# How to conduct confirmatory factor analysis with small sample size?

I plan to conduct a confirmatory factor analysis, wherein there are 12 observed variables and 3 latent variables. My sample size is 30. However, I read that to conduct a factor analysis, the sample size needs to be big.

Is there a way to conduct confirmatory factor analysis with a small sample size? I heard about regularized exploratory factor analysis is used for small sample sizes. Is there an equivalent of it with confirmatory factor analysis?

Also, what softwares can I use to run these? I currently have SPSS, AMOS, and LISREL.

With 12 observed variables and 3 latent variables, you are going to struggle with CFA if your sample size is only 30, as you will most likely have insufficient power.

There are many rules of thumb for determining adequate samples size, $N$, in CFA. For $p$ variables and $q$ model parameters, some of these are:

• $N \geq 200$
• $N/p \geq 10$
• $N/q \geq 5$

Another approach would be to determine statistical power by simulation.

Myers, N.D., Ahn, S. and Jin, Y., 2011. Sample size and power estimates for a confirmatory factor analytic model in exercise and sport: A Monte Carlo approach. Research Quarterly for Exercise and Sport, 82(3), pp.412-423.

https://doi.org/10.1080/02701367.2011.10599773

Wolf, E.J., Harrington, K.M., Clark, S.L. and Miller, M.W., 2013. Sample size requirements for structural equation models: An evaluation of power, bias, and solution propriety. Educational and psychological measurement, 73(6), pp.913-934.

https://doi.org/10.1177/0013164413495237