Timeline for Create positive-definite 3x3 covariance matrix given specified correlation values
Current License: CC BY-SA 3.0
10 events
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| Feb 22, 2012 at 19:27 | comment | added | whuber♦ | @cardinal Sure: that approach may help you (and it's similar to how I think about the situation, too) but given that the OP has indicated that it does not help them to the same extent, alternative explanations using familiar concepts appear worth attempting here. | |
| Feb 22, 2012 at 19:23 | comment | added | cardinal | @whuber: The eigendecomposition helps me understand the situation since it tells me exactly what a covariance matrix must look like both operationally and intuitively: It must be one that takes an arbitrary vector, rotates it into a new coordinate space, then fiddles with its coordinates in such a way that it stays strictly inside the orthant it started in, and then rotates the new version back to the original space. In the rotated space a vector will lie exactly on the boundary between orthants after the "fiddling" if and only if it started on the same boundary. | |
| Feb 22, 2012 at 17:57 | comment | added | whuber♦ | I think the essence of the answer can be captured in statistical language: correlations are covariances of standardized versions of the variables. Therefore you can arbitrarily rescale (and recenter) the variables without changing the correlation matrix. In conjunction with any algorithm to test for symmetry and positive (semi)definiteness, that fully answers question 1 and question 2. Eigendecompositions are useful (for constructing variables with a given correlation matrix) but are really not essential to understanding the situation. | |
| Feb 22, 2012 at 17:36 | history | tweeted | twitter.com/#!/StackStats/status/172374247451275264 | ||
| Feb 22, 2012 at 17:19 | answer | added | Brian Borchers | timeline score: 0 | |
| Feb 22, 2012 at 16:56 | answer | added | caracal | timeline score: 7 | |
| Feb 22, 2012 at 16:20 | comment | added | cardinal | Sure. Give me a bit and I'll be glad to do so. | |
| Feb 22, 2012 at 16:17 | comment | added | Mike Lawrence |
No reason but for ignorance! Care to post an answer that elaborates on how to do an eigendecomposition (ideally in R)?
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| Feb 22, 2012 at 15:53 | comment | added | cardinal | I'm not sure I quite understand your question. Is there a reason you don't like or can't do an eigendecomposition? Without loss of generality you can assume all variances are one. | |
| Feb 22, 2012 at 14:55 | history | asked | Mike Lawrence | CC BY-SA 3.0 |