Skip Navigation

Biometrika 2003 90(3):679-701; doi:10.1093/biomet/90.3.679
© 2003 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Boik, R. J.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Principal component models for correlation matrices

Robert J.Boik1

1 Department of Mathematical Sciences, Montana State University, Bozeman, Montana 59717-2400, U.S.Arjboik{at}math.montana.edu

Distributional theory regarding principal components is less well developed for correlation matrices than it is for covariance matrices.The intent of this paper is to reduce this disparity. Methods are proposed that enable investigators to fit and to make inferences about flexible principal components models for correlation matrices. The models allow arbitrary eigenvalue multiplicities and allow the distinct eigenvalues to be modelled parametrically or nonparametrically. Local parameterisations and implicit functions are used to construct full-rank unconstrained parameterisations. First-order asymptotic distributions are obtained directly from the theory of estimating functions. Second-order accurate distributions for making inferences under normality are obtained directly from likelihood theory. Simulation studies show that the Bartlett correction is effective in controlling the size of the tests and that first-order approximations to nonnull distributions are reasonably accurate. The methods are illustrated on a dataset.

Key Words: Bartlett correction; Correlation matrix; Fisher scoring; Implicit function; Likelihood; Principal components analysis; Sphericity

Received October 2002. Revised February 2003


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.