Q-mode factor analysis of geochemical and petrologic data matrices with constant row-sums

Abstract

Matrices of data representing all the major constituents in a suite of rock samples tend to have constant row-sums, a property that has caused considerable difficulty in attempts to interpret rock genesis from the correlations among matrix columns. Q-mode factor analysis may be used to interpret rock genesis from relations among matrix rows, and the constant row-sum is a definite asset. The constant can be used to compute sealers, which, in turn, can be used to adjust the factor loadings and scores to conform with the original data. Therefore, principal components and varimax models and a variety of oblique models may be derived that can be used to recompute estimates of the data in, for example, percent or parts per million. Any real or hypothetical composition may also be tested as a possible end-member in a petrologic mixing problem.