I am running a factor analysis and have a couple of questions.
I have 10 variables, all of them come from a survey, with each answer is in the scale of 1 to 7. I have calculated a correlation matrix between the 10 variables, and looked for correlations of 0.5 or higher. These made me notice of 4 groups of correlated variables, two groups of 3 variables and two groups of 2 variables.
Then I ran the factor analysis. According to the scree plot, I should take 4 factors. According to the eigenvalues, the 4th eigenvalue is 1.006, so it's slightly on the line, it is larger than 1, but not by much…In addition, after 4 factor the cumulative variance is 82%. After 3 it is only 72%.
My question is, should I choose 4 factors or 3 ? Is it OK to have a factor with only two variables that construct it ? I know that a single variable factor is something we don't want, just like we don't want a sample-specific factors. But what is the rule regarding two variables in a factor ? I looked on the net, and found one document saying the minimum is 3. I didn't see any mathematical explanation and I am not convinced. What can you recommend me ?
Thank you in advance !
Best Answer
With factor analysis, we have a lot of guidelines and no strict rules. Eigenvalues over 1, scree plot, number of variables to a factor, amount of variance explained and others are all guidelines.
My suggestion is that you look at the two solutions and see which one makes more sense. Are the three factors useful constructs? When you go from 3 to 4, do you more-or-less keep the original 3 and add a 4th, or does the whole solution change? If the former, then is the 4th factor useful? If the latter, then is the new solution more sensible or less sensible?