Summary: Airoldi, J.-P. & Flury, B. (1988). An application of common principal component analysis to
cranial morphometry of Microtus californicus and M. ochrogaster (Mammalia, Rodentia). J.
Zool., Lond. 216 (1) : 21-36
Principal component analysis (PCA) is a one-group method. Its purpose is to transform correlated
variables into uncorrelated ones and to find linear combinations accounting for a relatively large
amount of the total variability, thus reducing the number of original variables to a few
In the simultaneous analysis of different groups, similarities between the principal component
structures can often be modeled by the methods of common principal components (CPCs) or
partial CPCs. These methods assume that either all components or only some of them are
common to all groups, the discrepancies being due mainly to sampling error.
Previous authors have dealt with the k-group situation either by pooling the data of all groups or
by pooling the within-group variance-covariance matrices before performing a PCA. The latter
technique is known as multiple group principal component analysis or MGPCA (Thorpe, 1983).
We argue that CPC- or partial CPC-analysis is often more appropriate than these previous
A morphometrical example using males and females of Microtus californicus and M. ochrogaster
is presented, comparing PCA, CPC and partial CPC analyses. It is shown that the new methods
yield estimated components having smaller standard errors than when groupwise analyses are
performed. Formulas are given for estimating standard errors of the eigenvalues and