The correlation coefficient be can interpreted as the cosine of the angle between centered or standardized variable vectors in subject space. Using this interpretation of the correlation, the space occupied by 3x3 correlation matrices first demonstrated by Rousseeuw and Molenberghs (1994) can be re-portrayed. Once the cosine transformation is imposed on the space, the space occupied by 3x3 correlation matrices becomes a regular tetrahedron. Extensions of this space in higher dimensions are discussed and explored. Uniform sampling from the regular tetrahedron produces non-uniform sampling from the 3x3 correlation space, such that correlation matrices with more extreme elements are sampled more frequently. Simulations demonstrating this phenomenon are presented and compared to established generation methods.
| Identifer | oai:union.ndltd.org:VANDERBILT/oai:VANDERBILTETD:etd-11162016-123646 |
| Date | 21 November 2016 |
| Creators | Hadd, Alexandria Ree |
| Contributors | Kristopher J Preacher, Andrew J Tomarken, Joseph Lee Rodgers |
| Publisher | VANDERBILT |
| Source Sets | Vanderbilt University Theses |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.vanderbilt.edu/available/etd-11162016-123646/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Vanderbilt University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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