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From |
"Francesco Burchi" <fburchi@uniroma3.it> |

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

Subject |
st: R: RE: RE: Factor Analysis: which explained variance? |

Date |
Wed, 23 Dec 2009 11:14:36 +0100 |

@ Jay The theoretical reason for this aggregation is that the different variables indicate different types of health knowledge. The following are the results of tetrachoric correlation: Var1 Var2 Var3 Var4 Var1 1 Var2 .1819233 1 Var3 .3699331 .25242738 1 Var4 .18371493 .27407531 .40299934 1 I was specifically asked whether I could justify my choice of one single factor on the basis of the variance explained. Following your reasoning, I could argue that with more than 1 factor it would be unidentified. Just to be sure about the procedure I am following, I have tried to get results keeping the 4 factors: factormat R, n(6926) ipf factor(4) Factor analysis/correlation Number of obs = 6926 Method: iterated principal factors Retained factors = 3 Rotation: (unrotated) Number of params = 6 -------------------------------------------------------------------------- Factor | Eigenvalue Difference Proportion Cumulative -------------+------------------------------------------------------------ Factor1 | 1.28200 1.06199 0.8049 0.8049 Factor2 | 0.22001 0.12912 0.1381 0.9431 Factor3 | 0.09089 0.09108 0.0571 1.0001 Factor4 | -0.00019 . -0.0001 1.0000 -------------------------------------------------------------------------- Could I state that the first factor explains 80% of the common variance? Finally, I have tried to add one or two further indicators to improve the analysis. However, I had some theoretical doubts on the inclusion of these variables, and the factor analysis with tetrachoric correlations gave me loadings for these variables much lower than 0.1, thus I was convinced to use only 4 variables. Thanks, Francesco -----Messaggio originale----- Da: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Verkuilen, Jay Inviato: lunedì 21 dicembre 2009 19.54 A: 'statalist@hsphsun2.harvard.edu' Oggetto: st: RE: RE: Factor Analysis: which explained variance? Nick Cox wrote: >P.P.S. the whole notion of variance is perhaps a little suspect when the originals are indicator variables. < @Nick: I don't know, you have variances, they're just functions of the mean (proportion)! However, there are covariances that aren't redundant. @The original poster: With four indicators, you really can only afford a one dimensional factor analysis. Anything higher dimension will be, essentially, unidentified, and thus even more indeterminate than usual for factor analysis. Three indicators is exactly identified. Four indicators with correlated factors that have two indicators per factor is also identified, but if the solution says that you have three and one you're really out of luck. Without knowing the tetrachoric correlation matrix (these are indicators, i.e., binary, so polychoric is just tetrachoric anyhow) it's very hard to say on any statistical grounds. Is there a theoretical reason to form a sum score from these indicators? For instance, do they operate like items on a quiz where you want to know the total score? Jay * * 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/ * * 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**:**st: RE: R: RE: RE: Factor Analysis: which explained variance?***From:*"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>

**References**:**st: RE: RE: Factor Analysis: which explained variance?***From:*"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>

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