Factoring Analysis and Principle Components

Factor analysis and principal component analysis (PCA) are mathematically related: they both rely on calculating eigenvectors (on a correlation matrix or on a covariance matrix of normalized data), both are data reduction techniques that help to reduced the dimensionality of the data and outputs will look very much the same. Despite similarities, factor analysis and PCA solve different problems. PCA is a linear combination of variables (so that the principal components are orthogonal); factor analysis is a measurement model of a latent variable. PCA is a data reduction technique that calculates new variables from the set of the measured variables. A factor analysis also will lead to data reduction, but it answers a fundamentally different question. Factor analysis is a model that tries to identify a “latent variable.”.