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From |
"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Negative eigen values in factor, pf command? |

Date |
Tue, 28 Apr 2009 12:39:35 -0400 |

Jean-Gael Collomb wrote: <<I am having trouble interpreting the results of a principle factor analysis I am conducting. <snip> >> This has nothing to do with Stata whatsoever and has to do with the structure of the problem. Stata is honest about its reporting, unlike far too many other stats programs, and generally doesn't hide issues from you when there are problems. Anyway, confusing principal factor PF with principal components is a common mistake, because the names are similar. In fact, PF is PCA applied not to the correlation matrix, R, but to C = R - U where U is an estimate of the variables' uniquenesses (unreliability, a measure of the variables' error variances). The usual estimate used in this kind of a procedure is U = diag(1 - rsq_jj), where rsq_jj is the multiple R-squared from the regression of variable j on all other variables. R is guaranteed to be positive semi-definite. C is not, and often isn't. Slight violations are no big deal. Substantial ones, signaled by big negative eigenvalues, are a sign that the model does not apply. In a sense you can think about removing the uniquenesses as the opposite of ridging. Ridging adds positive value to the main diagonal of a matrix relative to the off-diagonal to push it towards being positive definite. This deemphasizes the off-diagonal. Because the goal of a factor analysis is to analyze what the variables have in common, which is measured by the covariances (or correlations), removing the influence of the diagonal helps focus on this in a way that PCA does not. See, e.g., Chapter 5 in Lattin, J., Carroll, J. D. and Green, P. (2003). Analyzing Multivariate Data. Duxbury Press. (Aside: PF is an antiquated method that belongs on the dustbin of history as far as I am concerned.) * * 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/

**Follow-Ups**:**Re: st: RE: Negative eigen values in factor, pf command?***From:*"Michael I. Lichter" <mlichter@buffalo.edu>

**References**:**st: Negative eigen values in factor, pf command?***From:*Jean-Gael Collomb <jg@ufl.edu>

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