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khigbee@stata.com |

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statalist@hsphsun2.harvard.edu |

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

Date |
Tue, 28 Apr 2009 10:02:12 -0500 |

Jean-Gael Collomb <jg@ufl.edu> asks: > I am having trouble interpreting the results of a principle factor > analysis I am conducting. The command and results are shown below. > Several things puzzle me about the results table. Why are some > eigenvalues < 0? Why are some of the proportions <0? Why are most of > the cumulative values >1. I suspect the answer to one of these > questions applies to all three. My understanding of factor analysis is > that I would interpret the results table as retaining all factor with > an eigen value >1 because they explain more of the variance than the > original variable and that the set of retained factors explains the > "cumulative" percent of the variance in the dataset. I thought that > all the variance (100%) would be explained by all the factors, but > that a subset of those factors would therefor only explain less than > 100%. In my case, I would retain factor 1 and by itself it would > explain 133% of the variance, which does not make much sense to me. > When I run a principle component analysis on the same data, I get a > two component solution explaining 52% of the variance. That result > table is more similar to what I have seen elsewhere, but I am puzzled > as to why there seems to be such a difference between procedures on > the same data (and the single factor solution of the pfa also makes > more theoretical sense as this point) > > I am not a statistician but would like to understand in general terms > what is happening with the factor command and how to interpret its > results. I have spoken with two statisticians I work with and they are > surprised to see eigen values<0 and cumulative values >1, but they are > not STATA users. Maybe we are misinterpreting the results or maybe I > am doing something wrong with the software. If the results were not > valid, I would have expected STATA to give me some sort of error > message rather than an aberrant result. Take a look at pages 421-423 of Rencher (2002), especially the top half of page 423. For the principal factor method you are examining the eigenvalues of R - Psi_hat. Rencher says "... are not necessarily positive semidefinite and will often have some small negative eigenvalues. In such a case, the cumulative proportion of variance will exceed 1 and then decline to 1 as the negative eigenvalues are added." If this property/behavior of the default -pf- option for -factor- is not something you want, consider using one of the other method options (such as -pcf-). Rencher, A. C. 2002. Methods of Multivariate Analysis. 2nd ed. New York: Wiley. Ken Higbee khigbee@stata.com StataCorp 1-800-STATAPC * * 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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