Dear Statlistserv members,

`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
``
``--------------------------------------------------------------------------
`
Jean-Gael "JG" Collomb
PhD candidate

`School of Natural Resources and Environment / School of Forest
``Resources and Conservation
`University of Florida
jgcollomb@gmail.com
jg@ufl.edu
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