Parameter Estimation in Factor Analysis: Maximum Likelihood versus Principal Component

Factor analysis (FA) is a multivariate statistical technique to uncover latent constructs of observed variables while principal component analysis (PCA) is a technique to reduce the number of variables in large data sets. While both are different techniques with different objectives, they often produced the same factor solution. In this paper, the multivariate statistical theory behind PCA and FA is discussed to highlight their differences and similarities. In particular, the factor extraction technique of PCA is compared to the extraction procedures of principal axis factoring (PAF) and maximum likelihood estimation (MLE) in factor analysis. Results from applying the procedures on a published data set will be discussed and the appropriate use of each will be suggested.