A generalized principal components model in petrology

Principal components analysis of elemental distributions among minerals elucidate chemical, thermal, and equilibrium effects. Previous approaches in applying this multivariate statistical method to petrologic data are united into a single model, so-called three-mode principal components analysis. The major advantage of the model lies in the separate analysis of each of the three modes: element, mineral, and sample. The three sets of principal components are related through a “core matrix”. The model accommodates the ordination of pair-wise combination of the modes, such as samples and minerals in visualization of multidimensional tie-lines. Because of its generality, the model permits great flexibility in the study of petrologic data.