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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

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

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

Date |
Tue, 28 Apr 2009 15:40:48 +0100 |

This is normal. The key point is not that some of the eigenvalues are negative, but that some of them are near zero. It may well be that if the data were as you would like them to be that all the eigenvalues could come out positive, but Stata is not going to lie to you. With just this number of variables, you would be well advised to set aside factor and principal component analysis and look first at the results of -graph matrix- and -correlate-, and screen out variables not really related to any of the others, as they won't add worthwhile flavour to the multivariate analysis. Nick n.j.cox@durham.ac.uk Jean-Gael Collomb 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. Thank you very much for your help. FACTOR ANALYSIS WITH PRINCIPLE FACTOR EXTRACTION factor att2r att3r att9r att20r att22 att23, mineigen(1) ------------------------------------------------------------------------ -- Factor | Eigenvalue Difference Proportion Cumulative ------------- +------------------------------------------------------------ Factor1 | 1.34388 1.21292 1.3335 1.3335 Factor2 | 0.13096 0.14728 0.1300 1.4635 Factor3 | -0.01632 0.04961 -0.0162 1.4473 Factor4 | -0.06593 0.09743 -0.0654 1.3819 Factor5 | -0.16336 0.05812 -0.1621 1.2198 Factor6 | -0.22148 . -0.2198 1.0000 ------------------------------------------------------------------------ -- LR test: independent vs. saturated: chi2(15) = 304.22 Prob>chi2 = 0.0000 PRINCIPLE COMPONENT ANALYSIS quietly pca att2r att3r att9r att20r att22 att23, mineigen(1) rotate ------------------------------------------------------------------------ -- Component | Variance Difference Proportion Cumulative ------------- +------------------------------------------------------------ Comp1 | 2.05242 .95265 0.3421 0.3421 Comp2 | 1.09977 . 0.1833 0.5254 ------------------------------------------------------------------------ -- * * 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/

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

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