Factor extraction aims at simplifying the data complexity by finding the set of latent factors that are associated with the observed variables. Researchers choose specific factor extraction methods based on the theoretical understanding of their study. The most common extraction methods are principal component analysis (PCA) and common factor analysis. These extraction methods can easily be distinguished based on their variance partitioning.
- Principal Component Analysis (PCA)
PCA is a linear transformation method that identifies and explains the maximum variance present in the data. PCA works on the assumption that the variance extracted does not have unique variances or measurement error.
- Common Factor Analysis
Common factor analysis is also a data reduction method that assumes that the total variance extracted by a factor can be categorized as common variance and unique variance. The common variance accounts for the variance shared among a set of observed variables measuring the underlying latent factor, whereas the unique variance represents the measurement error associated with each observed variable. The following are examples of extraction methods that uses the common factor analysis: principal axis factoring (PAF), maximum likelihood (ML), generalized least square (GLS), unweighted least square (ULS). Note that each of these extraction methods has their pros and cons.