Q-mode factor analysis of compositional data

An extended form of the method of Q-mode factor analysis may be used if the rows of the data matrix sum to a constant. The constant row-sum provides a means for scaling the factor model to conform to the units of the original data in such forms as proportions, percentages, or parts per million. The scale factors for an m-factor model are used to derive composition scores and loadings, which lead to the same reproduced data regardless of the choice of reference axes (end-members). Factor-variance diagrams may be constructed to show the proportion of the variance that will be accounted for in each compositional variable by models containing various numbers of end-members. The method may be used to develop a petrologic mixing model by searching for end-members that are geologically plausible. ?? 1976.