Use of an artificial model of monitoring data to aid interpretation of principal component analysis

An artificial data matrix of element concentrations at sampling locations was created which included six simulated gradients of correlated variables (Ca+Mg, Ni+V, Pb+Cu+Zn, Cd, Fe and K), representing a simplified model of a National survey. The data matrix model was used to explore the efficiency with which Principal Components Analysis (PCA), without and with Varimax rotation, could derive the imposed gradients. The dependence of PCA on outliers was decreased by log-transformation of data. The Components derived from non-rotated PCA were confounded by bipolar clusters and oblique gradients, both resulting in superimposition of two independent gradients on one Component. Therefore, erroneous interpretation of results could result from assessment of variable loadings on Components, without assessment of coupled independent gradients. Varimax rotation greatly improved the results, by rotation of too few Components led to the same problems, and rotation of too many Components led to fragmentation of correlated variables onto single-element Components. The best configuration matching the original model could be selected after investigation of element concentrations superimposed on sample ordinations.