CPC - Common Principal Component Analysis Program

This page provides links for the Common Principal Component Analysis software written by Patrick Phillips (many of the analysis algorithms are translated from FORTRAN versions written by Bernhard Flury). Common Principal Components (CPC) is a data analysis technique created by Bernhard Flury that allows two or more matrices to be compared in a hierarchical fashion. The ideas are most completely presented in Flury (1988), Common Principal Components and Related Multivariate Methods (Wiley, New York). Further details are available in the readme file (HTML version).

Executables

DOS version
Windows 3.1 version
Windows95 or NT 32 bit version (runs in a console window).
Linux (Intel) version.
Macintosh version (68K)
Macintosh version (PowerPC/Intel)
NeXT Motorolla
DEC alpha -Digital UNIX
DEC alpha -Ultrix
Source files. It does not appear that I can distribute the source files right now because of copyright considerations (I make extensive use of Numerical Recipes routines). I will see what I can do about this, including using routines without a copyright. If you want to run the software on a particular platform without a current compiled version, get in contact with me to see what we can do.

Support Files

Readme file (text version) (HTML version) with a basic background of the technique and an explaination of the program.
Sample covariance matrices for North American Marten (Martes americana) leg bone measurements used in Flury (1988) [two matrices - four traits].
Sample output of the above example
Sample covariance matrices for vole (Microtus californicus) skull dimensions also used in Flury (1988) [four matrices - three traits].
Sample output of the above example

Other Software

It is possible to carry out these calculations in LISREL. See Dolan, C. 1996. Principal component analysis using LISREL 8. Struc. Eq. Model. 3:307-322.
You also might be interested in looking at DCPC: Common Principal Components for dependent random vectors, a SAS program written by Christian Peter Klingenberg. This approach is a generalization of the CPC approach used here, as it allows the compared matrices to share associations. This might be useful in the analysis of developmental patterns, for example. This program is part of the Morphometric Software collection at Stony Brook.

References

Airoldi, J.-P., and B. D. Flury (1988): An application of common principal component analysis to cranial morphometry of Microtus californicus and M. ochrogaster (Mammalia, Rodentia). J. Zool. Lond. 216:21-36.
Arnold, S.J., and P.C. Phillips (1999): Hierarchical comparison of genetic variance-covariance matrices. II. Coastal-inland divergence in the garter snake Thamnophis elegans. Evolution 53:1516-1527.
Camara, M. D., and M. Pigliucci (2000): Mutational contributions to genetic variance/covariance matrices: an experimental approach using induced mutations in Arabidopsis thaliana. Evolution, in press.
Cowley, D. E., and W. R. Atchley (1992): Comparison of quantitative genetic parameters. Evolution 46:1965-1967.
Flury, B (1987): A hierarchy of relationships between covariance matrices. Pp. 31-43, in A. K. Gupta (ed), Advances in Multivariate Statistical Analysis. Reidel, Boston.
Flury, B. (1988): Common Principal Components and Related Multivariate Models. Wiley, New York.
Klingenberg, C. P., B. E. Neuenschwander, and B. D. Flury (1996): Ontogeny and individual variation: analysis of patterned covariance matrices with common principal components. Syst. Biol. 45:135-150.
Klingenberg, C. P., and M. Zimmermann (1992): Static, ontogenetic, and evolutionary allometry: a multivariate comparison in nine species of water striders. Am. Nat. 140:601-620.
Neuenschwander, B. (1991): Common Principal Components for Dependent Random Vectors. Unpublished Ph.D. Dissertation. University of Bern.
Phillips, P.C. (1998): Designing experiments to maximize the power of detecting correlations. Evolution 52:251-255.
Phillips, P.C., and S.J. Arnold (1999): Hierarchical comparison of genetic variance-covariance matrices. I. Using the Flury hierarchy. Evolution 53:1506-1515.
Pigliucci, M., K. Cammell, and J. Schmitt (1999): Evolution of phenotypic plasticity: a comparative approach in the phylogenetic neighbourhood of Arabidopsis thaliana. J. Evol. Biol. 12:779-791.
Roff, D. (2000): The evolution of the G matrix: selection or drift? Heredity 84: 135-142.
Roff, D. A., and T. A. Mousseau (1999): Does natural selection alter genetic architecture? An evaluation of quantitative genetic variation among populations of Allonemobius socius and A. fasciatus. J. Evol. Biol. 12:361-369.
Roff, D. A., T. A. Mousseau, and D. J. Howard (1999): Variation in genetic architecture of calling song among populations of Allonemobius socius, A. fasciatus, and a hybrid population: drift or selection? Evolution 53:216-224.
Shaw, R. G. (1992): Comparison of quantitative genetic parameters: reply to Cowley and Atchley. Evolution 46:1967-1969.
Steppan, S. J. (1997): Phylogenetic analysis of phenotypic covariance structure. I. Constrasting results from matrix correlation and common principal components analyses. Evolution 51:571-586.

Page last modified December 18, 2000 by Patrick Phillips.

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