What should be the sample size for explanatory and confirmatory factor analysis and for item response theory?
opinions vary regarding a good variable-to-sample size ratio: the 3–6 range (Cattell, 1978), a minimum of 5 (Gorsuch, 1983), at least 10 (Nunnally, 1978), and 20 (Hair, Anderson, Tatham, & Black, 1995; Hogarty, Hines, Kromrey, Ferron, & Mumford, 2005).
Cattell, R. B. (1978). The scientific use of factor analysis in behavioral and life sciences. New York: Plenum.
Gorsuch, R. L. (1983). Factor analysis (2nd ed.). Hillsdale,NJ: Erlbaum.
Nunnally, J. C. (1978). Psychometric theory (2nd Ed.). New York: McGraw-Hill.
Hair, J. F. J., Anderson, R. E., Tatham, R. L., & Black,W. C. (1995). Multivariate data analysis (4th ed.). Saddle River, NJ: Prentice Hall.
Hogarty, K. Y., Hines, C. V., Kromrey, J. D., Ferron, J. M., & Mumford K. R. (2005). The quality of factor solutions in exploratory factor analysis: The influence of sample size, communality, and overdetermination. Educational and Psychological Measurement, 65, 202-226.
I recommend to use at least 10 or larger ratio.
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