Orthomax Rotation of a PCA model

 

In factor analysis rotations of the loadings are very often applied, whereas in chemometrics these methods are very seldom used. This is in spite of the fact that it is possible to obtain better conditions for interpretation of PCA models on complex data.

We here provide an algorithm by which it is possible to apply rotations from the Orthomax family (quartimax and varimax) to a PCA-model.

 

Back-transformed loadings corresponding to the first twelve components derived from a PCA model based on 1H NMR spectra of 24 preparations of St. John’s wort. (A) and the corresponding rotated PCA model (loadings rotated) (B). The score plot of the sixth and seventh component of the rotated PCA model shows a tight clustering of preparations (C).

 
The above figure shows how rotations can make complex loadings much simpler, and thus easier to interpret. The example clearly illustrates how interpretation of the influence of a specific compound on the observed clustering is facilitated using the rotated loadings (B) as compared to the non-rotated loadings (A). Interpretation is aided since the influence of this compound on the observed clustering is partitioned over many components in the non-rotated PCA model, whereas in the rotated PCA model the influence is described mainly by the sixth and seventh components. A score plot of the sixth and seventh component of the rotated PCA model is shown in C. The plot shows, that the clustering of preparation 3 in the positive direction of the seventh component is due only to higher levels of the specific compound as compared with other preparations.

The example shows an example of rotation of loadings, but it is also possible to rotate the scores. This can be particularly useful when you want simpler conditions for understanding the influence of variables on the clustering of individual samples.

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Please refer to the below paper when using the function:

A Juul Lawaetz, B Schmidt, D Stærk, JW Jaroszewski, R Bro ,Application of rotated PCA models to facilitate interpretation of metabolite profiles: Commercial preparations of St. John's wort, Planta Medica, submitted (2008)