr 4, 2015 at 10:03
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$\begingroup$ @rnso: You are welcome. Hope they will be helpful. $\endgroup$ Commented Apr 4, 2015 at 10:21