You mention sample size but not number of variables, I assume there is multiple. I also assume that the same variables were captured for all samples.

Factor analysis works without any a priori knowledge. If variables are uncorrelated with another they will not appear in the same factor but will be described in a different factor. So you do not need to address this in advance. A variable totally uncorrelated with any other would be the sole contributor to the relevant factor.

It does assume some inherent correlation structure so if variables have been designed to be largely uncorrelated at study design phase then it may not be relevant tool for analysis (although it could be used to check if the condition was met). If however the variables are designed that they capture overlapping information then factor analysis is a sensible choice.

Hi Asheek,

The usual recommendation is a loading of .40.  James makes some good points as well.  Here is a ResearchGate thread on this subject:

https://www.researchgate.net/post/What_is_the_cut_off_for_factor_loading_in_factor_analysis_using_SPSS

Thanks...Nick

Asheek,

As Renwick Beattie points out, there does need to be some relationship among your variables in order to build a case for common, underlying factors.  In general, you could say that higher is better, but that's pretty vague.  Nicholas Beutell's suggestion refers to variable-factor correlations, which would be a subsequent concern--that of which individual variables are salient for identifying the factor, once the factors have been extracted.

Here's a  couple of examples for sake of illustration (in each case, I'm presuming a single underlying factor): Each uses 5 hypothetical variables (v1-v5).

(a) Each variable correlates .20 with the others: A one-factor solution will emerge with all variable-factor loadings = sqrt(.20) = .447; the solution will perfectly reproduce the observed correlations; and the Kaiser-Meyer-Olkin measure of sampling adequacy (MSA)will be .719 ("middling", according to Kaiser).

(b) Each variable correlates .30 with others: Again, a one-factor solution emerges, with all variables having loadings = sqrt(.30) = .548.  MSA = .783.  Factor loadings perfectly reproduce observed correlations.

(c) Each variable correlates .40 with others.  One-factor solution; all variable-factor loadings = ..632 (square root of .40).  MSA = .829 ("meritoriious").

(d) Each variable correlates .50 with others.  One-factor solution; all loadings = .707 (square root of .50).  MSA = .862.  Loadings again perfectly reproduce observed correlations.

While an artificial set of examples, this should show that even low inter-variable correlations can be satisfactory to identify an existing factor structure.

Good luck with your work!

i would recommend the answer of David Morse.

Thank you all, very specially David Morse. It was really helpful.

Best,

Asheek

thanks

i was actually stuck at this point.

The problem is when the correlation is high, let us say 0.98. In this case, the factor loading becomes low. Any suggestions to solve this problem?