Journal of the International Association for Mathematical Geology
, Volume 12, Issue 6, pp 523538
First online:
Scaling variables and interpretation of eigenvalues in principal component analysis of geologic data
 A. T. MieschAffiliated withU.S. Geological Survey
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The dominant feature distinguishing one method of principal components analysis from another is the manner in which the original data are transformed prior to the other computations. The only other distinguishing feature of any importance is whether the eigenvectors of the inner productmoment of the transformed data matrix are taken directly as the Qmode scores or scaled by the square roots of their associated eigenvalues and called the Rmode loadings. If the eigenvectors are extracted from the productmoment correlation matrix, the variables, in effect, were transformed by column standardization (zero means and unit variances), and the sum of the plargest eigenvalues divided by the sum of all the eigenvalues indicates the degree to which a model containing pcomponents will account for the total variance in the original data. However, if the data were transformed in any manner other than column standardization, the eigenvalues cannot be used in this manner, but can only be used to determine the degree to which the model will account for the transformed data. Regardless of the type of principal components analysis that is performed—even whether it is Ror Qmode—the goodnessoffit of the model to the original data is given better by the eigenvalues of the correlation matrix than by those of the matrix that was actually factored.
Key words
Rmode andQmode analysis scaling variables correlation Title
 Scaling variables and interpretation of eigenvalues in principal component analysis of geologic data
 Journal

Journal of the International Association for Mathematical Geology
Volume 12, Issue 6 , pp 523538
 Cover Date
 198012
 DOI
 10.1007/BF01034742
 Print ISSN
 00205958
 Online ISSN
 15738868
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Rmode andQmode analysis
 scaling variables
 correlation
 Industry Sectors
 Authors

 A. T. Miesch ^{(1)}
 Author Affiliations

 1. U.S. Geological Survey, 80225, Denver, CO, USA