A Note on Unwanted Variance in Exploratory Factor Models

Abstract

One strategy of exploratory factor analysis is to decide on the number of factors to extract by means of the eigenvalues of an initial principal component analysis. The present article proves that there is a non zero covariance of the factors with the components rejected when the number of factors to extract is determined by means of principal components analysis. Thus, some of the variance declared as irrelevant or unwanted in an initial principal component analysis is again part of the final factor model.

Keywords:

• Exploratory factor analysis
• Factor analysis
• Principal component analysis

Mathematics Subject Classification:

• Primary 62H25
• Secondary 91G70