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From |
Michael Lichter <lichter@uclalumni.net> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: PCA vs. Factor Loadings |

Date |
Thu, 17 Dec 2009 09:56:18 -0500 |

Thanks again, Nick. I've downloaded -cpcorr-. It will be helpful for this project and elsewhere. I now have a different but related problem that could be a bug but could also represent a gap in my understanding of PCA (which would not be a surprise). Checking the correlations between the observed variables and the extracted components requires the estimation of component scores using -predict-. Once the component scores are estimated, it's easy to check the correlation between components. There should be no correlation between the initially-extracted components, and none between components after orthogonal rotation. I found the former but not the latter; in fact, my rotated components are all moderately correlated! The correlations between components for a three-component model extracted from the auto.dta data (program at end of this message) look like this: | c1 c2 c3 -------------+--------------------------- c1 | 1.0000 c2 | 0.6248 1.0000 c3 | -0.4571 -0.4338 1.0000 What's going on? When I the same (give or take) factors using -factor, pcf- and do the same orthogonal (varimax) rotation, the rotated factors are, as expected, uncorrelated. Does this indicate a bug in one or more of the relevant programs (-pca-, -rotate-, or -predict-), or is there some aspect of PCA that I'm not taking into account? Thanks. Re. Jay's response: Thanks to you also. I wasn't suggesting that the results of -pca- and -factor- should look the same; I am/was only looking to have results from the two be on comparable scales, which, as both of you observed, is a function of the normalization used. Michael // ----- program to // - extract components/factors // - show correlations between vars and components/factors // - show correlations between components/factors // - compare -pca- results to -factor- results sysuse auto pca price mpg rep78 headroom trunk weight length displacement, mineigen(1) predict c1 c2 c3 cpcorr price mpg rep78 headroom trunk weight length displacement \ c1-c3 corr c1-c3 rotate, varimax drop c1-c3 predict c1 c2 c3 cpcorr price mpg rep78 headroom trunk weight length displacement \ c1-c3 corr c1-c3 factor price mpg rep78 headroom trunk weight length displacement, pcf predict f1 f2 f3 cpcorr price mpg rep78 headroom trunk weight length displacement \ f1-f3 corr f1-f3 rotate, varimax drop f1-f3 predict f1 f2 f3 cpcorr price mpg rep78 headroom trunk weight length displacement \ f1-f3 corr f1-f3 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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