There is sometimes confusion between principal component analysis (PCA) and factor analysis (FA). Both methods have the aim of reducing the dimensionality of a vector of random variables. However, the most fundamental difference is that factor analysis explicitly specifies a model relating the observed variables to a smaller set of underlying unobservable factors. This assumed model may fit the data or not. In contrast PCA is just a data transformation method. Furthermore while Factor Analysis aims at explaining (covariances) or correlations, PCA concentrates on variances.