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

 From "Nick Cox" To 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

------------------------------------------------------------------------
--

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