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


From   "Steichen, Thomas J." <SteichT@RJRT.com>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Negative eigen values in factor, pf command?
Date   Tue, 28 Apr 2009 11:06:34 -0400

Use of the -altdivisor- option likely will provide you with an answer more to your expectations:

  factor att2r att3r att9r att20r att22 att23, mineigen(1) altdivisor


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jean-Gael Collomb
Sent: Tuesday, April 28, 2009 10:24 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: Negative eigen values in factor, pf command?

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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