Timeline for Can I somehow compute variance explained by PC after Oblique rotation in PCA?
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| May 6, 2014 at 4:03 | comment | added | user45042 | I have encountered the same problem. And I have also seen others reporting % of variance explained after using Oblimin rotation. So I think there is a way of computing it? Have you managed to it and may I know how if so? | |
| May 27, 2012 at 17:39 | comment | added | user11576 | I do not think that summing up the coefficients is equal to the variations accounted for by each PC's coefficient, either un-rotated or rotated one. I'm in the same boat; I need to know how calculate the variations explained after rotation! Thanks | |
| Feb 15, 2012 at 23:30 | comment | added | rolando2 | The solution as a whole explains the same % of variance, whether you rotate the components obliquely or not. In the case you describe, that % is 80%. | |
| Feb 15, 2012 at 19:58 | comment | added | Noro | Yes, but we are solving 2 things: Is statistically right to count variance explained by PC after oblique rotation? Second: If yes, is my equation good to do this? | |
| Feb 15, 2012 at 19:30 | comment | added | rolando2 | In my view there's nothing wrong with reporting the variance explained by each of a set of correlated components, just as there's nothing wrong with showing each predictor's zero-order r-squared in a regression context. Just don't make the mistake (as has been noted) of thinking you can add all of these up to arrive at the overall variance explained. | |
| Feb 15, 2012 at 19:30 | comment | added | ttnphns | Must be very interesting papers, thank you @Noro. I will read them at some length. Unfortunately, I'm too busy currently to respond. | |
| Feb 15, 2012 at 19:30 | comment | added | Noro | And second thing, if rotated sums of squared loading are "not" informative in oblique solution, why SPSS write them in output? | |
| Feb 15, 2012 at 19:13 | comment | added | Noro | Ok but I have fount several papers in which authors were able to report proportion of variance explained after oblique rotation. Are they not right?share.eldoc.ub.rug.nl/FILES/root2/2001/Qualoflip/… - page 118 pubman.mpdl.mpg.de/pubman/item/escidoc:726189:6/component/… - page 458 gump.qimr.edu.au/general/daleN/SNPSpD/Horne2004.pdf and xa.yimg.com/kq/groups/15062060/2048952508/name/Henson+2006.pdf - PAGE 410 - read expectation 6 | |
| Feb 15, 2012 at 16:23 | history | edited | Noro | CC BY-SA 3.0 |
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| Feb 15, 2012 at 8:03 | comment | added | ttnphns | Yes, in orthogonal rotation these sum of squared loadings are the proportion of variance explained. I don't think that in oblique rotation they are informative. In your place, I wouldn't explore or report them. | |
| Feb 15, 2012 at 7:26 | comment | added | Noro | Ok, my fault. So what these rotation sums of squared loadings for PC can tell me? Because in orthogonal rotation they are something like eigenvalues, from which I can compute this way amount of variance explained. | |
| Feb 15, 2012 at 6:34 | history | edited | ttnphns |
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| Feb 15, 2012 at 6:15 | comment | added | ttnphns | Another note. The question title is strange. As far as you are aware, there's two types of loadings after oblique rotation, pattern coefficients (which are regression coef-s) and structure coefficients (which are correlation coef-s). Then, what else "loadings" are you striving to compute? | |
| Feb 15, 2012 at 6:10 | comment | added | ttnphns | You can't speak of "eigenvalues" after rotation, even orthogonal rotation. Perhaps you mean sum of squared loadings for a principal component, after rotation. When rotation is oblique, this sum of squares tells nothing about the amount of variance explained, because components aren't orthogonal anymore. So, you shouldn't report any percentage of variance explained. | |
| Feb 14, 2012 at 23:30 | history | tweeted | twitter.com/#!/StackStats/status/169564237289619458 | ||
| Feb 14, 2012 at 22:51 | history | edited | Noro | CC BY-SA 3.0 |
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| Feb 14, 2012 at 21:49 | answer | added | rolando2 | timeline score: 1 | |
| Feb 14, 2012 at 21:25 | history | edited | Noro | CC BY-SA 3.0 |
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| Feb 14, 2012 at 21:16 | history | asked | Noro | CC BY-SA 3.0 |