Necessary Number of Factors in Factor Analysis

Hi everyone I am trying to determine the number of factors I need to explain a certain percentage of variance in my data. I am using the "factoran"-function and cannot figure out which of the parameters returned can be used to do that. The doc of the principal component function "princomp" contains a nice demonstration using the latent variable returned:

cumsum(latent)./sum(latent)
ans =
      0.86597
      0.97886
       0.9996
            1

Is there any way to do this for factoran() as well to determine the number of factors necessary? Thanks a lot

Answer 1

[Peter Perkins]

PCA and Factor Analysis (at least the form of FA that factoran performs, known as common factor analysis) are completely different models. In effect, FA fits the off diagonal elements of a cov matrix, and then assigns any left over variance in the data to the specific variances. So in that sense, it explains ALL of the variance. Perhaps you want to compare those specific variances to the raw variances.

I'm not sure what the standard practice is for the question you're asking. You should consult a text book on factor analysis, but beware that what many people refer to as FA is really a form of PCA, usually known as Principal Factor Analysis.

As far as how many factors, this is somewhat of an art. But factoran does include an output for testing the hypothesis of M factors.